integrated sensing of movement and forces in a … ant legs...integrated sensing of movement and...

ESA / EUROPEAN SPACE AGENCY ESTEC / EUROPEAN SPACE RESEARCH AND TECHNOLOGY CENTER ACT / ADVANCED CONCEPTS TEAM BIOMIMETICS

JUSSI MÄKITALO

Project Antleg: INTEGRATED SENSING OF MOVEMENT AND FORCES

IN A TECHNICAL LIMB

-Stage report-

Stagiaires report submitted in the end of traineeship in ESTEC. Noordwijk, 28.8.2009 Supervisor: Leopold Summerer, Staff Scientific supervisor: Tobias Seidl, Research Fellow

Project Antleg: Jussi Makitalo Integrated sensing of movement and forces in a technical limb

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Acknowledgements I had great times living in Leiden and working at ESTEC. I met tons of interesting people at work and on free time. Thank you all. Great thanks to my flatmates both at Steenstraat 3c and also at Morsstraat 39. I like to give thanks to all the amazing people involved with the project. Thanks go to Tobias for making some of the groundwork for the project and of course for picking me from the vast amount of applicants. Thanks to Professor J. Schmitz for the interesting information on stick insects. Thanks to Pantelis Poulakis for 20-sim guidance and helping out with the contact model. Thanks to Alexandros, Laura and the rest of the robotics team. Thanks go to all of my good friends back in Finland and to the ones that found the time during my stay in the Netherlands to visit me. Ville, Olli, Jussi, thank you all. Hanna and Mikko, thanks for the short visit. The weekend was short, but full of action. Thanks for Tom, for crashing in my flat for a week, it was awesome. Thanks to the locals for introducing me to local life, thanks Larissa, Anton, Marjolein, Klaas and Stefan. Thanks to all the colleques, JC and David, thanks for the company. And lastly I’d like thank my fiancée for letting me go away for the summer, I know it wasn’t easy at times. Much love and respect. Noordwijk, 28.8.2009 Jussi Mäkitalo


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Outline of activities I started working on this project in 2.6.2009 at ESTEC, Noordwijk, The Netherlands. I appreciate the opportunity given and I did my best to come up with useful results and also tried to learn as much as possible from the people working at ACT and ESTEC in general. My first tasks were preparatory work for the project. I was given a stack of papers for research as well as instructed to get to know the contents of the shared drive, the ACTWiki and the Intranet among other information sources. The first few weeks flew by while getting to know the people in the ACT, new stagiaires and YGT’s and my flatmates. Working the days and attending various parties in the evenings. At work, the first days went on by attending trainee sessions and studying my project materials. Simultaneously I had to prepare a Powerpoint presentation about myself for my new colleagues, write down my personal information and specific competences into the ACTWiki. Other minor tasks given, was to update the ACT web pages under ‘Bioengineering’ and ‘Biomimetics’ to match the current state of progress. I also applied for administrator rights for my computer to install all the needed software that I would be using throughout the summer. On my second week of work, I finally met my supervisor, Tobias Seidl, who returned from his vacation for a day to let me know what I’m expected to do during the summer. The same week I started writing this report with loads of research behind and still an incredible amount of research ahead. On 18th of June I had a meeting with my supervisor Tobias Seidl and Professor Josef Schmitz from the University of Bielefeld, Germany. He’s areas of expertise include neurobiology, invertebrate neurophysiology, neuroethology, biological cybernetics and systems theory, motor control, control of legged locomotion in insects and crustaceans and biorobotics. He will act in the project as a support person for me and Tobias. [Schmitz] After the meeting we gave a tour around the ESTEC facilities for Professor Schmitz and he held a Science Coffee for the people at ACT. From the meeting I compiled a memo for the project participants and the management. The project required me to do extensive research about ants, insects, robotics, control, biomimetics and engineering. I was constantly reading papers and making notes and drawing various sketches. The project is about identifying the potential working principles of a desert ant’s odometer as well as outlining the principles for force based odometry in legged robots. This will be carried out by creating a simulation model of the leg and it’s kinematics and then measuring the stresses in the links and torques in the joints and connecting them to appropriate environments. I had tried out the trial version of the simulation software, 20-Sim, required for creating the simulation model earlier and on my fourth week of work I finally


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got some guidance on the usage of it. In meantime I had to clarify some of our bibliography in use. I started working on the simulation model on a licensed version of 20-Sim in the middle of my fifth week. It turned out to be not so easy to use. On the sixth, I finally managed to get some arbitrary movement into my model. This was a great success even though I couldn’t control the movements perfectly. After a few trial and errors I managed to produce a movement that could be considered as a stride. On the seventh week, I created some relations between the leg and the soil. The relation seems difficult to create, since so many variables are part of the equation. Also, the results from this kind of leg-soil-interaction has to be viewed critically. A model more resembling the actual thing, could be perhaps delivering more accurate results. On my eight week I got professional advice on creating the contacts between the legs and the ground from Pantelis Poulakis, a contractor well experienced in 20-Sim and robotics. He even gave me a couple of simulation models with built-in contact models for my usage. They were simulations about balls bouncing on a surface and over obstacles behaving in a natural manner. However, for unknown reasons they refused to work on my computer. My ninth week started by me presenting my progress in a Power Point presentation to my working group and some work friends. Later on in the week, I finally managed to fuse together the contact model and my own modelling work to obtain some interaction between the robot and the ground. On the last hours of the week, I managed to get the contact working as it should be. Ten weeks in and there is still lots of work to be done. Interpreting the contact and measuring the forces caused by it seems to be a little troublesome as well. I also lost my license to 20-Sim shortly during my tenth week. My supervisor wanted me to make alterations to the model and this resulted in a total breakdown of the model, this shows that the contact model apparently isn’t working correctly. On the eleventh week I continued in hunting down the reasons for the contact model breakdown. I also created a couple of other types of models for reaching my goal. I also contacted some people in order to get help on the subject. I also appeared in the Dutch newspaper ‘Leidsch Dagblad’ on a small column in the TV-pages on Saturday. My 12th week started by analysing the data received from our model. The model was considered as complete as we can make it during my stay and we decided to analyse it’s outputs with varying terrain conditions. Major part of my week went by while writing this report. The final week began by correcting some errors noticed on the week before, after which I ran some more simulations that I’d been running on the earlier


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week with faulty values. On top of that, I needed to finish this report and my final presentation. During my stay here, I visited a couple of lectures held in Newton and Einstein, although that happened only on the first month or so. Also, I brought in some visitors from time to time to show them around ESTEC and to tell them about our work here. The progress of work is shortlisted on table 1 below. Table 1. Work schedule and activities realized.

MO

NTH

DA

TES

CA

LEN

DA

R W

EEK

WEE

K O

F ST

AY

AC

TIVI

TY

June 2.-5.6. 23 1 Settling to office, understanding project, introduction presentation

June 8.-12.6. 24 2 Reading papers, starting of report, website updates, sketches

June 15.-19.6. 25 3 Meeting of Professor Schmitz, MoM, reading, writing report, sketching, 20-Sim trial tryout

June 22.-26.6. 26 4 Guidance on 20-Sim, reading, sketching

June/July 29.6.-3.7. 27 5 20-Sim license, model making starts, reading, writing

July 6.-10.7. 28 6 Control of joints, reading, writing

July 13.-17.7. 29 7 Starting presentation, continuing 20-Sim, reading about contact kinematics

July 20.-24.7. 30 8 Reading about contact kinematics, 20-Sim, sitdown session on contact kinematics with Pantelis Poulakis

July 27.-31.7. 31 9 Intermediate presentation of project, working contact model, reading, writing

August 3.-7.8. 32 10 Interpreting contact, license trouble, altering model: tilted legs

August 10.-14.8. 33 11 Fixing model, generating alternative models, becoming a celebrity…

August 17.-21.8. 34 12 Data analysis, running inclinations, fixing gliches, starting final presentation

August 24.-28.8. 35 13 Error correction, re-runs, analysis of results, preparing final presentation, finishing report

Noordwijk, 28.8.2009 Jussi Mäkitalo


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ABSTRACT Navigation in exploration rovers is an important part of their mission. The rover must know where it is positioned and which direction it’s facing. Current navigation techniques are mainly concentrating on using visual cues. The purpose in this project was to develop a means of conducting odometry using proprioception and path integration focussing on legged locomotion, both robotic and biological. This project was inspired by desert ants, Cataglyphis fortis, and their so far unknown method of odometry. It is known that the Cataglyphis fortis can successfully monitor distances via integrating the steps taken but the mechanism behind it is still unknown. Step length varies with speed of locomotion but remains constant when running on inlined paths; any working model of a step integrator needs to account for these subtleties. Previous hypothesis like, e.g. monitoring joint angles, has proven to be wrong and hence, force monitoring along the leg remains as the currently most favoured hypothesis. The work was carried out by creating a simulation model of a walking robot and observing various outputs from the model. A connection was hoped to be found between the outputs and the distance travelled. The final two-legged version of the model was walking on the substrate with otherwise realistic looking behaviour except from the small bounces it experienced, when the legs hit the ground. Some measurements were derived from these contacts between the ground and the leg, but none of them were considered worthy of building an odometry system on. Other variations of the model were also conceived, but these proved out to be of limited use.


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Contents Abbreviations and terminology_________________________________________ viii 1 Introduction______________________________________________________1

1.1 Background__________________________________________________1 1.2 Research problem _____________________________________________2 1.3 Objective and scope ___________________________________________2 1.4 Methods_____________________________________________________2

2 State of art_______________________________________________________3 2.1 The foraging desert ant _________________________________________4

2.1.1 Campaniform sensilla ______________________________________6 2.2 Studied experiments ___________________________________________6 2.3 Robotics ___________________________________________________14

2.3.1 18-DOF robots __________________________________________16 3 Construction of the simulation model_________________________________19

3.1 Kinematic model_____________________________________________19 3.2 Simulation model evolution ____________________________________21 3.3 The gait ____________________________________________________24 3.4 Contact kinematics ___________________________________________25

4 Model variations _________________________________________________27 4.1 Six-legged walker ____________________________________________27 4.2 Ball-joint leg ________________________________________________29 4.3 Vertically limited 6-DOF joints in feet____________________________31

5 Results_________________________________________________________32 5.1 Force analysis _______________________________________________37

6 Discussion______________________________________________________44 6.1 20-Sim_____________________________________________________47 6.2 Development ideas ___________________________________________47

6.2.1 Spin-off ideas ___________________________________________48 6.3 Experiment ideas_____________________________________________48

6.3.1 Escalator _______________________________________________48 6.3.2 Labyrinth_______________________________________________48 6.3.3 Modified toblerone _______________________________________48 6.3.4 Modified lateral optic flow _________________________________49 6.3.5 Multilayer homing test ____________________________________49 6.3.6 Roughbox ______________________________________________49 6.3.7 Magnetic navigation ______________________________________49 6.3.8 Translation under forced movement __________________________49

7 Conclusions_____________________________________________________50 8 Bibliography ____________________________________________________50 APPENDICES ______________________________________________________52


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Abbreviations and terminology Abbreviations DOF Degree-of-freedom GNSS Global Navigation Satellite System GPS Global Positioning System Terms Allothetic Navigation based on external cues. Alternating tripod gait Method of walking, where three feet are on the ground

at a time. Alternating between right from, right back and left middle to left front, left back and right middle.

Attitude Inclination of the body of the robot. Dead reckoning Method for determining current position based on

knowledge from previous position, heading and velocity.

Degree-of-freedom The number of variables needed to know position and orientation in a robot or joint.

Egocentric Positional information is obtained by continuous path integration. Spatial position is known relative to starting point.

Exocentric “Map-based” system of navigation. Idiothetic Navigation via monitoring self movement. Odometer A device or method for measuring distance travelled. Odometry Determining distance with respect to previous

position. Path Integration Determining position relative to initial position via

monitoring own movement. Proprioception Monitoring of relative position of neighbouring parts of

the body. Quadruped gait Method of walking, where two diagonal pairs of legs

move at the same time. I.e. right rear and left middle, right middle and left front.

Vestibular Sense of balance, equilibrium in higher vertebrate species.


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1 Introduction Navigation is an important task when exploring new uncharted areas. In planet surfaces other than the Earth, this task becomes more complex. We do not have the help of an absolute external referencing system such as GNSS working on other planets, so the rovers need to rely on their own in-built sensors. Navigation in principle can be performed by following external cues like landmarks or beacons. Another way of doing this is egocentric path integration. By integrating ones own path, no external cues are needed and navigating in a featureless environment is made possible. Dead reckoning was used by early sailors when navigating the seas. They calculated their current position according to the previous position, heading and velocity. The drawback of this method is it’s natural tendency for cumulating errors in positioning, since the positions are calculated solely based on previously calculated positions. Desert ants and bees are known to be the masters in path integration in the animal kingdom. For accurate path integration, information about direction, distance and inclination is needed. In absence of an absolute external referencing system, self movement has to be monitored and integrated. This can be done via visual cues or via proprioception. By proprioception, the position and orientation of body parts is known. Through the movement of body parts, step length can be calculated and path integration is made possible. Visual distance estimation nowadays is the standard in most rover applications with it’s particular characteristics such as the need for a CCD camera, good sight, reliable and fast visual processing, feature tracking etc. Here, we investigate on the potential of odometry as it is observed in desert ants and transferring the ant’s hypothetic strategies into legged robotics.

1.1 Background Neuroethological studies on the Cataglyphis Fortis, the foraging desert ant, show that they have a very robust system for navigation and measuring distances. Step integration isn’t disturbed by slippage, speed of locomotion or inclination of substrate. This seems to point towards force sensors in the legs or torque sensors in the joints, rather than angular position sensors. This assumption is also supported by behavioural experiments with the Cupinnius-spiders. And on top of that, it is known that the stress sensors, Campaniform Sensilla, in the ants’ legs’ cuticle are involved in locomotion control. [ToSe:ACTWiki]


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The research done in this project is beneficial not only in robotics and control but also for biologists as it could help us understand better the ants’ proprioception. In robotics and control technique the profit would be a new way of practicing odometry, hopefully resulting in simple algorithms and in cheap and robust control. Extensive experiments on ants, their navigation and locomotion etc. have been performed by various researchers. Their theories on ant navigation are considered when determining the control theory for the simulation.

1.2 Research problem Odometry in walking robots is cumbersome and even more so when slippage or inclination changes of substrates is introduced. The trajectories of the rovers’ legs can be calculated mathematically and thus step length can be determined. But the leg-soil-interaction is more complex than that, legs can roll or sink into substrate, slippage can occur or the substrate can be inclined.

1.3 Objective and scope The objective is to study ants and insects, their way of proprioception, their locomotion and the way they sense and control slippage. The desired deliverable of the project is a 3D-model of an ant leg-type robotic limb and some data about the stresses in the limbs and angles of the limbs. Also all ideas about, or involving, an actual ants proprioception is more than welcome. The results of this project is hoped to bring some insight to ants odometry and also introducing a new way of navigating for walking robots. Connection to an actual ants’ odometer has to be proven after receiving results from the simulation. It is desirable to have some sort of preliminary plans for experimentations on ants alongside the simulation data. The main task in this project is to identify potential working principles of a desert ant’s odometer and implementing it to a simulation model. Forces and torques will be measured from the model, trying to find correlation with speed of locomotion, inclination of the substrate it’s moving on and controlling of slippage, ultimately resulting in a robust method of doing odometry.

1.4 Methods The task will be tackled by applying knowledge from selected literature, expert discussions and simulation. The literature varies from the field of biology, mechatronics, control, mechanics and engineering.


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The experts to be consulted during this project include professionals from biology, mechatronics, biomimetics, modelling, programming and various other fields. Mainly the experts consist of people working at ACT, but also from DG-TEC and a professor from University of Bielefeld, Germany. Expert discussion will be engaged whenever possible during this research. The simulation model will be created using 20-Sim, a simulation program that lets you create 3D-model with all the kinematics, modelling with block diagrams, inserting equations and variables and finally simulating movement and analysing outputs such as forces or angles.

2 State of art Existing studies of similar robots, the desert ants, other ants and also other insects is used to get familiar to the subject. Ants belong to the family Formicidae and to the order Hymenoptera along with other insects such as wasps and bees. They range in size from under one millimetre to over five centimetres and have an exoskeleton like other insects. The exoskeleton provides an attachment point for the muscles and a casing to provide protection around the whole body. Like other insects, ants don’t have lungs. They breathe through their spiracles, which are like tiny valves found all over their body. Insects have hemolymph in their body, like vertebrates have blood, and they also lack closed blood vessels. Instead they have a long thin tube that goes through the body called the dorsal aorta, which pumps the hemolymph towards the head. [Wiki:Ant] Nowadays more than 12 000 species of ants are classified. Ants live in colonies of between few dozen to multiple million individuals and are known to inhabitat almost anywhere on Earth with exemptions of Antarctica and other remote or inhospitable islands such as Greenland and Iceland. The largest colonies are formed by various castes of ants, with specific assigned tasks. Most of the ants in a large colony consist of sterile wingless females of castes such as soldiers, workers etc. Nearly all the colonies have at least one fertile female, the queen, and some fertile males for reproduction, the drones. [Wiki:Ant] The anatomy of an ant can be seen in figure 1 below. Here, we will concentrate on the ants head and other sensory organs such as the Campaniform sensilla in the ants’ legs, which detect the forces in the leg segments. These force-signals are thought to contribute to the path integration –mechanism of the insect.


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Figure 1. The ant’s anatomy [Wiki:Ant]

The ant’s head is abundant with sensory organs. The eyes, like on most insects, are compound eyes, which comprise of multiple tiny lenses working together. They do not produce a high resolution but they’re still good for movement detection. On the top of the ant’s head, there are three small ocelli to detect light levels and polarization, which is used to aid in navigation. The ocelli “are sensitive in the ultraviolet region of the light spectrum”. The antennas on the ants head detect chemicals, air currents and vibrations but can also act as a communication tool between ants. [Wiki:Ant]

2.1 The foraging desert ant The ant Cataglyphis fortis belongs to the subfamily Formicinae and the genus Cataglyphis [AntWeb] and is approximately 1.6cm long [WehTax] and can be seen on figure 2. Unlike some other ants, like the leaf-cutter ant [MagOri], the Cataglyphis fortis can not navigate according to the Earths magnetic field.


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Figure 2. Cataglyphis fortis drone. Adapted from: [WehTax]

The foraging desert ant, Cataglyphis fortis, is found in the deserts of Tunisia. When foraging, they go individually to gather dead arthropods in the hot deserts or even salt pans. The foraging is done during the hottest times of day, since that is the time of most heat related deaths [SmellAnt]. They can go for distances over 150 meters when foraging and in the homogeneous deserts [WehTax], this requires very sophisticated navigation methods. They conduct navigation mainly through vector navigation (path integration) and spotting landmarks. They also use systematic search patterns and target expansion strategies for finding the nest while in the vicinity [WehArc]. The Cataglyphis fortis can also navigate according to odours, when trained. In their natural habitat, they do not however spread odours [SmellAnt].


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2.1.1 Campaniform sensilla The ants’ sensing organs in the legs are called the Campaniform sensilla. They exist in many species ranging from cockroaches to stick insects and can be found all over in the joints of the insects. These sensors are mechanical receptors responding to stresses in the cuticle. [Pringle] The leg of a cockroach can be seen in the figure below. The percentages represent the distribution of the sensilla.

Figure 3. Campaniform sensilla on a cockroach. [ZillLoSe]

2.2 Studied experiments Previous experiments on ants have given us important information about the ants’ locomotion, navigation and proprioception. Sommer and Wehner concluded in ‘The ant’s estimation of distance travelled: experiments with desert ants, Cataglyphis fortis’, that the desert ants must use path integration in finding they way around the deserts. The tests comprised of straight channels, where the ant were first let from nest to feeder and then translated to a parallel test channel. The ants ended up searching for the nest at the same distance than the actual nest was from the feeder. The test set-up can be seen in figure 4.

Figure 4. The test set-up of Sommer and Wehner. [EstDist]


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Wehner and Wehner in ‘Insect navigation: Use of maps or Ariadne’s thread’ studied more on the path integration skills of the Cataglyphis fortis. The ant ran for 18.8min in a desert, performing non-straight foraging pattern of 592.1m in distance before finding food. The inbound run was 1.06 times the straight distance between the feeding point and the nest resulting in a 6.5min, 140.5m journey home. In figure 5 the foraging route can be seen. The open circle represents the nest, the big dot the food source and the small dots intervals of one minute. [WehAriadne]

Figure 5. Cataglyphis fortis in a foraging trip. [InsNavi] In the same paper, they contemplated the ants’ navigation skills while walking in corridors with angles. The ants went through a couple of different corridor constructions and then released into open ground after which their homing direction was recorded. The difference with the actual nest direction and the mean value of homing directions was significant. The results can be seen in figure 6.


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Figure 6. Ants homeward bound trip. [WehAriadne]

In ‘Visual navigation in insects: Coupling of egocentric and exocentric information’ Wehner et al. described the working principles of the ants eyes. The ants can use polarization of the observed sky in different sun angles to derive compass information. The stereotypic interpretation of their polarization vision is pictured in figure 7.

Figure 7. Polarization in the sky on different angles of the sun. [WehVisEgo] In ‘Vision-independent odometry in the ant Cataglyphis cursor’ Beugnon determined that the fore mentioned ant doesn’t need any external cues for navigation, they can navigate solely on proprioception. The experiments were conducted while painting the ants’ compound eyes with light blocking paint.


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The foraging desert ant can use landmarks based on the grounds surface roughness. This was proofed by Seidl in ‘Visual and tactile learning of ground structures in desert ants’. In figure 8, the training set-up shows the ants’ nest location to be right after the rough spot in the ground. In the test, the rough spot is translated closer to releasing point resulting in wrong estimation of the nests location.

Figure 8. Ants’ navigation by landmarks and by path integration. [ToSe:VisTac] In ‘Is active locomotion a prerequisite for path integration’, Seidl tested on ants’ active locomotion. The ants’ homing vectors were reset by capturing the ants at their nest, when returning from foraging and then put through ‘treatment 1’ or ‘treatment 2’ and then tested their homing skills. In ‘treatment 1’, the ants were let freely slide down a slope of 52° with horizontal distance of 2.4m. ‘Treatment 2’ was inserting the ants into a pipette and translating it in a trolley in a horizontal line at regular ants locomotion speed for 4m, with no active locomotion done by the ant. Figure 9 shows the ‘treatment 2’ trolley construction and the two experimental set-ups can be seen in figure 10. After either of the treatments, the ants were put on a horizontal channel and their homing behaviours were observed. The ants started basically looking for their nest in the releasing spot, not 2.4m (‘treatment 1’) or 4m (‘treatment 2’) away. This shows, that the ant must actively locomote in order to integrate its path.

Figure 9. ‘Treatment 2’ trolley set-up. [ToSe:Dissertation]


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Figure 10. Experimental set-ups by Seidl. [Tose:Dissertation]

Seidl filmed ants running on different inclination in ‘How do desert ants integrate inclination’ and noticed, that the ants’ kinematics in the legs do not change dependently on the inclination. Figure 11 shows the experimental set-up and figures 12 and 13 show some remarks made on the high speed camera.

Figure 11. The experimental set-up. [ToSe:Dissertation]


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Figure 12. An ant running uphill on a slope of 60°. [ToSe:Dissertation]

Figure 13. Dorsal view of Cataglyphis fortis running. The triangles represent the contact points of the tarsi and the ground. The points on the body being the head-thorax joint, petiolus and center-of-mass. [ToSe:Dissertation]


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Lipp et al studied on ‘Walking on inclines: energetics of locomotion in the ant Camponotus’ the metabolism in ants while locomoting. The results show that ants’ metabolism accelerates when speed of locomotion or the inclination of the terrain rises. [WalkInc] Wittlinger had ants running from the nest to a feeder and then modified the ants’ legs by extending or shortening them and then let them return to their nest. He discovered that the ants would then search the nest at distances further and shorter, respective. By first modifying the legs and then doing the nest to feeder and back to nest cycle, the ant would actually adapt to the leg length and find the nest in its actual location. This was studied in ‘The desert ant odometer: A stride integrator that accounts for stride length and walking speed’. A picture of a test specimen with stilts can be seen in figure 14. This gives out the first impression that ants only count steps, which was proven wrong in Wohlgemuths experiments in ‘Distance estimation in the third dimension in desert ants’, where he had ants running over a series of hills with lateral distance of 6m and 10m of total distance going in 54° angles. The results show that the ants could in fact find their way back to the nest when testing on a flat surface. So the ants perceived the lateral distance perhaps by calculating the distance from the inclination angles. If they would have only relied on counting steps, they would have grossly overshot the target. Control experiments were conducted to exclude visual assessment of inclination.

Figure 14. The Cataglyphis Fortis walking on stilts [Nature]

Wittlinger’s other studies in ‘Hair plate mechanoreceptors associated with body segments are not necessary for three-dimensional path integration in desert ants, Cataglyphis fortis’, he blocked some of the ants sensors for measuring joint angles by shaving the sensor hairs or by gluing the joint in place. The joints the group worked on were in the ants’ body. The joints were between the head and alitrunk, between alitrunk and petiole and between


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petiole and gaster. The shaving test had no effects on the ants, while gluing had differing results in different configurations of glued joints. The most dramatic results came up when the gaster was glued upwards approximately 90° with respect to the ants’ body. The ants would then underestimate their direction from the nest. These differences, are however not too big and it seems that these sensors are not affiliated in sensing slopes and navigating. Figure 15 illustrates the treated joints.

Figure 15. A: The treated joints Receptors: B: Before treatment C: After treatment [HairPlate]


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Seidl in ‘spooling & wind’ experimented on ant running on a substrate with low grain size (100nm). This is a kind of environment, where almost all insects have trouble attaching to the substrate and this causes the ants to slip on the surface. When combining the slippery surface and wind coming from assigned direction, the ants would then wrongly estimate their distance from the nest, resulting in shorter or longer homing vectors depending on the wind direction. Hind wind resulted in the ants searching the nest at shorter distances, while head wind resulted in correctly judged distances. The experimental set-up can be seen in figure 16.

Figure 16. Experimental set-up of ‘Slippery surface experiment’. [SeidlSSE]

2.3 Robotics A six-legged robot’s walking pattern is usually carried out by alternating tripods. This means that three legs are in contact with the ground at all times. The first and the last leg on one side and the middle leg on the other. [SILO6] If the legs are at the same distance from the longitudinal axis of the robot, then the middle legs always carry half of the robots weight, while the fore and hind legs carry only one quarter of the total weight. And this leads to bulkier middle legs with more need for torque to operate them [SILO6]. In the case of Cataglyphis fortis, the hind legs are the longest, while the front legs are the shortest. The configuration of the legs contribute largely to the robots balance and need of torque. If the robot’s stance is closer to a human or a mammal, it needs less torque while walking, but the balance is more difficult. While the configuration is insect-like, the balance is no problem, but the torques needed are much higher. The different stances can be seen in figures 17 and 18. [SILO6]


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Figures 17 & 18. SILO6 robot in pseudo-mammal and insect configuration of the legs. [SILO6]

The mammal configuration of the legs is also more energy efficient because of the lower need for torque. When walking on an approximate flat surface this stance is much better. On a rough surface the insect-like stance is more convenient because of it’s higher stability. [SILO6] The locomotion in these kinds of robots is usually divided into feedbacked sub-controllers, with integrated feedback loops. In figure 19 one alternative for such a control system can be seen.

Figure 19. Control concept for six legged walking machine MAX. [PfeifferTUM]


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In the figure 19 above, the locomotion is controlled by six Leg Coordination Modules, which interact with the Single Leg Controllers. By this arrangement, the system takes care that the gait is desired and at least three legs are in contact with the ground at the same time. Also, ground reaction forces and torques are kept within limits to avoid slippage. [PfeifferTUM] The feet design for a walking robot is usually either an articulated flat sole or a ball fixed to the ankle. While the ball can roll when the angle of attack changes during strides the articulated sole maintains it’s contact with the surface unchanged. Usually the flat soles are more convenient when walking on soft substrates and the ball-type feet are better for walking on harder substrates. [SILO6]

2.3.1 18-DOF robots Many robots resembling an insect have been made in the past. There have been ant-like robots and stick insect-like robots as well as crab-like robots from various people with varying number of legs. Here we limit our research to six-legged 18-DOF robots. Three degrees-of-freedom per leg enables the robot to carry out more complex movements with compared to only 2-DOF legs, such as strafing and walking in an angle. Tarry I & II Tarry I and Tarry II were built in 1992 and 1998, respectively, with the aim of developing an autonomous walking robot with six legs. The design was based on stick insects. The legs have three degrees-of-freedom thus making the total of 18 degrees-of-freedom. The robots use contact switches in their legs to detect leg-soil contact, measure power consumption in leg actuators to detect a collision and use ultrasonic sensors in front to detect larger obstacles. They also have strain gauges in their legs for measuring during movement and an inclinometer for maintaining horizontal body posture. [BILL-Ant]

Figure 20. The TARRY I [IntContLab]


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Robot II Robot II pictured in figure 21 by Case Western University Biorobotics Lab is actually a 24-DOF robot, but one DOF in each leg is a passive spring-loaded translational joint. Robot II is implemented with algorithms for finding foothold and leg elevation for clearing larger obstacles. The gaits vary from slow to fast with varying the velocity of locomotion. Joint positions are measured with potentiometers in joints and forces are measured in the legs to control leg movement and to avoid obstacles. [CaseWest]

Figure 21. Robot II [CaseWest]

BILL-Ant-p BILL-Ant-p constructed and designed by Lewinger as a part of his Master’s Thesis in 2005. It’s an interesting project because it basically comes with instructions for building such a robot, with CAD-drawings and cost calculation sheets showing that the entire robot can be realized in only 2822.95$ including tools components and materials. The ant comprises of six 3-DOF legs and has strain gauges in it’s feet. The head of the robot houses mandibles for operating and manipulating objects. The head has three DOF plus one DOF for the mandibles, which are actuated by a servo through a pulley actuated Kevlar fibre string. Depending on the adjusted speed, the gait is gradually changed from one leg at swing at a time to quadruped and alternating tripods. [BILL-Ant]


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Figure 22. The inverse kinematics calculation flow chart of BILL-Ant-p for moving one leg into desired position. [BILL-Ant]

Figure 23. BILL-ant-p [CaseWest]


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SILEX The SILEX by Active Structures Laboratory has decentralized controllers for each leg which solve inverse Jakobian equations in real time. It’s also equipped with a two-way inclinometer. The hierarchy in SILEX is divided into three categories. Level A is concerned with navigation and path planning. Level B focuses on gait, attitude and altitude control, and also calculates the force distribution. And finally level C “handles the leg trajectory and the servo control as well as the force control of the leg (active suspension). The force feedback is provided by force sensors based on strain gages that are included in the feet.” [SILEX]

Figure 24. SILEX [SILEX]

Also various other robots were studied. A good source for information about multiple robots can be found at ‘Walking Robots’ –webpage held by Prof. Dr. Karsten Berns at http://www.walking-machines.org/.

3 Construction of the simulation model The simulation model will be made to resemble an ant with it’s six legs. Although in the first phases only one leg will be modelled and studied further. The creation begins with deciding kinematics, degrees-of-freedom, dimensions, the measured outputs and points of measuring them.

3.1 Kinematic model The ant leg will be comprised of three joints and four links, thus giving it only three degrees-of-freedom. For the body, initially two degrees-of-freedom will be applied resulting in a total of five DOF. The initial kinematic model made for the leg can be seen in figure 25. The initial model will consist only of one leg, the body and the substrate. If time, a more developed model will be constructed, it will consist of all six legs, the body and the substrate, 18 degrees-of-freedom altogether resulting in a robot of 24 DOF considering the positioning and orientation of the body.


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BODY Y,B

X,BZ,B

Y,1

X,1

Z,1

X,2Y,2

Z,2

Y,4

X,4Z,4

Y,0

X,0Z,0

Y,3

X,3Z,3

SUBSTRATE

3.3

1.1

2.6

0

D=0.7

Figure 25. The ant legs’ initial kinematic model. The ant leg will be simplified to only consist of coxa, femur and tibia. The coxa will be further simplified as only two degree-of-freedom joint. The measurements used in the making of the model are actual measurements of the ants’ multiplied by 1 000. The measurements used in the model can be seen in table 2.

Table 2. The model measurements.

PART LENGTH WEIGHTHead width 1.9 1

Alitrunk 2.8 1Gaster 2.8 1Coxa 0 1

Femur 2.6 0.01Tibia 3.3 0.01

Tarsus 0.7 0.01

BODY PARAMETERS

The body will be modelled initially as a box with the coordinate system in the middle of the fore end of it. The coxa will be at a distance of 1.4m of the body coordinate system to the direction of X,B-axis and 1.1m in the direction of Y,B-axis.. In the coxa, two separate hinges will be modelled. One for lateral yaw of the leg and one for pitch. The femur will be between the coxa and the tibia. The end of the tibia is in contact to the tarsus, which is considered to be in contact with the substrate. Forces experienced here in the joint between the tibia and the tarsus will be considered potential for measuring odometry.


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3.2 Simulation model evolution The simulation modelling was first tried out on the unlicensed version of the program. The problem with this was the fact that you could not save in this. Although it acted as learning tool for me before getting to the serious business. A simple model created with the trial version can be seen in figure 26.

Figure 26. First simulation results with the unlicensed version.

The licensed version enabled to do a little more complex model. The body of the ant was created out of three bodies and two weld joints. The leg out of four bodies, three rotational joints and one weld joint. The result can be seen in figure 27. The screenshot is taken from the animation and the joints are left visible. The weld joint inside the tarsus can easily be seen because of it’s box-shape inside the spherical tarsus. The links in the leg are improperly modelled because of users limited knowledge of the software. Also, at this point the alitrunk of the model was locked to the world and it was just swinging its legs.

Figure 27. The first steps of my ant.


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The model was constructed increasingly complex with added features. The next phase included modelling a single surface acting as the ground and adding some reactional forces into it. The model structural elements can be seen in figure 28, while figure 29 illustrates the control structure.

Figures 28 & 29. The model structure. For controlling the leg movement only two of the three leg joints are active. The joints are given controls by continuous pulses, these pulses are controlled with a PD-controller, which is controlling the torques fed into the gears connected to the joint angles. The final model included contact models for modelling the interaction between the robot and the terrain. The resulting model can be seen in the figures 30 and 31 below.


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Figure 30. The final walking model, with fixed limbs and modified coxa-femur-joint location.

Figure 31. The model structure.

Coxa

Femur

Tibia

Tarsus


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3.3 The gait The legs move according to figure 32 below. The readings in the figure illustrate the time and place the tarsus is in. For example for the left leg, movement from zero-position starts at 0 seconds, it arrives to the posterior position at 2.45s, lifts off at 2.5s, starts moving forward at 2.55s, reaches uppermost position at 3.75s, starts descent at 4.5s, arrives at anterior position at 4.6s and finally hits the ground at 4.95s. Both of the cycles are repeated every five seconds.

Figure 32. Gait control for the legs.

Figure 33 below illustrates the football patterns resulted from the gait control. The black stripes indicate the stance phase and the white stripes the swing phase. Thusly, a gait consists of 2.55s of stance and 2.45s of swing, resulting in a gait of 5s giving a duty factor of 0.51 according to formula 1. Thus the gait is considered to be walking, since duty factors above 0.5 are considered walking and below that, running.

Figure 33. Stance and swing phases of the robots gait.

0s 2.45s

2.5s

2.55s

3.75s4.5s

4.6s

4.95s

2.5s 4.95s

0s

0.05s

1.25s2s

2.1s

2.45s

Left leg tarsus positions

Right leg tarsus positions

LEFT

RIGHT

2.55s 5s

0.05s 2.45s


25

51.0555.2

stridetimestancetime

===DF (1)

The gait is controlled by submodels seen in figure 34 below. The signal generators generate continuous signals that are delivered to the PD-controllers only if the ‘walk’-signal is given to the ‘OnOff’-blocks, otherwise the ant will be standing in place.

Figure 34. Controls for the joint angles.

3.4 Contact kinematics The contact model is an adapted version received from Pantelis Poulakis. He has been applying the same models into simulating a wheeled rover over obstacles [Poulakis]. The models received from him included simulations of balls bouncing on a surface and over obstacles. The tarsi interact with the terrain via 6 DOF power ports inserted into them. The orientation and position information is extracted for calculations with an H-matrix in each of the tarsi. The contact model calculates the normal force exerted by the terrain to the tarsus and derives the tangential forces from this. For a more precise


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description of this see ‘Port-based modelling and simulation of planetary rover locomotion on rough terrain’ by Pantelis Poulakis. [Poulakis] The complete contact model can be seen in the figures below. The contact models are the same for both tarsi.

Figure 35. The contact model.

The contact model in figure 35 is given the Homogeneous-matrix and bond graph of the tarsus’ power port, which by the nature of bond graph, will allow interaction between the tarsus and the world. The power indication meter is used for potential odometry information. The World-block contains the code illustrated in figure 36, which sets the world H-matrix as identity-matrix, the world velocity as 0 and declares the first_cycle-variable as true. The input of the H-matrix of the tarsus position is not necessary for the World-block since it’s not used anywhere.

Figures 36 & 37. The contents of the world and interaction-blocks.

The interaction between the world and the tarsus is expressed in figure 37. The both bond graphs are connected to each other with a 0-junction, which is also connected to MTF. The 0-junction makes all efforts equal and the sum of all flows equal to zero. So the forces between the world, tarsus and MTF-junction are the same, while the speeds between MTF and tarsus are also the same, because the velocity of the world is zero.


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Figures 38 & 39. Contents of H and MTF-blocks.

The H-block defines the H-matrix of the point in the tarsus in contact with the world by multiplying the H-matrices of the tarsus and the point in the tarsus in contact with the world. The MTF-block is a transformer between the contact block and the 0-juntion and neither generates nor dissipates no power. It defines the H-matrix of the world with respect to the point of the tarsus in contact with the world by inverting the H-matrix received from the H-block. It then generates an adjoint of the newly found H-matrix and calculates the effort (force) of the tarsus with respect to the world expressed in world coordinates and flow (velocity) of the tarsus with respect to the point in tarsus in contact with the world expressed in world coordinates. The contents of the XRC contact-block can be seen in appendix A. The block calls out for four different Matlab functions in the beginning to find out the initial contact points of the terrain and the tarsus. The source code for the Matlab functions can be seen in appendix B. The XRC contact-block defines the forces between the terrain and the tarsus, the velocities are derived from these forces according to other model parameters.

4 Model variations Other types of models were created in the meantime, trying to obtain measurements of forces in the contact.

4.1 Six-legged walker The six-legged walker was constructed from the two-legged version with multiplying the number of the legs and applying the same contact models and controls to the legs. The main point in building this, was to see if it works correctly since the body isn’t constrained.


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The body of the walker was let loose of the constraints and hence, the walker was entirely relying on the ground contact. The contact however proofed to be too bouncy and the model ended up being jumping up and down, turning sideways and eventually flip around finding a more favourable equilibrium position with it’s center-of-mass underneath the contact points. Figure 40 below illustrates the look of the model, while figure 41 shows the 20-Sim model.

Figure 40. Six-legged walker, tibia-tarsus-joint circled.

Figure 41. The six-legged model structure.


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Figure 42 below shows the forces measured from the left front legs tibia-tarsus-joint circled in figure 40.

model

-2000

-1000

0

1000

2000 Fx

-2000

-1000

0

1000

2000 Fy

0 1 2 3 4 5 6 7 8 9 10time {s}

-1000

-500

0

500Fz

Figure 42. The forces received from tibia-tarsus-joint of the left front leg. The contacts between the legs were not modelled and thus they were going through each other, like they wouldn’t exist. Also on the figure 40 the legs consist of short limbs because of a bug in the software. Perhaps the model could be perfected by tuning the contact model to be stiffer and not suspend that much. Perhaps the flipping motion is because of the increasing bounce. Also the model should be made with more spread legs in order to obtain a bigger surface area for the contact tripod.

4.2 Ball-joint leg A simple version of the model was created from scrach with only one leg and rotationally constrained body. In fact, two different versions of this type of walker were made. One was with a 6-DOF joint in the body that was constrained in C-code to keep the orientation of the body as a constant. This model can be seen in figure 43 below. The movement produced by this was swinging around the pivot point without changing orientation of the body. This resulted in breaking the joint connection between the tarsus and the ground. This could perhaps be fixed by tampering with the C-code of the model, or then revising the model and re-establishing the connection between the tibia and the tarsus.


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Figure 43. Tarsus locked into place with a 3-DOF rotational joint with the tibia-tarsus-joint circled. The other one was otherwise similar, but instead of the 6-DOF joint, there were three translational joints, one for each axis, and two dummy bodies between them. The model seemed to work properly, but yet again, the force measurements, seen in figure 44, received from tibia-tarsus-joint, circled in figure 43, give unexplained signals.

model

-200

-100

0

100

200 Fx

-200

-100

0

100

200 Fy

0 1 2 3 4 5 6 7 8 9 10time {s}

-1000

-500

0

500

Fz

Figure 44. Force signals from the tibia-tarsus-joint during two gaits. The weight of the models body in this case was set to 5 kilos, while the leg parts formed altogether 0.04 kilos and the dummy bodies 0.001 kilos. The supporting force for the joint under inspection is at about -49 N, which more or less corresponds to the weight of the ants body and undergoes some vibration during stopping for next gait at approximately 4.5s. The X- and Y-directional forces show non-logical patterns when compared to movement. The forces should show four repeating cycles during a gait, for X-directional


31

forces should show pull-push-pull-push and for Y-direction push-pull-push-pull, changing at approximately 1.1s, 2.5s, 3.7s and 4.6s according to the joint angles. Changes at these times can be seen in the figure 44 above, but these should be the times, when the forces change from negative to positive or vice versa.

4.3 Vertically limited 6-DOF joints in feet This version had 6-DOF joints in both of it’s feet, with constraints set into them for not going through the ground. This was done in order to avoid using the contact model. However, this was only tried out for one of the legs, but since the results didn’t seem promising enough, we decided not to go any further with these versions. The first version included the contact model, just to observe the behaviour, while the second one did not. Neither of them provided valuable information for odometry. The models for both were the same and can be seen in figure 45.

Figure 45. The model in the middle and left tarsus with the dummy bodies, the circle marks the tibia-tarsus-joint once more. No forces were measured from the first one since the behaviour was nothing like desired. The forces measured from the second model can be seen in figure 46. By removing the contact models, the only constraint was that, the left legs tarsus couldn’t penetrate the ground, except from the body constraints of all rotations and translation in Y-axis.


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model

-50

0

50

100Fx

-50

0

50

Fy

0 1 2 3 4 5 6 7 8 9 10time {s}

-5000-4000-3000-2000-1000

01000200030004000 Fz

Figure 46. Forces in the left leg of the contact model-less model during two gaits. The forces plotted from this version in figure 46, show believable results on the X- and Y-axis, since the ant isn’t moving from it’s position except up and down since there is no friction, the forces and peaks emerge due to acceleration of the tarsus. The Z-directional force seems to be showing correctly until 2.6s, when ant starts to lift it’s leg and plummets through the ground never returning to the same value showing peaks and near zero values.

5 Results The first walking model appeared to work correctly. It walked across the ground like anticipated. However it jumped into the air a little bit whenever the right leg was hitting the ground, also the legs were experiencing some shaking when about to leave the ground. Even though the animation showed that the model is working like it should, the forces measured from the joints between the tibia and tarsus showed arguable results. The body is constrained in all rotations and translation in the Y-axis. The legs are of three degree of freedom, of which one is kept constant. The active degrees include rotation around Z-axis to create thrust and the other for lifting the leg of the ground. The first walking model can be seen in figure 47, the picture is raytraced for illustration purposes.


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Figure 47. Raytraced rendered version of a walking simulation model. Tibia-tarsus-joint circled.

The forces and torques measured on the model’s left leg on the joint between the tibia and tarsus, which is highlighted in figure 47, are displayed in figure 48 below. The forces and torques are in SI-units. The timeline shows two stance-swing-phases, both of which last for 2.5 seconds.

model

-300-100100300500

Mx

-5000

500 My

0

30000

60000Mz

-2000

0

2000Fx

-2000

0

2000Fy

0 1 2 3 4 5 6 7 8 9 10time {s}

-600-400-200

0200 Fz

Figure 48. Forces and torques experienced in the left joint between tarsus and tibia during two stance-swing-phases on flat terrain.

Z

X Y


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Figure 49 and 50 show the X, Y and Z-directional forces in a close up experienced by the joint between tibia and tarsus of the left leg during stance on a flat terrain. The X-directional force, Fx, seems to oscillate from a small negative value to a small positive value, resulting in positive forward motion. The Y-directional force, Fy, oscillates around a sinusoidal curve, which would indeed make sense because of the tarsus’ moving pattern across the ground resembling an arch, but the zero-crossing point in the time-line is incorrect. The Z-directional force, Fz, is also oscillating, but it’s oscillating around -50 N, which corresponds to the weight of the model, which is 5.06 kg, in a gravitational field of 9.81 m/s^2. The torques displayed in figure 48 however, do not show intuitive values. By intuition, the torques should be close to zero, since the torque-arm is only the radius of the tarsus, which is 0.35m. Regardless of this, Mz shows increasing values up to 50 000 N.

model

0 0.5 1 1.5 2 2.5time {s}

-2000

-1500

-1000

-500

0

500

1000

1500

2000 FxFyFz

Figure 49. X, Y and Z directional forces in the joint between tibia and tarsus during stance on flat terrain.


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model

-1000

-500

0

500

1000 Fx

-2000-1500-1000

-5000

50010001500 Fy

0 0.5 1 1.5 2 2.5time {s}

-400

-300

-200

-100

0

100

200 Fz

Figure 50. X, Y and Z directional forces in the joint between tibia and tarsus during stance on flat terrain. On average, the ant ran 1.4m/s which is equivalent to 0.2 body lengths per second. The global maximum of the model ants speed was 0.47m/s, while the local maximums were around 0.33m/s. The figures illustrating the position and velocity can be seen in figure 51. In this figure, also the vibrations are clearly shown. Especially for the second stride of the left leg, which is the third bump on the red velocity gauge.

Figure 51. The position of the ants body in forward direction and the corresponding velocity.


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The final model was altered a little bit and the limb shortages were fixed. The model in close up can be seen in figure 52 below, while the structure is viewed earlier from figure 30 onwards until ‘Chapter 3.4 Contact kinematics’. An animation capture with an added background can be seen in figure 53.

Figure 52. Final walking model with highlighted tibia-tarsus-joint.

Figure 53. The final version of the walker, with added background for effect.

Z

X Y


37

5.1 Force analysis The simulation was run on various inclinations in order to get data for comparison. This was hoped to be useful for odometry. The following curves display X, Y and Z-directional forces extracted from the tibia-tarsus-joint of the final models left leg displayed in figure 54. The inclination is considered also as shown in figure 54.

Figure 54. Profile view of the walker displaying the tibia-tarsus-joint, inclination and coordinate system. The force curves, in figures 55-66, display the forces in Newtons and in the same coordinate system as seen in figure 54. The time scale are from the first left legs stance, 2.5s. The inclination was simulated by altering the gravity vector in 20-Sim. The gravity vector was given values according to table 3.

Table 3. Inclination angles and corresponding gravities. Angle (°) X (m/s^2) Y (m/s^2) Z (m/s^2)

45.0 -6.936717523 0 -6.93671752325.0 -4.145885148 0 -8.89087939115.0 -2.539014832 0 -9.47573235610.0 -1.703488623 0 -9.6609640575.0 -0.854997836 0 -9.7726699880.0 0 0 -9.81-5.0 0.854997836 0 -9.772669988

-10.0 1.703488623 0 -9.660964057-15.0 2.539014832 0 -9.475732356-25.0 4.145885148 0 -8.890879391-45.0 6.936717523 0 -6.936717523

α

Z

X


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model

-1000

-500

0

500

1000 Fx

-2000-1500-1000

-5000

50010001500 Fy

0 0.5 1 1.5 2 2.5time {s}

-200

-100

0

100

200Fz

Figure 55. Inclination 45 degrees, time scale one stance.

model

-2000

-1000

0

1000

2000 Fx

-2000

-1000

0

1000

2000 Fy

0 0.5 1 1.5 2 2.5time {s}

-500-400-300-200-100

0100200300400 Fz

Figure 56. Inclination 30 degrees, time scale one stance


39

model

-1000

-500

0

500

1000 Fx

-2000-1500-1000

-5000

50010001500 Fy

0 0.5 1 1.5 2 2.5time {s}

-200

-100

0

100

200Fz

Figure 57. Inclination 25 degrees, timescale one stance.

model

-1000

-500

0

500

1000 Fx

-2000-1500-1000

-5000

50010001500 Fy

0 0.5 1 1.5 2 2.5time {s}

-200

-100

0

100

200Fz



40

model

-1000

-500

0

500

1000 Fx

-2000-1500-1000

-5000

50010001500 Fy

0 0.5 1 1.5 2 2.5time {s}

-200

-100

0

100

200Fz


model

-1000

-500

0

500

1000 Fx

-2000-1500-1000

-5000

50010001500 Fy

0 0.5 1 1.5 2 2.5time {s}

-400

-300

-200

-100

0

100

200 Fz



41

model

-1000

-500

0

500

1000 Fx

-2000-1500-1000

-5000

50010001500 Fy

0 0.5 1 1.5 2 2.5time {s}

-400

-300

-200

-100

0

100

200 Fz


model

-1000

-500

0

500

1000 Fx

-2000-1500-1000

-5000

50010001500 Fy

0 0.5 1 1.5 2 2.5time {s}

-400

-300

-200

-100

0

100

200 Fz

Figure 62. Inclination -5 degrees, timescale one stance.


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model

-1000

-500

0

500

1000 Fx

-2000-1500-1000

-5000

50010001500 Fy

0 0.5 1 1.5 2 2.5time {s}

-400

-300

-200

-100

0

100

200 Fz


model

-1000

-500

0

500

1000 Fx

-2000-1500-1000

-5000

50010001500 Fy

0 0.5 1 1.5 2 2.5time {s}

-200

-100

0

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200Fz



43

model

-1000

-500

0

500

1000 Fx

-2000-1500-1000

-5000

50010001500 Fy

0 0.5 1 1.5 2 2.5time {s}

-200

-100

0

100

200Fz


model

-1000

-500

0

500

1000 Fx

-2000-1500-1000

-5000

50010001500 Fy

0 0.5 1 1.5 2 2.5time {s}

-200

-100

0

100

200Fz

Figure 66. Inclination -45 degrees, timescale one stance. The forces seem to be remarkably similar, no noticeable differences can be seen between the stances of the left leg. The following gauge was plotted from 20-Sim while running a 20 second simulation. The third step of the left leg initiates a jumping motion after which, only peaks are detected. The reason for the jumping action remains unknown. Also the oscillation seemed to get worse over time in all cases, when running longer simulations.


44

model

-1000

0

1000

2000

3000 Fx

-4000

-3000

-2000

-1000

0

1000 Fy

0 5 10 15 20time {s}

-2500

-2000

-1500

-1000

-500

0 Fz

Figure 67. Inclination -45 degrees, time scale four gaits. Out of these force curves, it’s very difficult to say anything concrete, since the behaviour of the model in animation is not like expected. Also because of the unreliable measurements received from the alternative designs displayed in ‘Chapter 4 Model variations’, it seems as if there is something wrong with our model or the contact kinematics. Figure 67 illustrates what happens on longer simulations, the model starts jumping after a few steps when inclination is bigger than 45 degrees or smaller than -45 degrees.

6 Discussion On our walking model, the forces seemed quite strange, although plausible. Fx oscillates around a value, which seems to change from a small negative to just above zero, Fy displays a sinusoidal curve fitting well the motion of the tarsus and Fz oscillates around -50 N, which is correct for maintaining vertical position. The oscillation of all forces makes them all difficult to read. Figure 68 below illustrates our force curves, where the blue lines mark for the approximate curve of plot drawn by freehand.


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model

-1000

-500

0

500

1000 Fx

-2000-1500-1000

-5000

50010001500 Fy

0 0.5 1 1.5 2 2.5time {s}

-400

-300

-200

-100

0

100

200 Fz

Figure 68. Inclination 0 degrees, timescale one stance, approximate curves drawn by freehand. The fact that the modelled ants body was fixed in all but X and Z-translation may have also contributed to distortion on the results. Whether we had enough time on this project, a model with six legs would have been produced and then the ant would have found it’s own equilibrium, allowing it to tilt and turn depending on the ground reaction and joint flexibility. Comparing the speeds of the model ant and an actual ant shows that the speeds are remarkably different. The reason for this is to be able to see the movements better. An actual desert ants speed of around 0.5m/s, which is around 50 times it’s own body length is far more greater than the model ants, which is 1.4m/s and is equivalent to 0.2 body lengths per second since the body is 7 meters long. 7 meters is also the length of one stride. When comparing force curves received from the model and the actual measured forces exerted by a wood ant, as measured by Reinhardt et al, some similarities can be seen. Figure 69 shows the forces exerted into wood ants legs. Notice that the coordinate system is different from ours. X direction is pointing right from the locomotion direction, Y forwards and Z direction is up. The coordinate system can be seen in figure 70. Ours can be seen in figure 52. The forward force (our Fx, Reinhardt’s Fy) shows differences, as ours is oscillating around a positive value and the real one displays a sinusoidal curve. The lateral force (our Fy, Reinhardt’s Fx) has the most similarities to the hind leg of the real ants. The vertical force (our Fz, Reinhardt’s Fz) in our model is oscillating around a constant, since the body is kept at a constant level and there is only one leg in contact with the ground.


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Figure 69. The forces exerted on the wood ant legs, notice different orientation of coordinate system. [DynKinLoc]

Figure 70. Coordinate system used by Reinhardt et al. [DynKinLoc]

In order to obtain reliable information about the odometry, the body should be let loose of all constraints. This would also show us how the orientation differs between gaits. And due to the orientation changes, we could start working on the means to derive the actual changes in position and orientation One reason for unreliable simulation might be the fact that the contact model was originally made for a wheel which was actually modelled as a sphere. Now, in our case the wheel is changed to a sphere in the end of a leg. This is closer to the original model as it’s a sphere, but then again now the orientation of the sphere is changing throughout the stance phase. When changing the femur-tibia angles to a more realistic angle regarding an actual ant, i.e. at a flatter angle to the substrate, the model basically crashed. This could be 20-Sim’s fault, because it refused to compile the model properly and resulted in the leg parts moving to undesired locations. When finally managed to compile properly after several attempts, the model did not walk correctly, instead it was more like jumping. This could be because of the


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elastic properties of the joints or errors in the contact model. Parameter tweaking has so far proven no considerable effect. Perhaps the model should have been made to original scale (ants scale) from the beginning with real weights, sizes and kinematics. None of the variations of the model performed correctly and did not deliver the desired results, so we will leave them out of discussion in here. A brief discussion on them can be found in ‘Chapter 4 Model variations’ along with an explanation of their structure.

6.1 20-Sim Working with 20-Sim version 4.1 proved to be more challenging than initially thought. The software has lots of annoying bugs. One of the most visible one is that it changes the way the model looks when displaying animations. In the animation, the links are cut shorter and they appear not to be connected to the joints. Although this was later discovered, how to fix this problem, but still this was notified to Controllab Products B.V., the creators of the software and they promised to fix this in the next version. When creating the 3D-model in 3D Mechanics Editor, the changes made there did not always carry on to the 20-Sim Editor mainly used for simulation and creating the controls. This was quite frustrating at times, since you had to make the same changes all over again whenever changing something in the model. Also, when applying multiple joint chains into a link in the model, the software crashed the model by exploding some of the parts into places they shouldn’t be. This happened especially for the version of the model with the contact model replaced by using a ball joint in the tarsus. The code requires Matlab to do some of the calculation and I experienced some difficulties with the compatibility. For me, the version 7.0 R-14 of Matlab did not work. Version 7.7.0 R2008b did however work.

6.2 Development ideas The model should be made to scale with proper kinematics for all six legs. The model should be constructed to produce real-like movement, with no constraints in the body. After achieving this, the forces and torques etc. should be monitored for realizing working odometry. By getting rid of slippage, the odometry could be done with current technology with very high precision. This would need some sort of subsystem to avoid slippery substrates or means to get a firm grip in even the most slipperiest surfaces. Such a grabbing mechanism could be imitated from an ants tarsi and pretarsi. The mechanism relies in both micro- and nanostructure of the


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attachement devices as well as the kinematics of contact formation and release [GladInsect].

6.2.1 Spin-off ideas We could create a robot with a battery charging nest. The robot would explore around a limited area and always return to the location of the nest using the ants navigation method of integrating strides and using the searching algorithm or other signalling from the nest. The nest could consist of heavier equipment for scanning the surroundings and assisting in navigation. The robot could have several tools in the nest with varying functions, an extra battery for lengthened operation or tools for digging etc. The nest could also be equipped with means for moving.

6.3 Experiment ideas Several ideas about experiments on ants came to question while conducting this research. The most prominent ones are introduced and described below.

6.3.1 Escalator How would the ants’ odometer work if travelling in an escalator. Escalators would be installed in lateral and with inclinations travelling both backwards and forwards. Also marking the walls with stripes in horizontal, vertical and in 45° angles would be tested, whether the do any difference on successful navigation.

6.3.2 Labyrinth Train the ant to go from nest to feeder and back. After training, the ants go from nest to feeder and are then passively translated into a labyrinth, from where it would have to find back to the nest. Will the ants start searching for the nest at it’s correct location? The labyrinth could even have some parts with inclinations.

6.3.3 Modified toblerone The ants train to go to the feeder from the nest in a ‘toblerone’. After training, the ants will have to go from nest to feeder, after which, they are passively translated into a ‘toblerone’ with a different slope.


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6.3.4 Modified lateral optic flow The ant’s are trained to run from nest to feeder in a straight channel with striped walls. Then the test run would be conducted by moving the walls of the channel, so that the ant would be fooled to see itself moving. Even the floor could be constructed of plexi glass with stripes moving on it too.

6.3.5 Multilayer homing test The ants are trained and then put into a horizontal narrow channel with various ladders to change between levels, at least five levels should be constructed. We would observe the ants’ behaviour in homing. Would the ant search the nest location in every level on the same distance, or just stay in the same plane.

6.3.6 Roughbox The ants’ nest is surrounded by a box with rough floor. The roughness is kept constant with a selected sandpaper roughness, with the exception of a path leading from nest to feeder, which is considerably different roughness. The path could be a straight line or a curvy road. Then in the actual experiment, the path would be totally different and leading to a feeder in a different location. Would the ant use the sandpaper to find the feeder?

6.3.7 Magnetic navigation Ants’ would be trained in a cross shaped corridor, with feeder in the intersection and the nest in one of the branches. In the test, the ant would be taken at the feeder and put into a similar cross assembly into the intersection. The assembly should be made independent of visual cues perhaps by isolating it from sunlight in a tent and then light up by identical lamps in each corner. Then, by altering the magnetic field around the assembly, the ants’ homing direction would be observed.

6.3.8 Translation under forced movement The ants would be translated in a carriage which would force the legs, leg or a segment of a leg to move in a realistic manner with respect to locomotion speed. The test would be prepared to show, whether the ants would observe this translation or not, resulting in differing homing vectors.


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7 Conclusions The project did not deliver desirable results, however while reading papers about ants some ideas for such experiments arose. These ideas however need some more refining. Odometry based on measuring forces is still considered plausible, but for testing this, a properly working validated model should be compiled.

8 Bibliography [AntWeb] AntWeb –webpages. Cited 3.7.2009, link: http://www.antweb.org/browse.do?subfamily=formicinae&

genus=cataglyphis&name=fortis&rank=species&project=africanants

[BILL-Ant] Lewinger W. (2005). Master’s Thesis: Insect-Inspired,

Actively Compliant Robotic Hexapod. [CaseWest] Case Western Reserve University, Center for Biologically

Inspired Robotics Research. Cited 25.6.2009, link: http://biorobots.cwru.edu/

[DynKinLoc] Reinhardt L. et al. (2009). Dynamics and kinematics of

ant locomotion: do wood ants climb on level surfaces? [EstDist] Sommer at el. (2004). The ant’s estimation of distance

travelled: experiments with desert ants, Cataglyphis fortis. [Gaspa:spider] Gasparetto A. et al (2008). Attaching mechanisms and

strategies inspired by spiders leg, Extended Study. [GladInsect] Gladun D. et al (2007). Insect walking techniques on thin

stems. [HairPlate] Wittlinger et al (2006). Hair plate mechanoreceptors

associated with body segments are not necessary for three-dimensional path integration in desert ants, Cataglyphis fortis.

[InsNavi] Lambrinos et al (2000). A mobile robot employing insect

strategies for navigation. [IntContLab] Intelligent Control Lab, Kwangwoon University. Cited

7.7.2009, link: http://earth.kwangwoon.ac.kr/Robots/node_t.html


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[MagOri] Banks et al (2003). Orientation by magnetic field in leaf-cutter ants, Atta colombica (Hymenoptera: Formicidae).

[Nature] Nature. Cited 10.8.2009, link: http://www.nature.com/nature/journal/v442/n7098/full/442

004a.html [PfeifferTUM] Pfeiffer F. (2009). The TUM walking machines. [Pringle] Pringle, J.W.S. (1937). Proprioception in insects: II. The

action of the Campaniform sensilla on the legs. [Poulakis] Poulakis P. (2007). Port-based modeling and simulation

of planetary rover locomotion on rough terrain. [Schmitz] Professor Josef Schmitz’s personal information. Cited

18.6.2009, link: http://www.uni-bielefeld.de/biologie/Kybernetik/staff/josch/ [SeidlSSE] Seidl T. (?). Slippery surface experiment. [SILEX] Active Structures Laboratory –webpage. Cited 26.6.2009,

link: http://www.ulb.ac.be/scmero/documents/Research/robotics/robotics_walking.html

[SILO6] Department of Automatic Control, Spanish National

Research Counsil –webpage. Cited 26.6.2009, link: http://www.iai.csic.es/users/silo6/SILO6_WalkingRobot.htm

[SmellAnt] Steck K. et al (2009). Smells like home: Desert ants, Cataglyphis fortis, use olfactory landmarks to pinpoint the nest. Cited 28.6.2009, link:

http://www.frontiersinzoology.com/content/6/1/5 [ToSe:ACTWiki] Seidl T. (2009). ACTWiki, the Brewery. [ToSe:AntNav] Seidl T. (2008). Workshop presentation: Ant Navigation.

Filename: ACT-PRS-2008-28-01-Tobias-ACWorkshop-AntNavigation.pdf

[ToSe:VisTac] Seidl et al (2006). Visual and tactile learning of ground

structures in desert ants. [WalkInc] Lipp et al (2004). Walking on inclines: energetics of

locomotion in the ant Camponotus.


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[WehArc] Wehner R. (2008). The architecture of the desert ant’s navigational toolkit (Hymenoptera: Formicidae)

[WehAriadne] Wehner R. et al (1990). Insect navigation: Use of maps or

Ariadne’s thread? [WehTax] Wehner R. (1983). Taxomie, Funktionsmorphologie und

Zoogeographie der saharischen Wüstenameise. [WehVisEgo] Wehner R. et al (1996). Visual navigation in insects:

Coupling of egocentric and exocentric information. [Wiki:Ant] Wikipedia article about ants. Cited 30.6.2009, link:

http://en.wikipedia.org/wiki/Ant [Wiki:GPS] Wikipedia article about GPS. Cited 23.6.2009, link:

http://en.wikipedia.org/wiki/Global_Positioning_System [ZillLoSe] Zill et al (2004). Load sensing and control of posture and

locomotion.

APPENDICES APPENDIX A: Contact model code APPENDIX B: Matlab functions source codes APPENDIX C: List of associated files

APPENDIX B: Matlab function source codes

B-1

PlaneInitConditions.m This function gives out the values of c1, c2 and d by calculating from the given values a certain set of functions, it also calls for Distance2Plane to give it some variables. The outputs are two 2x1-matrices and an integer, which describe the points in contact and the distance between them. The m-file contains the following: function [c1, c2, d] = PlaneInitConditions( P2init, r, thetaX, thetaY ) ; % Starting guess of the solution. For the wheel (sphere) we know that they % initial point will be at the lower part. For the terrain "body" we always % cosider the origin coicides with the World Frame. q0 = [ 0; 0; -pi/4; pi/4 ] ; % Optimization options options=optimset('Display','iter', 'TolX', 1e-13, 'Tolfun', 1e-13, 'MaxFunEvals', 5000, 'MaxIter', 2000) ; % Nelder-Mead uncostrained minimization algorithm [q, D] = fminsearch(@(q) Distance2Plane(q, P2init, r, thetaX, thetaY), q0, options) ; % Parametrization coordinates of the two closest points %c1 = plane(q(1:2), thetaX, thetaY) ; %c2 = sphere(q(3:4), r) ; c1 = q(1:2) ; c2 = q(3:4) ; d = -D ; Distance2Plane.m Distance2plane.m is an m-file, which initializes a function for finding the shortest distance between the plane and the point in tarsus which are in contact or about to be in contact. It also calls out for plane.m and sphere.m, which give it the coordinates of the sphere and the ground. Distance2Plane.m contains the following: function D = Distance2Plane( q, P2, r, thetaX, thetaY ) ; % Parametrized coordinates of PLANE (with optinal slope thetaX in the X-direction and thetaY in the Y-direction) g = plane( q(1:2), thetaX, thetaY ) ; % Parametrized coordinates of SPHERE f = sphere( q(3:4), r ) ; % Distance between the two points D = norm( P2 + f - g ) ;

APPENDIX B: Matlab function source codes

B-2

plane.m This function gives g a value in a 3x1-matrix. It represents the ground coordinates. plane.m contains the following: % Parametrized coordinates of a PLANE (with angles thetaX & thetaY) function g = plane( x, thetaX, thetaY ) ; g = [ x(1) ; x(2) ; x(1)*tan(thetaX) + x(2)*tan(thetaY) ] ; %g = [ x(2) ; % x(1)*tan(thetaX) + x(2)*tan(thetaY) ] ; % x(1) ; sphere.m This function gives f the values in a 3x1-matrix. It represents the sphere coordinates. sphere.m contains the following: % Parametrized coordinates of SPHERE function f = sphere( x, r ) ; % My parametrization %f = [ r * cos(x(1)) * cos(x(2)) ; % r * cos(x(1)) * sin(x(2)) ; % r * sin(x(1)) ] ; % The parametrization that works in 20sim f = [ -r * sin(x(1)) ; r * cos(x(1)) * sin(x(2)) ; -r * cos(x(1)) * cos(x(2)) ] ; % Martijn's parametrization %f = [ r * cos(x(1)) * cos(x(2)) ; % -r * cos(x(1)) * sin(x(2)) ; % r * sin(x(1)) ] ;

APPENDIX C: List of associated files

C-1

Documents: Stage report (this document). Presentations: Intermediate and final presentations of the stage.

• antleg_final_presentation.ppt • antleg_intermediate_presentation.ppt

Videos: Fourteen video files created from different animation results of the models behaviour. 20-Sim files: About nineteen different folders, containing models for project antleg. Each folder contains the associated emx-, 3dm-, scn- and png-files for creating a separate model. Matlab files: Four m-files containing formulas for calculating the shortest distance between the sphere (tarsus) and the terrain received from Pantelis Poulakis. Parts of the final version of the ant model converted from 20-Sim.