design and integration of a multi-axis force/moment sensor for a … · 2019-02-22 · 4 sensor...

Semester project report

Design and Integration of a

Multi-Axis Force/Moment Sensor

for a mobile quadruped platform

Nicolas Sommer

Supervisors:

Alexander SprowitzRicko Mockel

Professor:Auke Jan Ijspeert

June 11, 2011

Abstract

Cheetah is a quadruped robot developed at the EPFL, featuring three-segment pantographic legswith passive compliant knee joints. It is used as a testing platform and a toolkit to study CPGalgorithms and locomotion principles.

In this semester project, we designed a 6-axis force-torque sensor – based on strain gauges – tobe integrated in each leg of the robot.The project based itself on a previous work aimed at integrating such a sensor on another robot :the Roombot. During the previous project, the experimental results did not match the simulationsregarding the sensitivity of the sensor. We therefore started by analyzing the possible causes ofthat issue and found a problem with the isolation of the gauges on the prototype used (for the lastproject).In the design of this sensor, we focused on measuring only one force/torque component per bridge.The simulation results showed that we were successful in separating the components measured byeach bridge. The estimated sensitivities seem well sufficient to detect the range of forces the robotwill have to deal with. The first prototype proposed has been manufactured and will be testedsoon.

Contents

1 Introduction 31.1 Context and motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.1 Understand the problems with the existing sensor . . . . . . . . . . . . . . . 51.2.2 Adaptation of the Roombot’s sensor design to the Cheetah-robot . . . . . . . 51.2.3 Link the sensor to the electronics . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.4 Gant chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Background and literature 72.1 Load cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Strain gages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Literature review: multi-axis force/torque sensors . . . . . . . . . . . . . . . . . . . . 9

3 Roombot’s sensor prototype 113.1 Bad results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1.1 Asymmetric measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.1.2 Possibles causes for asymmetric behaviour . . . . . . . . . . . . . . . . . . . . 123.1.3 Short-circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 Experimental setup for the roombots . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2.1 Top beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2.2 Pulleys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2.3 PCB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Sensor Design 184.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.1.1 First hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.1.2 3 axis design versus 6-axis design, complementary hypothesis . . . . . . . . . 204.1.3 Forces computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.1.4 Position of the sensor on the leg . . . . . . . . . . . . . . . . . . . . . . . . . 224.1.5 First design draft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.1.6 Material resistance and stress concentration . . . . . . . . . . . . . . . . . . . 23

4.2 Sensor’s sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2.2 Estimation of the range of forces submitted to the leg . . . . . . . . . . . . . 244.2.3 Sensing elements design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

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4.3 Final model of the 6-axis sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3.1 Sensor prototype production . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5 Results 305.1 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305.2 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.3 Possible future improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

6 Conclusion 336.1 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

A Solidworks 35A.1 How to estimate the deformation at one point, along one axis . . . . . . . . . . . . . 35

B Labview 38B.1 About acquisition in Labview: differential and RSE modes . . . . . . . . . . . . . . . 38

C Electronics 39

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Chapter 1

Introduction

Here is presented the context of the project as well as its objectives.

1.1 Context and motivation

Force sensing in robots is important to provide feedback in controllers and informations about therobot’s state. Several robots currently being developed in the Biorob laboratory require this kindof information. Latest project by Joel Rey [1] focused on a 4-axis sensor to be implemented on theRoombots [2], the goal here is to complete and transpose his work onto the Cheetah platform [3].Some other recent example of force sensing application is its use in Machine learning, for instancewith the iCub [4].

Roombots

This information comes from Joel Rey’s report[1]

Roombots [2] are modular robots for adaptive and self-organizing furniture. They are beingdeveloped at BioRob. Figure 1.1 shows a Roombot module.

They are designed for two main research tasks. On one hand, they serve as building blocks forself assembly and reconfiguration of static structures such as intelligent furniture. The second taskis to serve as a platform for research on distributed locomotion, especially based on central patterngenerators (CPGs).

The main characteristics of the Roombots are:

• 3 degrees of freedom

• homogeneous and autonomous modules

• 10 active retractable connectors by module

• size: 110 x 110 x 220 mm

• weight: 1.4 kg

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Figure 1.1: Two Roombots modules [2]

Information about forces and moments applied to the modules would be of great benefit to boththe tasks the Roombots are designed for.

For the reconfiguration task, it would allow the modules to get into position easier by detectingcontacts between modules. For the locomotion task, it would detect the contact with the groundand could be used as feedback information to close a control loop. The roombots were the objectof Joel’s work with force sensors during the first semester this year.

Figure 1.2: Sen-sor integration oncheetah-robot’s leg

.

Cheetah: compliant quadruped robot [3]

The Cheetah is a compliant quadruped robot first developed by S.Rutishauser in a semester project. Cheetah features three-segment legs withpassive compliant knee joints. Each leg has two degrees of freedom, the kneeand hip joints can be actuated using RC servo motors. Though, the leg iscomposed of 3 segments. The segments’ dimensions influence the stiffness ofthe legs. A CPG network has already been implemented and enabled up toa 1m/s gait.[5]It is possible to use sensory information in a CPG so that the oscillator isbetter coupled with the mechanical system [6], hence adding a force/torquesensor on each leg of the cheetah-robot would then enable to integrate thisfeedback information in the controller and possibly improve it.Indeed, knowing the GRF (Ground Reaction Forces) thanks to a multi-axissensor would enable to know in which phase of the gait – stance or swing–the robot is, while moving.Besides, the sensor would be able to detect obstacles touching the leg or achange in the slope.[7]

Furthermore, the sensory information given by this sensor could lead to abetter understanding of the locomotion with a CPG.

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Figure 1.3: Picture of ”cheetah”

1.2 Objectives

My project can be seen as divided in two parts : the first involves the sensor for the Roombot madeduring the previous semester, the second deals with a new sensor for the Cheetah-robot.

1.2.1 Understand the problems with the existing sensor

Joel Rey has been working on a multi-axis force and torque sensor to be integrated in the Roombot[2], inspired by the sensor on the iCub’s arms [4]. The goal of my semester project is to design asimilar sensor on the Cheetah-robot [3]. Before getting started on the module for ”Cheetah”, I haveto validate Joel’s sensor. As his tests did not match the results from simulation, I have to redesignan experiment and run new tests to find out where the incoherent results come fromand obtain new results.

1.2.2 Adaptation of the Roombot’s sensor design to the Cheetah-robot

After having either validated the sensor for the Roombots or having found a plausible explanationfor its problems, the following work of this project is to continue with its adaptation for the cheetah-robot, which is a structure that leaves much less space for the design. This implies the designof a new sensor to be integrated in Cheetah-robot’s leg and its characterization, bysimulations and confirmed with experiments.

Remarks about the implementation on Cheetah-robot :

- The sensor will probably be situated between the third leg segment and the foot.

- It will be approximately 2 cm large, to fit on the leg.

- The choice of the number of axis is yet to be made.

1.2.3 Link the sensor to the electronics

Rico Mockel already designed the electronical part of the Roombot’s acquisition component, whichis roughly composed of a Microchip 32-bit dsPic (33F) and AD7192/7193 converters specialized fordifferential signals acquisition. This structure will by carried out on the Cheetah design. Basically,

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the microcontroller would send the processed data to the main controller onboard or the raw datato a computer for testing purpose. Testing the operation of the signal acquisition by the electronicswould then simplify the measurements for the system characterization and permit to validate thispart of the system.

1.2.4 Gant chart

The Gant chart is an indication of the work schedule over the semester

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Chapter 2

Background and literature

In this project, we use the load-cell technology, it is here presented as well as some papers relatedto the use of this technology.

2.1 Load cells

Most of the information required is already present in Joel’s report, here is a short review. Ipresent the strain gage technology as well as the possible Wheatstone bridges configurations totake advantage of them, and the corresponding equations.

2.1.1 Strain gages

Introduction to load cells principles and circuits :

Principle

Forces or torques are determined by measuring the deformation of a body, designed expressively tobe deformed by the measured force components. Gauges glued on the body vary in resistance alongwith the variation in size i.e. the deformation. The measure of the force/torque is then equivalentto the measure of an electrical resistance.

Electrical scheme of the sensors

Since resistor variations with the deformation are very small, Wheatstone bridges (see Figure 2.1)can be used to measure such resistor variations. If it is alimented by a voltage source (P) alongone diagonal (A-C), there is a null voltage Vout along the other diagonal (B-D) at the equilibrium.Variation of one of the resistors leads to a variation of this voltage Vout, which can be measured(here by G). The output voltage for small variations follows (neglecting higher order terms) [8] :

Vout =Vin4

(∆R1

R1− ∆R2

R2+

∆R3

R3− ∆R4

R4

)(2.1)

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Figure 2.1: Wheatstone bridge, figure taken from [8]

Gauges position and electronics

According to (2.1), the signal is maximal when gauges are positioned so that the ∆RR are maximal

and the + and - sign terms add to each other.When several dispositions are available, it is possible to choose the one that simplifies the wiring.

Quarter-bridge The simplest configuration : one resistor is replaced by a strain-gauge. Theoutput is nonlinear with the variation of the deformation. For small deformations, this can beneglected. For example: R1 = R2 = R3 = R (resistors), R4 = R+ ∆R (the strain gauge), we have:

Vout = Vin

(∆R

4R+ 2∆R

)=Vin∆R

4R(2.2)

Half-bridge Two active gauges, one possibility is to choose each one measuring opposite defor-mations (the case of a beam in flexion, one gauge on the top and one gauge under the beam). Thisleads to:R1 = R2 = R (resistors), R3 = R+ ∆R, R4 = R−∆R (gauges with opposite deformations).The resulting equation is:

Vout = Vin

(∆R

2R

)(2.3)

The difficulty is that this configuration works only if the body is not subject to parasite strains.As an example, if a beam in flexion is also in traction, it is false that ∆R1 = −∆R2. Compared tothe first configuration, the output is linear and compensated in temperature.

Full-bridge Four gauges are used, hence the sensitivity is 4 times higher as the quarter-bridge.It can be used with two gauges compensating for the Poisson effect in a beam in compression. Itcan also be used as the precedent examples in the half-bridge, with two gauges under and two ontop of a beam in flexion. If the wiring is so that each deformation (negative or positive) adds toeach other, and each gauge has the same resistivity R, we obtain:

Vout = Vin

(|∆R1|+ |∆R2|+ |∆R3|+ |∆R4|

R

)(2.4)

This is the configuration and formula used on the new sensor designed for cheetah-robot’s legs.

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Quarter bridge Half-bridge Full-bridgeAdvantages Less gauges (easier and

cheaper)LinearLess gauges

LinearWhen used for bendingstrain, rejects axial strainTemperature compensa-tion

Drawbacks Low sensitivityNot completely linear(very small nonlinearity)No temperature compen-sation

No temperature compen-sation if used for axialstrain measurement, butcompensated for ”bend-ing” strain (the case here)

More gauges (harder toplace and more expensive)

Table 2.1: Wheatstone bridges configurations : advantages and drawbacks

Wheatstone bridges comparison The Full-bridge is always the best when looking at the per-formances, regarding temperature compensation and axial strain compensation (even with onlybending strain due to Poisson effect), its main advantage compared to half bridge is the bettersensitivity. Its only drawback being the higher number of gauges used and its consequences.

Mechanical design of the sensor

The design of a sensor, or more specifically its body, is often related to simple material resistancecases (traction, flexion, torsion). The gauge’s resistance varies with the deformation according to :

∆R/R = K ∗ ε (2.5)

With formula (2.1), we obtain the signal Vout/Vin in mV/V. We can also determine the sensi-tivity in mV/N or mV/Nm.Since the AD converters output directly Vout

Vin, formula 2.6 is used by the computer :

VoutVin

= K ∗ (ε1 − ε2 + ε3 − ε4) (2.6)

For more information about Load cells, friction, looseness, choice of metal for the body, non-linearities, thermal variation and electric compensations and zero drift, you can refer to [8].

2.2 Literature review: multi-axis force/torque sensors

Several papers with some of their main ideas that have been useful or inspiring for this project arepresented in this section.

Development of a small 6-axis force/moment sensor for robots fingers [9]

Details about a two-levels 6-axis 35mm*35mm*85mm sensor for robot’s fingers. Moments intensitiesare calculated in order to determine the position of the force on the robot’s finger. The authorsmanaged to obtain a maximum of 10% of error betwwen simulation and practice. Interference

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between strain gauges was also reduced to a maximum of 4% thanks to the design. This simplifiesthe compliance matrix of the system as the less interference, the more the matrix is diagonal.This leads to more precise results because each load-cell only measures one force/torquecomponent. It can be obtained by the design of the body.

A criterion for optimal design of multi-axis force sensors [10]

The principal goal of this paper is to identify a mathematical objective function, whose minimizationcorresponds to the optimization of sensor accuracy. It focuses on the mathematical aspect of theoptimization of the gauges number necessary, depending on the number of force components todetermine. In general, having more sensors than forces to read is not optimal.

Multi axis force and torque sensor [11]

Introduction to multi axis force and torque sensors, they suggest to add ”stops” to prevent thedeforming body to break when a force too big is applied. This enables to measure lowerforces and still have a system that can resist much higher forces.

Design and fabrication of a six-component force/moment sensor[12]

Another design of a 6-axis force/moment sensor : a theoretical analysis is used to model the sensorwhich gives the equations of deformation. It allows to design the elements afterwards starting withthese characteristics :

1. The rated capacity of the forces Fx , Fy and Fz is 100 N. The rated capacity of the momentsMx and My is 1 N.m and the rated capacity of the moment Mz is 2 N.m

2. The rated strain of each sensor is 1000 (micro) m/m,

3. The attachment locations of strain gages are 3 mm from the end of the plate-beams for Fx,Fy, Fz, Mx , My sensor and the locations of strain gages are 5 mm from the end of theplate-beams for Mz sensor in the length direction.

They use full-bridge circuits and obtain a maximal error of 6% between theory andexperiment, 2% interference error. This paper is the main inspiration for the designof the sensor for ”Cheetah”.

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Chapter 3

Roombot’s sensor prototype

The sensor designed by Joel last semester shows different behaviour in simulation and in practice.I have been working on resolving this issue.This chapter presents the different explanations found for that problem as well as the experimentalsetup developed for the sensor’s characterization.

3.1 Bad results

3.1.1 Asymmetric measures

Getting different results than predicted, I used the existing setup with Labview to make some testmeasurement to check that the behaviour of the gauges has some logic, that is does not behaveinconsistently. One simple way to measure consistency is to apply a force symmetrically relativelyto several sensors. Symmetric results should be obtained. When applying a vertical force on thesensor (along the z axis), 3 of the 4 bridges should output the same voltage, at most opposite incase of wrong wiring. Instead, the results obtained were far from symmetry : voltages varied fromsimple to double. Further similar tests delivered other contradictory results.

Figure 3.1: Roombot’s sensor

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3.1.2 Possibles causes for asymmetric behaviour

Gauges sensitivity

One factor that would be a legitimate cause of the precision issue is the difference in sensitivitybetween the 4 gauges. The gauges’s specifications give a sensitivity of 150 ± 10, this is one of themain causes of the difference between simulation and practice : it is not really predictable. However,this cannot explain the huge differences in the previous symmetric tests. In addition, the precisionof the orientation of the glued gauges has an effect of similar importance.

Position of the gauges pairs

In order to use formula 2.3, the two gauges composing each bridge should measure an oppositedeformation. This stands only for examples in the case of putting a gauge on each side of beam inflexion. On the roombot’s prototype sensor, this is not the case. Therefore, we must use detailedsimulation results for each gauge to recover their true deformation. Thereby, the precise position ofeach gauge has a real importance : we can see this on the figure 3.2 showing the deformation alongthe axis of one of the gauges: the two gauges (in the middle of the two axis drawn) do not sustainthe same deformation. On the top of the beam, a displacement of 1 cm can give results that varyfrom simple to double.

Figure 3.2: Plot of the deformation along the axis of gauge 1b

Nominal values of the gauges and resistors

The resistivity values of the gauges are not precise. In our case, they are meant to be 340 Ω butactually vary between 320 Ω and 360 Ω.

Can this variation cause big errors ? I simulated in an excel worksheet the outputs of the bridgewith different values for the gauges’ resistivity. I also varied the values of the resistors (half-bridgecase). The results are displayed in Figure 3.3.

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The result is that the values of the resistors have no effect on the final output, whereas the resistancevalue of the gauges has a very small effect. Except huge divergence between the resistance of thegauges, this effect cannot be a factor of error at the scale of precision we are aiming. The followingdata give more information :

Simulation data :

• Half-bridge

• Two gauges get opposite 1E-4 deformations

• Gauges sensitivity are fixed at 150

Resistor/Gauge: R1 R2 S3 S4 Bridge output errorNominal value (Ω) 200 200 200 200 0.0%

Real Values set 1 (Ω) 300 280 280 280 0.0%Real Values set 2 (Ω) 300 280 280 320 0.4%Real Values set 3 (Ω) 300 280 380 420 0.2%Real Values set 4 (Ω) 300 280 500 500 0.0%Real Values set 5 (Ω) 300 280 280 180 5.3%

Figure 3.3: Excel simulations to see the effect of different resistor values. The values for S1 and S2do not matter (they are corrected by the offset-correction). The formula here uses no linearization(like high order terms neglection), it is thus the true error value without noise.

For example, if the two gauges in a bridge have a resistivity of 280Ω and 320Ω instead of200Ω both, the resulting error on the output is 0,4% (”Real Values” set 2 on Figure 3.3). Aswe see, the gauges resistivity values in absolute have no effect (RV set 1), it is the differencebetween the gauges that create a distorsion. The smaller the values, the higher the difference hasimportance (comparison RV set 2/3). Therefore, gauges with higher nominal resistance can havehigher dispersion without disturbing much the precision.

3.1.3 Short-circuits

Even though the gauges are internally isolated, since the body is made of aluminium – a very goodelectric conductor –, the gauges are glued on a surface that has previously been laqued to furtherisolate from the metal.However, I measured the resistivity between the body and each point of the bridges. Since all thebridges are linked by the Ground and +5V wires, one ”short-circuit” is enough to make all thebridges have a connection to the aluminium.It appeared that one point had a complete short-circuit to the aluminium (0.4Ω measured betweenthe extremity of a bridge and the metal). I then disconnected all the wires from all the bridgesto be able to discern real short-circuits from other non-infinite resistivity values that might appearbecause of the links between the bridges. On one hand, some of the short-circuits were caused bythe unisolated golden wires touching the surface of the aluminium where no laque was applied. Thiswas not a problem and could be corrected. On the other hand, it was clear that there was someconnection between the gauges and the body : some of the gauges show a resistivity between 200Ω

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and 1000Ω to the body. This issue concerns approximately half of the gauges. We can concludethat the protocol to glue the gauges is not entirely wrong but shows weaknesses.

Bridge 3 Bridge 4G1a ∞ 505ΩG1b ∞ 209ΩG2a ∞ ∞G2b ∞ ∞

Figure 3.4: Resistivity values for two of the bridges

Theses ”short-circuits” or ”connections” between gauges and the body make a good explanationfor the unsatisfying results found until now. The gluing process should be taken into account inthe design, for instance by placing the gauges at positions easy to access for gluing. Also, gluingtests should be carried on as well as a review of the different methods for gluing.

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3.2 Experimental setup for the roombots

In order to both characterize the system precisely and to be able to make a correspondence betweenthe simulation and the experimental results, we need an experimental setup that enables us to getreproducible and accurate measurements. We hereby propose a setup, the CAD files are includedin the report CD.

3.2.1 Top beam

We want to measure forces and moments along several axis. It is already possible to apply a forceor a moment along the x and y axis, and less precisely a force along the z axis. In order to be ableto apply a moment along the z axis and a precise force along the same axis, a beam will be screwedon the top extremity of the central lever. Two forces applied at each of its extremities in the xyplan will provide a moment along the z axis and two forces applied at the same points verticallywill ensure a force along the z axis without perturbations creating moments along the other axis.The beam will be maintained by two screws onto the lever.

Figure 3.5: Prototype of the roombots sensor with a lever and the beam on top

3.2.2 Pulleys

Figure 3.6 : The prototype is held in place onto a metal plate with a clamp (f ). To apply a momentalong the axis x or y, two ropes are attached on the lever at (a) and (b) and run through a pulleyat (e) (the second pulley on the other side is not drawn). The pulley is maintained at the rightheight with two stopping rings. When applying a moment along z, two ropes are attached to (c)and (d), the pulleys’ height should be modified in accordance. For the force along z, two ropes areattached to (c) and (d) and knotted together in order to pull the same force at each point.

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Figure 3.6: Schematic of the experimental setup

Figure 3.7: Rendered view of a magnetic foot with pulley. Magnetic foot to be replaced withanother system : firstly ordered components should insufficient holding forces. New foot or fixationwill be required.

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3.2.3 PCB

Until now, the Wheatstone bridges were realized by resistors soldered together with the wiresand attached onto the body. Since this setup is not clean and may be a cause of short-circuits,I manufactured a few PCBs of Wheatstone bridges that allow a much cleaner setup. The PCBcontains two bridges as the bridges 1 and 2 are very close. It also requires two less power-supplywires. For the other bridges, only one of them is used on the PCB. Figure 3.8 shows the schematicof the double bridge and figure 3.9a the only layer of the PCB with legend.

Figure 3.9b shows an updated double Full-bridge version used for the cheetah-robot.

Figure 3.8: Schematic of the double Wheatstone bridge. Files and schematics are provided on theCD

(a) PCB of the double wheatstone bridge (b) PCB of the double Full wheat-stone bridge

Figure 3.9: The two PCBs : half and full Bridge

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Chapter 4

Sensor Design

In this chapter, we consider each step of the approach we followed to design the force/torque sensorfor the Cheetah-robot.

4.1 Introduction

Here are presented the first considerations for the design of the sensor, starting by the considerationsleading to the choice of the number of axis followed by the study of the range of forces the sensorwill have to measure and resist, as well as the placement of the sensor on the robot’s leg.

4.1.1 First hypothesis

In order to choose the number of axis necessary for the force/torque sensor, we have to make somehypothesis on the kind of contact between the foot and the floor.

z is the vertical axis, y is the direction of forward motion and x is perpendicular to the robot(see figure 4.1).

First set of hypothesis:

• (a) Three forces can be applied from the foot onto the floor : The force along z supports therobot’s weight, the force along y thanks to friction and the force along x is not negligible.These are also called GRF (Ground reaction forces).

• (b) If the floor is not sticky, it cannot transmit a moment to the foot at the point of contact.However, the position of this point of contact has an influence on the moment perceived bythe sensor due to the forces applied on the foot and the gap between the foot and the sensor.We must therefore make an hypothesis on the position of the contact or be able to determineit.

• (c) Angular position of the foot segments (two angles) and orientation of the body (two otherangles) are known thanks to position sensors and gyroscopes. (see Figure 4.2).

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Hypothesis (c) was considered at the beginning but dropped because of the reasons explainedin 4.1.2.

These hypothesis can be summarized in Figure 4.1 x’,y’ and z’ axis’ orientations are knownthanks to the sensor’s information

Figure 4.1: Last segment and foot of the leg. A : position of contact. B : position of force sensor.xAB is not drawn here.

Figure 4.2: Angles used to determine R’. One angle cannot be displayed from this perspective, itis the orientation of cheetah-robot’s body along the y axis. Hypothesis dropped, see 4.1.2

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The transposition of the forces/torques from the contact in A to the sensor in B leads to :

Tfloor→foot =

Fx 0Fy 0Fz 0

A

=

Fx Mx,B = Fy ∗ zAB − Fz ∗ yABFy My,B = −Fx ∗ zAB + Fz ∗ xABFz Mz,B = Fx ∗ yAB − Fy ∗ xAB

B

(4.1)

4.1.2 3 axis design versus 6-axis design, complementary hypothesis

3 axis

Advantages

• 3 axis only require 3 bridges : there are less gauges so that the installation is easier.

• The 3-axis design is easily upgradeable to 6-axis.

Drawbacks

• The 3 bridges must be calibrated for the 6 forces/torques anyway: they each measure adifferent linear combination of these.

• Based on the hypothesis that the point of contact of the foot with the ground is always thesame (a) and known (b).(a) It seems unlikely that the point of contact (where the resulting force from the ground tothe foot is applied) is the same at each step, not even during one step. Furthermore, thecheetah-robot is meant to walk on uneven terrain.We should also keep in mind that if the foot is small enough, this variation might be neglected.(b) The relative position of the foot to the sensor is then to be determined by the cheetah-robot’s sensors. This is quite complicated because it assumes that the foot lays flat on thefloor, or always keeps the same angle relatively to the floor. The initial scheme about thiswas Figure 4.2 on page 19, which is here redrawn as Figure 4.3.An alternative solution is to add a joint angle sensor between the foot and the 3rd segment.

6 axis

Advantages

• A 6-axis sensor enables to determine the point of contact with the ground, there is no needfor the angular position from the sensors to know what the angle of the foot is.

• The design is not much different from the 3-axis design.

Drawbacks

• More bridges are required, it means more gauges and more wires that lead to a more complexinstallation.

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Figure 4.3: To determine the relative position of contact in relation to the sensor in B given thatthe contact is always at the same point on the foot, the first idea was to use data from the othersensors to determine the angle between the foot and the last segment (not drawn here). This isactually not possible since the foot does not lie on the floor as drawn here, but can have differentorientations – which is part of the gait.

• We must first determine the force’s components in the referential of the segment hosting thesensor. The information from the gyroscopes and joint angles are then again required totranspose these components onto a referential with the plane xy parallel to the the ground(which is assumed to be the desired referential for control use of the forces) .

Chosen : 6 axis sensor The main arguments for choosing a 6-axis sensor are the unconstrainedposition of contact of the force as well as the relative simplicity of the extension from a 3-axis design.

4.1.3 Forces computation

If our hypothesis is that only 3 forces can be transmitted to each foot, there are only three forceunknowns at the point of contact and three distance unknowns that create the moments perceivedby the sensor and the sensor should only be able to measure 3 out of the the 6 parameters ofTfloor→foot,B .

Each half-bridge outputs a voltage Vi, linear combination of the 6 components Fx, Fy, Fz,Mx,My,Mz

in B :

V1 = a1 ∗ Fx′ + b1 ∗ Fy′ + c1 ∗ Fz′ + d1 ∗Mx′,B + e1 ∗My′,B + f1 ∗Mz′,B






(4.2)

We would therefore have 6 equations and 9 unknowns. Our other hypothesis assuming that nomoment can be transmitted at the point of contact enables us to obtain a set of another 3 equations:

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Mx,B = Fy ∗ zAB − Fz ∗ yABMy,B = −Fx ∗ zAB + Fz ∗ xABMz,B = Fx ∗ yAB − Fy ∗ xAB

(4.3)

The hypothesis lays in that there is no ”M∗,A” term added on the right part of the equations. Itmeans there are no moments transmitted in A.

Choice of the axis, bridges placement

As explained previously, the sensor should output 6 different linear combinations of the deformations(due to the forces) in B. It should be possible to measure with each bridge a different component inthe referendum R’ defined by x’, y’ and z’ (see Figure 4.1). The coefficients in (4.2) are estimatedby simulation and determined precisely by calibration of the sensor.One goal could be to design the sensor as to obtain a1 = b2 = c3 = d4 = e5 = f6 = k 6= 0 and allother coefficients equal to zero. Equations (4.2) would then be (expressed in R’) :

V1 = k ∗ Fx′

V2 = k ∗ Fy′V3 = k ∗ Fz′V4 = k ∗Mx′

V5 = k ∗My′

V6 = k ∗Mz′

(4.4)

Because the position of the forces relative to the sensors varies, it is not difficult to measure onlyforces and not moments with one bridge, therefore it is not really a possibility here. However, theidea of measuring the least components by each bridge is useful and used on the designed sensor.

4.1.4 Position of the sensor on the leg

One idea is to locate the sensor on the last segment before the foot, which allows it to be close tothe point of contact on the floor. The benefit being that knowing only the angle between the sensorand the foot enables to have enough information to transpose the forces to the point of contact.However, the sensor is designed to be used as a 6-axis sensor instead of 3-axis, so the angularinformation matters even less because the point of contact is analytically determined from theforce/torque sensor data. Situating the sensor on the first segment (near the hip) would also havebe possible, possibly saving space on the last segment, reducing the inertia of the leg and enabling todetect unexpected contact situated higher in the leg (in case of an obstacle for instance). However,the final choice is the last segment, for the simple reason of the place available.

4.1.5 First design draft

Our finally chosen design is inspired from [9] (Figure 4.4). It can be used as a 3-axis sensor or asa 6-axis. It is drawn in Figure 4.4. Some examples of the stresses with different forces applied canbe seen in Figure 4.5.

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Figure 4.4: First design, CAD view

(a) Fx (b) Fy (c) Fz

Figure 4.5: Different deformations

Each ”level” of the sensor is designed to deform the most according to the force/torque alongonly one axis. This enables the mixing matrix of the system to be diagonal and simplifies thesystem design.

4.1.6 Material resistance and stress concentration

The stress we want the structure to sustain is the one corresponding to the deformation enablingprecise measurements and should be maximum at the position of the gauges. Therefore, the designshould avoid stress concentrations, some of which can be seen very clearly on Figure 4.6 betweenthe first two ”levels” of the sensor. In this example, the stress at the concentration point reaches 60MPa whereas the stress at the gauge’s location is merely 30 MPa. This situation can be improvedby rounding the edges, which is any which way necessary for the manufacture of the body.

4.2 Sensor’s sensitivity

4.2.1 Introduction

The sensitivity of the sensor depends on a lot of parameters. First, we should define the sensitivitybecause there are several possibilities.

The goal of the sensor is to output voltages which vary according to the forces and torques

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Figure 4.6: Stress concentration with Fy

submitted to it. These outputs are directly proportional to the deformation at the gauges positionsand can be estimated by simulation, then confirmed by experiments. Here, the inputs are forcesand moments. The ”force” applied to the sensor has no meaning unless given with its pointof application. Indeed, the sensor will not have a similar reaction to forces applied at differentpositions. On the contrary, moments do not have a position of application.

In our case, we want to determine forces – only – on the foot. However, the relative position ofthe foot to the sensor varies with the position of the leg, such that it is impossible to calibrate thesensor in relation to the forces at the real point of contact (Figure 4.7, point A). Nevertheless, itis possible to calibrate the sensor for forces and moments at a point fixed relatively to the sensor(Figure 4.7, point B).It could also be possible to calibrate for the forces directly next to each part of the sensor designedto measure each one of the components (Figure 4.7, points C1, C2, C3). This approach makes moresense relatively to the design of the sensor since for example the two first levels (to measure Fx andFy) are symmetrical and have the same sensitivity in relation to forces that are relatively at thesame distance from each of the ”levels”.

Since calibrating the sensor is equivalent to finding 6 linearly independent equations, the pointwhere the forces are applied only have influence on the sensitivity of the measures, hence theprecision of the calibration. It is therefore more interesting to apply forces not too close to thesensors so that the moments benefit from a bigger lever.

With these results, it is then possible to find the forces at the point of application, which isour goal, either by using the sensory information about the orientation of the ”Cheetah” plus theangles of the leg’s segments, or by measuring 6 components of the forces/torques at the ”point ofmeasure” and then solving for the point where there are no moments.

With this, we still cannot define the sensitivity relatively to the forces’ components at A in areferential where xy is parallel to the ground. The additional information on the robot’s orientationand the leg’s segments’ angles is required.

4.2.2 Estimation of the range of forces submitted to the leg

The robot weights approximately m = 2kg. 1

1 Updated to 3kg, (June 2011). Following results to be multiplied by 1.5The design of the sensor has been done with the m = 2kg value. Characteristics such as plates thickness should beupdated to fit the new

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Figure 4.7: Possibles points for the chosen input forces. A : position of contact. B : after the sensor.C : after each ”level” of the sensor (C1: for Fy, C2: for Fx, C3: for Fz)

• When idle, the force is aroundm ∗ g

4= 5N on each leg2 (depending on the weight repartition

of the robot). We want to be able to measure a force a little smaller than this one, an estimatecould be 1 N for the smallest force detectable, hence 1 N being then the resolution.

• In case of shock, all the kinetic energy of the cheetah-robot would have to be absorbedby one leg only. In a very primitive estimation, we could estimate the force resulting as8 ∗m ∗ g = 8 ∗ 2 ∗ 9.8 = 157N (very rough estimation3). The direction of this force would beshared between the vertical axis z and the horizontal axis y in the length of the robot.

4.2.3 Sensing elements design

Minimum forces

Linking the forces applied in A must be translated to the measuring point B to help designing thesensing elements of the sensor.

Tfloor→foot =

Fx 0Fy 0Fz 0

A

=

Fx Mx,B = Fy ∗ zAB − Fz ∗ yABFy My,B = −Fx ∗ zAB + Fz ∗ xABFz Mz,B = Fx ∗ yAB − Fy ∗ xAB

B

(4.5)

2Updated value : 7.5N3Updated value : 235N

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Approximated hypothesis on xAB , yAB and zAB : 1 < xAB < 3cm2 < yAB < 4cm4 < zAB < 6cm

(4.6)

We obtain:

Tfloor→foot,Fx=1N =

1 00 00 0

A

=

1 00 −zAB0 yAB

B

=

1 00 −(0.04→ 0.06)0 (0.02→ 0.04)

B

(4.7)

The same for Fy and Fz :

Tfloor→foot,Fy=1 =

0 zAB1 −xAB0 0

B

=

0 (0.04→ 0.06)1 −(0.01→ 0.03)0 0

B

(4.8)

Tfloor→foot,Fz=1 =

0 −yAB0 xAB1 0

B

=

0 −(0.02→ 0.04)0 (0.01→ 0.03)1 0

B

(4.9)

These values are used to estimate the effect of the forces at the level of the sensor and for thedesign of the sensing elements.

Maximum forces

Given the previous hypothesis of a 157N maximum force4 (§4.2.2) applied on the foot in case of shockand assuming that the angle between the force and the z axis of the sensor can vary approximatelybetween -10 and 20 degrees when an important force is applied. (See Figure 4.8)

So with θ the angle between the force and the z axis of the sensor:

Tfloor→foot,Fmax(θ) =

Fx 0Fy 0Fz 0

A

=

0 Fmax ∗ sin(θ) ∗ zAB − Fmax ∗ cos(θ) ∗ yABFmax ∗ sin(θ) Fmax ∗ cos(θ) ∗ xABFmax ∗ cos(θ) −Fmax ∗ sin(θ) ∗ xAB

B

(4.10)Study of the stresses for θ between -10 and 20 degrees is ran through simulations to check if thesensor can withstand the worst situation.The main variables to adapt the design to resist such forces are the thicknesses of the sets of plates.The first set is composed of the two PPB (Parallel Plate Beams [9]) on the bottom part of thesensor. Their value is set to 1mm. The second set are the PPBs on the middle part of the sensor(the cross-like part), their value is set to 1.1mm.5

4Updated value : 235N5These values probably will have to be modified for the updated value of the cheetah-robot’s weight. No value is

proposed here, feedback from the first prototype will have to be used first.

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Figure 4.8: Hypothesis on the angle of the force when the foot touches and leaves the floor

4.3 Final model of the 6-axis sensor

Given the considerations of the previous chapter, the first design has been modified. Here arepresented each force/torque simulation with the picture of the ”level” designed to measure theaccording deformation (see Figure 4.9).

4.3.1 Sensor prototype production

The prototype is produced by the AEM (Atelier d’electromecanique), one of the mechanical work-shops of the EPFL, whose responsible is Jean-Paul Brugger.

Modifications for production

• Rounded edges for milling (for internal angles) and to avoid stress concentrations.

• Attachment points at the extremities for fixation with the rest of the leg or a setup board.

• Third part created to ease installation of the gauges. It is glued on top of the second level ofthe sensor.

Technical drawings for production

Each part has been drafted through solidworks (Figure 4.10):

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(a) Fx (b) Fy (c) Fz

(d) Mx (e) My (f) Mz

Figure 4.9: Different deformations for Fx, Fy, Fz, Mx, My and Mz. Gauges intended to measureeach force are represented with a red rectangle. The color represents the deformation along oneaxis on every figure.

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(a) Part 1 (Bottom) (b) Part 2 (Middle) (c) Part 3 (Top)

(d) Pictures

Figure 4.10: Extracts from the parts’ drawings and picture of the sensor

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Chapter 5

Results

5.1 Simulation results

Characterization

The simulations under Solidworks give the following results (Figure 5.1 and 5.2):

Figure 5.1: Sensitivity in mV/N for each bridge and force

Figures 5.1 and 5.2 use the deformation data collected with Solidworks for each gauge and fitthem together to obtain the output values of each bridge, also using the the gauge factor (150).

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Figure 5.2: Sensitivity in mV/(N.m) for each bridge and torque

From the simulations we can see several points :First, the bridges are nearly completely independent. Each one depends almost only on one forceor torque.

However, the two bridges B4 and B5, designed to measure respectively Mx and My, also measurerespectively Fy and Fx. This is expected because forces Fx and Fy both create moments My andMx, it thus cannot be avoided.

Second remark, the bridge B3, designed to measure Fz, has a very low sensitivity compared tothe other bridges. This is due to the design width restriction, since no big lever can be used onFz. However, a 1N force on Fz still produces a 2mV voltage (with 5V power). Even the Labviewacquiring system, about 0.5mV precise, would enable a 1

4N resolution on Fz.

Short sensitivity to noise considerations

From the sensitivity data (Tables 5.1 and 5.2), we can deduce the effect of noise on the readings: forexample, since the sensitivity for Fz is approximately equal to 2mV/N , a 0.5mV noise will producea 1

4N error.

Since Fz produces little sensitivity, the voltages it produces (mostly on B3) has to be amplifieda lot to obtain its value. Therefore, it is also much more subject to noise than other components.

5.2 Experimental results

The simulations are approximations of the behaviour of the sensor and the values it will output.As it happened with the previous project, results from simulations and experiments can strongly

31

diverge for different reasons. Apart from the numerical errors in simulation, the precision in theplacement and orientation of the gauges, the uncertainty on the gauges’s sensitivity, hardwaremalfunctionning (like unwanted short-circuits), the sensor must be calibrated to be able to outputthe most precise values of forces.

Characterization

No experiments were done during the project for time constraints reasons. Hopefully the experi-mentation will be done before the project’s presentation.

5.3 Possible future improvements

Besides the sensor calibration which is mandatory to complete this project, there are several otherpossible improvements. The software of the electronics are not complete, even though the mainstructure is ready, communication between the microcontroller and the analog-digital converter isnot finalized. A Matlab interface to receive the data from the dsPic should also be developed.

Since the weight of the Cheetah-robot changed during the project, the prevision of the range offorces to sustain in case of shock should be updated to the new values and some characteristics ofthe design changed accordingly, in order not to weaken the structure.An interesting experiment would be to carry some resistance tests on the sensor to confirm themaximum endurable load, maybe discover weak points in the structure and update the sensordesign accordingly.

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Chapter 6

Conclusion

The objective of this semester project was to design and integrate a multi-axis force/moment sensorin the Cheetah-robot in order to provide feedback information, mostly the ground reaction forces.The choice of a 6-axis sensor enables further access to information about the position of the contact.After the study of Joel Rey’s project that lead to a better understanding of the difference betweensimulation and experimental results, I designed a 6-axis sensor that fits in the third segment of therobot’s legs. The simulations results showed a good behaviour of the sensor regarding the sensitivityof each bridge to each force/torque component. Validating the simulations results is still to be donewith the available prototypes, i.e. by gluing the strain gauges and connecting the electronics.How the data provided will be used is yet to be studied, this is a promising topic for future work.

6.1 Acknowledgment

I would like to thank Alexander Sprowitz for his guidance during this project and Rico Mockel forhis contribution to the project with his knowledge in electronics. I also appreciated the expertiseof Alessandro Crespi for helping me produce prototype PCBs. I am very grateful to EmmanuelDroz from the DISAL for his assistance with the electronics. I also would like to thank ProfessorAuke Jan Ijspeert for welcoming me in his laboratory and giving me the opportunity to work onthis project in a dynamic environment.

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Bibliography

[1] J. Rey. Design and integration of a multi-axis force/moment sensor for the roombots. Technicalreport, EPFL, 2010.

[2] A. Sproewitz and Ijspeert A. J. (Dir.). Roombots: Design and Implementation of a ModularRobot for Reconfiguration and Locomotion. PhD thesis, EPFL, Lausanne, 2010.

[3] S. Rutishauser. Cheetah: compliant quadruped robot. Technical report, EPFL, 2008.

[4] http://www.robotcub.org/.

[5] A. Sproewitz, M. Fremerey, K. Karakasiliotis, S. Rutishauser, L. Righetti, and A. J. Ijspeert.Compliant leg design for a quadruped robot. Abstracts of Dynamic Walking, 2009.

[6] L. Righetti and A. J. Ijspeert. Pattern generators with sensory feedback for the control ofquadruped locomotion. Proceedings of the 2008 IEEE International Conference on Roboticsand Automation, 2008.

[7] A. Tuleu, A. Sproewitz, M. Ajallooeian, P. Loepelmann, and A. J. Ijspeert. Exploiting com-pliance with a cat-sized quadruped robot for trot gait locomotion. *Biomechatronics, TU-Ilmenau, Germany, Biorobotics Laboratory, EPFL, Lausanne, Switzerland.

[8] J.L. Le goer. Capteurs jauges extensomtriques. Les techniques de l’ingenieur, 1992.

[9] Gab-Soon Kim. Development of a small 6-axis force/moment sensor for robots fingers. Mea-surement Science and Technology, 2004.

[10] A. Bicchi. A criterion for optimal design of multi-axis force sensors. Dipartimento di SistemiElettrici e Automazione (DSEA) e Centro ’E. Piaggio’, 1992.

[11] Dwayne M. Perry. Multi axis force and torque sensing. Sensor Review, 1997.

[12] Gab-Soon Kim. Design and fabrication of a six-component force/moment sensor. Sensors andActuators, 1999.

[13] BJ. Furman. Data acquisition.

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Appendix A

Solidworks

Since a CAD software with FEA (Finite Element Analysis) capabilities is required for stresses anal-ysis, and Joel Rey - the previous student working on a multi-axis sensor - was using Solidworks, Icontinued using it.

A.1 How to estimate the deformation at one point, alongone axis

The goal of the simulations is to be able to compute the change in resistivity of the gauges at theirlocation depending on their orientation.

Create sensors

First, one should define ”Capteurs” (French version of Solidworks, ”sensor” in english), these sen-sors should be defined as ”Donnees de simulation” type and ”Autres capteurs de simulation” as”Quantite de donnes”. One should then select a point previously defined in the ”properties” field,or several points selected in a strict order as you can later more easily retrieve the data. (see figureA.1a)

Run simulation

Here is not explained how to run a simulation with defined forces, imposed displacements, materialsand meshing.To obtain the deformation along one axis, first define a new ”results” draw (see figure A.1b) andselection deformations. You can now either selection ”Z/X/Y normal deformation” if you areinterested in a deformation along one of the 3 main axis of you solidworks file.If you want the deformation another another axis, you should beforehand define that axis, thenin this menu select in ”advanced options” this axis ; this axis now defines a new referential andselecting the option ”Normal deformation along Z” will output the deformation along that axis.

35

(a) Create a sensor (b) Create a deformation result (c) Open a deformation result

Figure A.1: Solidworks explanations illustrations

Retrieve data

To obtain the deformations computed during the simulations, first select the deformation resultyou want (its name must be written in bold format), then right-click on it and select ”probe” (seefigure A.1c). You can now access the values (see figure A.2)

Figure A.2: Retrieve values from the points

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Surface measurement

With the explanations given above, the deformation value is taken at one point although eachgauge covers a certain surface. It is not possible with Solidworks to average the value on a surface,however, one can measure the values on several points covering each sensor. I did so on a fewgauges’ locations to test whether the information is different from the value in the middle of thegauges. In order to do that, I created extrusions the size of the gauges and very thin (< 0.001mmin order not to disturb the simulations). Here are the results (figure A.3):

(a) Points measured (b) Points values

(c) Points measured (Ex 2) (d) Points values (Ex 2)

Minimum value Maximum Value Average Value Middle point value ErrorlEx 1 -2.61E-4 -1.57E-4 -2.11E-4 -2.17E-4 < 3%Ex 2 -1.16E-4 -1.05E-4 –1.10E-4 -1.16E-4 < 6%

(e) Point values comparison

Figure A.3: Several points measured : illustrations

Given the precision we can achieve on the placement of the gauges, the error due to a little offsetin the placement will be much more important than the one due to the method of measure withSolidworks. The method used here for comparison is available we want to improve the precision ofthe simulations measures.

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Appendix B

Labview

The sensor measurements have been done using Labview with a National Instrument 6008 ”acquir-ing” device. It enables to measure several signals simultaneously and to record them. Moreover,we can manually define an offset to get rid of the deviation caused by the unprecise resistor values.

B.1 About acquisition in Labview: differential and RSE modes

There are several acquisition modes in labview, here are the two main ones. Information comesfrom [13](available on the report CD).Use differential mode when:

• The input signal is low level (less than 1 V).

• The leads connecting the signal to the device are greater than 3 m (10 ft).

• The input signal requires a separate ground-reference point or return signal.

• The signal leads travel through noisy environments.

• Note: requires 2 channels per signal.

Use Referenced Single-Ended mode when:

• The input signal is high level (greater than 1 V).

• The leads connecting the signal to the device are less than 10 ft (3 m).

• The input signal is floating.

Use Non-Referenced Single-Ended mode when:

• The input signal is high level (greater than 1 V).

• The leads connecting the signal to the device are less than 10 ft (3 m).

• The input signal is referenced to ground

We should here use the differential mode because of the noise as well as the low level of our signal.

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Appendix C

Electronics

Besides the Labview setup used to characterize the system, I have briefly tried to use the electronicsdesigned by Rico Mockel in order to try to use it for the characterization. Since I did not spenda lot of time on this issue, here are just a few informations about what seems to be working andwhat is not :

Communication between the board and the computers works, I wrote a new command ”com-mand values” in command.c that switches a led and sends the SPI commands to the ADC in orderto retrieve its data. This enabled me to trigger the communication with the ADC in order to checkits functioning. I recorded each channel necessary for the corresponding SPI communication inFigure C.1 and Figure C.2:It can be seen that all channels work fine and the ADC is responding. This first byte sent to the

Figure C.1: Blue : Clock (SCK), Green : Chip Select (CS), Orange : Data output (SDO), Red :Data in (SDI).

ADC ”01011100” is the command to set the ADC in ”continuous reading mode”, which enablesto retrieve data later without sending any special command, just by sending any bytes with ”Chip

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Select” at low level.

I did not have the time to finish the software to use this board for the characterization. TheMPLAB files and c code corresponding to the dsPic’s software as well as the draft for the Matlabcode to retrieve the data on the computer are included on the report CD.

Figure C.2: Setup to make measurements on the electronics board.

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