Self Study - II Semester

Humanoid Robots

Stability Analysis and Robustness of Robot Motion

Megha Rajasekhar

Need for Humanoid Robots• Human-like motion and kinetics help robots work in an

environment suited for humans .

• Humanoid construction helps interaction with humans and learn new tasks from these interactions.

• Human appearance makes robots more acceptable and allows generation of speech and gestures.

Components of a robotSensors• Proprioceptive SensorsProprioception is ability to vary movements in immediate response to incoming information regarding

external enivronment.Gyroscope sensors – specify direction of the robot by measuring

angles of rotation along x, y, z axes, called yaw, pitch and roll.Accelerometers - measure motion gradient in x, y, z axes.Force sensors – measure force and moment applied on it from

different directions. Help in locomotion, gripping, etc.

Components of a robotSensors• Exteroceptive sensorsExteroception is sensing things about the environment.Tactile sensors – usually present as an array of sensors. Mimics the

function of touch receptors in humans. Detects contact and measures contact forces.

Range sensors – measure distance between robot and obstacles. Help in robot navigation and obstacle avoidance.

Vision sensors – detect electromagnetic radiation.

Components of a robotActuatorsActuators are the motors responsible for motion in the robot.Each human-like part of the robot is called a sub-system. Smaller

components of a sub-system are modules. Combinations of actuators acting as muscles and joints make up modules.

Actuators can be either electric, pneumatic, hydraulic, piezoelectric or ultrasonic.

Components of a robotPlanning and ControlPlanning and control deals with development of algorithms and

strategies which control locomotion in a robot according to required task while accommodating constraints of robot motion.

It consists of breaking down a particular task into smaller discrete movements using a motion planning algorithm. In the process, obstacles are avoided, robot does not lose balance and it moves within it constraints.

Stability Analysis of Robot MotionHumanoid robots are expected to have bipedal motion. This

makes balancing the robot difficult. Several theories have been introduced to make robot motion more stable and help the robot calculate which paths to take to prevent loss of balance.

Zero Moment PointThe ZMP is a point on the ground where the feet of robot do not

produce an horizontal moment so that there is no sliding.Passive DynamicsThis refers to movement which isn’t supported by any power

sources. Motion is sustained due to the effects of gravity and inertia.

Stability Analysis of Robot MotionCapture Points and Capture RegionsCapture points are points on a plane

terrain where a robot can place it Centre of Pressure so that it comes to a complete rest. It can calculate the position of a Capture region to prevent falling if bumps into an obstacle.

Dynamic BalancingBalancing a dynamic body by offsetting centrifugal moments caused by it. This is not very efficient as it must be operated at slower speeds.

RobustnessRobustness refers to adaptability in unpredictable situations.Robust control is a method which deals uncertain situations. Robust motion of a robot, therefore, refers to the ability of the

robot to move efficiently in an area with unpredictable obstacles and react appropriately towards them.

Civil ComponentZero Moment Point The ZMP is defined as the point on the ground about which the sum of the horizontal moments of all the active forces equals zero. If the ZMP is within the support polygon i.e. polygon of all contact points between the feet and the ground, a bipedal robot is dynamically stable.•Mechanism of robot above the foot can be replaced by force FA and moment MA.

• The ground reaction force acts at point P. The force R and moment M have three components R(Rx, Ry, Rz) and M(Mx, My, Mz).• Friction acts on the foot. Hence horizontal components Rx and Ry represent frictional forces and balance horizontal component of FA.

Civil ComponentZero Moment Point• Friction acts on the foot. Hence horizontal components Rx and Ry

represent frictional forces and balance horizontal component of FA.• Rz balances the vertical component of force FA.• Mz represents the moment of frictional forces and balances the vertical component of MA.

Civil ComponentZero Moment Point• To balance the horizontal components of M, Rz must be shifted such that it causes a moment in the opposite direction.• Thus R gets shifted within the support polygon such that moment due to Rz = horizontal component of M.• As all moments are balanced horizontal moments Mx and My will not exist. The point P where R now acts is ZMP.• P cannot lie outside the support polygon. If horizontal components are not zero, P lies on the edge of support polygon causing robot to fall.

Physics ComponentCapture Points and Capture Region• A Capture Point is a point on the ground in which the Center of Pressurecan be placed in order to stop a robot. The Capture Region is the set of Capture Points.• Based on an inverted pendulum model whose equations can be solved to find capture point.• Linear momentum is directly coupled to the speed of the robot, so by controlling the angular moment andstability can be controlled• Helpful for push recovery

Physics ComponentPassive DynamicsPassive dynamics refers to movement which isn’t supported by any power sources.The equation of motion for a passive dynamic walker is given by

H(θ) ¨θ + C(θ, ˙θ) ˙θ + G(θ) = 0.A simulation of these dynamics produces a damped oscillation that will eventually result in the robot standing.For a given mass and moment of inertia, we can change the frequency i.e. speed of walking by changing the radius of the foot.

Math ComponentLimit Cycles• A limit cycle is a closed trajectory in phase

space having the property that at least one other trajectory spirals into it either as time approaches infinity.

• Each trajectory represents a path taken during oscillations.

• The closed trajectory describes perfect periodic behavior of the system. Any small disturbance from this closed trajectory causes the system to return to it, making the system stick to the limit cycle.

Math ComponentLimit Cycles• A Poincare return map can be used to investigate periodic

motions of a dynamical system. Limit cycle and other unstable trajectories can be plotted on it.

• By plotting Poincare map of oscillations stablity of the system can be determined.

Electrical ComponentSensors• Force sensors – also used in ZMP robots to find ground

reaction forces. Piezoelectric sensors which generate current proportional to force or pressure applied.

• Slip sensors – Used to calculated required frictional force in ZMP robots. Measures the acceleration of centre of mass.

• Torque sensors - Device for measuring and recording the torque on a rotating system. Consist of strain gauge which measure change in dimensions by measuring change in resistance.

Electrical ComponentActuatorsActuators are the motors responsible for motion in the robot.• Hydraulic - Have a very rigid behavior and operate well at low speed

and high load applications.• Electric - Better suited for high speed and low load applications• Piezoelectric - Generate a small movement with a high force. They

can be used for ultra-precise positioning.• Ultrasonic - Designed to produce movements in a micrometer order

at ultrasonic frequencies • Pneumatic - Operate on the basis of gas compressibility. Used for low

speed and low/medium load applications.

Thank You