Unformatted text preview: Robot Locomotion
ECE594d Prof. Katie Byl Robot Locomotion
ECE594d Prof. Katie Byl "Bill" 1. Locomotion overview
As roboticists, animals give great inspiration. But, locomotion involves challenges: Underactuation (by nature) Controllability (to perform well) Today: We'll look at some robot examples and discuss underactuation and controllability. ? Introduction to Underactuated Robotics
Katie Byl Introduction to Underactuated Robotics
Katie Byl aka... Agile robots: How? Goals for today: Define underactuation Define controllability Look at different legged robots Do they exploit their (passive) dynamics? Are they agile? (Do they recover well?) Get you to agree (perhaps): Control of underactuated robotics is essential for your own goals in robotics! Goals for today: Define underactuation Define controllability Look at different legged robots Do they exploit their (passive) dynamics? Are they agile? (Do they recover well?) Get you to agree (perhaps): Control of underactuated robotics is essential for your own goals in robotics! Quick note on notation... I use q for degrees of freedom (DOF) (e.g., joint angles (not vel.) in a robot): && & & q = f1 (q, q, t ) + f 2 (q, q, t )u (q matches the robot manipulator eqns...) ...and x for states (e.g., position and vel.) & x = Ax + Bu
(x matches statespace notation...) Underactuated vs Fully Actuated
Consider Newtonian, 2ndorder dynamics: F = ma && & q = f ( q, q, t , u ) More generally, acceleration is: Forward dynamics of robot are affine with torque: && & & q = f1 (q, q, t ) + f 2 (q, q, t )u Underactuated vs Fully Actuated
Consider Newtonian, 2ndorder dynamics: F = ma && & q = f ( q, q, t , u ) More generally, acceleration is: Forward dynamics of robot are affine with torque: && & & q = f1 (q, q, t ) + f 2 (q, q, t )u
Definition of fully actuated: Instantaneous acceleration possible in any, arbitrary degree of freedom Fully actuated: Underactuated: & rank[ f 2 (q, q, t )] = dim[q ] & rank[ f 2 (q, q, t )] < dim[q ] Controllability In words, can you take the system from its initial condition to a desired, final state using some set of actuator inputs (over a finite time interval)? For a linear system (statespace format): & x = Ax + Bu
R = [B AB (where n = dim(X) = # of states) R is the "controllability" matrix: A B L A B]
Controllable Not controllable 2 n1 rank(R) = n rank(R) < n Locomotion is hard
Underactuation examples feet push but cannot pull Flying and swimming ... even (often) manipulation [not always a rigid grasp...] Why give a machine legs, anyway? Traditional "trick" for fullyactuated robotics...
"Cancel out" natural (nonlinear) system dynamics
Standard manipulator eqn: && & Hq + Cq + G = Bu & m&& + bx + kx = f x
(Compare above to eq at left) Traditional "trick" for fullyactuated robotics...
"Cancel out" natural (nonlinear) system dynamics
Standard manipulator eqn: && & Hq + Cq + G = Bu & m&& + bx + kx = f x
(Compare above to eq at left) Inertia matrix H = H (q )
Centrifugal/coriolis Gravity G = G (q) & C = C(q, q ) Traditional "trick" for fullyactuated robotics...
"Cancel out" natural (nonlinear) system dynamics
Standard manipulator eqn: && & Hq + Cq + G = Bu
&& & u = B 1 (Hq + Cq + G ) & m&& + bx + kx = f x
(Compare above to eq at left) invert matrix B Turn nonlinear dynamics into linear dynamics We have lots of tools to control linear systems! Only works for VERY good model of dynamics... Only works if fully actuated Example: Honda's ASIMO Motivation: Can't we do better?! [Part 1 of 2] ASIMO strategy: Mimic a fullyactuated robot (34 servo motors) Use highgain feedback therefore, high torque required (short battery life) "Cancels out" natural dynamics Disadvantages: 20x cost of transport (energy use) of human walking Control limited to a small part of state space Must go slowly Cannot deal with much uncertainty in terrain Motivation: Can't we do better?! [Part 1 of 2] Motivation: Can't we do better?! [Part 2 of 2] Airplanes A4 Skyhawk: 720 deg/sec max roll Blackbird jet: 2000 mph = 32 body lengths / sec Birds Barn swallow: >5000 deg/sec max roll Pigeon: 50 mph = 75 body lengths / sec Birds and Insects adapt almost instantly to gusts, etc. Motivation: Can't we do better?! [Part 2 of 2] Airplanes A4 Skyhawk: 720 deg/sec max roll Blackbird jet: 2000 mph = 32 body lengths / sec Birds Barn swallow: >5000 deg/sec max roll Pigeon: 50 mph = 75 body lengths / sec Birds and Insects adapt almost instantly to gusts, etc. General approach for underactuated control:
1. Must reason about the future (path planning...) 2. Exploit coupling of natural dynamics (not cancel!) Passive dynamic walking: efficient but fragile
Purely passive (left) Actuated walker (right) Collins, Wisse and Ruina, 2001. Hobbelen, 2008. Actuation: impulsive toeoff at each step.
Leg = 1m, 0.005m drop in .34m step, or about 1 Introduction Kinodynamic Planning Quantifying metastability Optimizing Control ZMPbased humanoids: complexity is good and bad fullyactuated, sequential kinodynamic planning Canny, Donald, Reif and Xavier, 1988. highly choreographed Introduction Kinodynamic Planning Quantifying metastability Optimizing Control ZMPbased humanoids: complexity is good and bad fullyactuated, sequential kinodynamic planning Canny, Donald, Reif and Xavier, 1988. highly choreographed 1. find feasible kinematic poses 2. turn up speed (slower is safer) ASIMO (Honda) RRT : rapidlyexploring, randomized trees LaValle and Kuffner, 2000. HPR3 (Kawada / AIST) Vukobratovic, 1975. Fullyactuated regime. Zeromoment point (ZMP) planning e.g., Preview Control of ZMP Kajita, 2003. Introduction Kinodynamic Planning Quantifying metastability Optimizing Control Ruggedterrain robots: dynamically capable
RHex
Altendorfer, et al., 2001. Foothold selection not solved BigDog
Buehler, Playter, Raibert, 2005. Introduction Kinodynamic Planning Quantifying metastability Optimizing Control ...
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This note was uploaded on 12/29/2011 for the course ECE 594d taught by Professor Teel,a during the Fall '08 term at UCSB.
 Fall '08
 Teel,A

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