ECE594d_Lecture_1_Jan4

ECE594d_Lecture_1_Jan4 - Robot Locomotion ECE594d Prof...

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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 state-space notation...) Underactuated vs Fully Actuated Consider Newtonian, 2nd-order 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, 2nd-order 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 (state-space 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 n-1 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 fully-actuated robotics... "Cancel out" natural (non-linear) system dynamics Standard manipulator eqn: && & Hq + Cq + G = Bu & m&& + bx + kx = f x (Compare above to eq at left) Traditional "trick" for fully-actuated robotics... "Cancel out" natural (non-linear) 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 fully-actuated robotics... "Cancel out" natural (non-linear) 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 fully-actuated robot (34 servo motors) Use high-gain 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 toe-off at each step. Leg = 1m, 0.005m drop in .34m step, or about 1 Introduction Kinodynamic Planning Quantifying metastability Optimizing Control ZMP-based humanoids: complexity is good and bad fully-actuated, sequential kinodynamic planning Canny, Donald, Reif and Xavier, 1988. highly choreographed Introduction Kinodynamic Planning Quantifying metastability Optimizing Control ZMP-based humanoids: complexity is good and bad fully-actuated, 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 : rapidly-exploring, randomized trees LaValle and Kuffner, 2000. HPR-3 (Kawada / AIST) Vukobratovic, 1975. Fully-actuated regime. Zero-moment point (ZMP) planning e.g., Preview Control of ZMP Kajita, 2003. Introduction Kinodynamic Planning Quantifying metastability Optimizing Control Rugged-terrain 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.

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