Stable Gait Transitions While Changing Speeds on a RHex-like Platform

1. Stable Gait Transitions While Changing Speeds on a RHex-like Platform Dalton Banks and Matthew Hale March 1, 2011 ESE 313

2. Desired Behavior • In a real-world application of robots, it is logical that a robot will be commanded to move at different speeds • We want robots to make stable transitions between speeds • Implicit constraint: robots should move at (roughly) optimal efficiency • So we want a robot to change its entire gait as it changes its leg speed parameter so that the robot moves efficiently at each speed

3. Present Unavailability • Past and present research in gait transitions is largely motivated by changing terrain rather than changing speed [1] • For example, RHex robots often use one set of gait parameters for a terrain and then change speeds simply by scaling the leg rotation frequency • The issue of changing gaits while changing speeds is un(der)explored in the literature 1. G. Clark Haynes and Alfred A. Rizzi, "Gaits and Gait Transitions for Legged Robots", Proceedings of the 2006 IEEE International Conference on Robotics and Automation

4. Desirability of Bioinspiration • It is believed that animals transition between gaits as they change speeds in order to minimize the energetic cost of locomotion [1] • In certain speed regimes, energy-optimized gaits form a “kinematic continuum” [2] • We believe that stable speed transitions can be made along a continuum of efficient gaits http://visual.merriam-webster.com/animal-kingdom/ungulate-mammals/horse/gaits_1.php 1. Wickler SJ, Hoyt DF, Cogger EA, Myers G., "The energetics of the trot-gallop transition", Journal of Experimental Biology, May 2003 2. Robilliard JJ, Pfau T, Wilson AM., "Gait characterisation and classification in horses", Journal of Experimental Biology, January 2007

5. The Idea • First, we will optimize robot gaits for efficiency over a range of leg speeds using the Nelder-Mead descent algorithm [1] • Then, we will interpolate these data to generate a continuous path through gaitspace • Attempt to transition among commanded leg speeds along this path and assess stability 1. Joel D. Weingarten, Gabriel A. D. Lopes, Martin Buehler, Richard E. Groff, Daniel E. Koditschek, "Automated Gait Adaptation for Legged Robots", IEEE International Conference on Robotics Automation (ICRA), April 2004

6. Refutability • Binary conception of stability: does the robot body hit the ground? • Another possibility: a single discontinuity in gaitspace requiring a gait transition not produced by the aforementioned interpolation • Animals exhibit a discontinuous transition between “walking” and “running” gaits; this could be a result of parallel local gait minima for energy expenditure [1] • Not intuitive whether this will occur in robots or not Here, parallel local minima produce a discontinuous minimum path 1. RobilliardJJ, Pfau T, Wilson AM., "Gait characterisation and classification in horses", Journal of Experimental Biology, January 2007

7. Necessary Means • A robot which is able to run many different gaits defined by different parameter sets (which in turn define different Buehler clocks) • A cost function which can normalize the cost of a gait over different speeds (we intend to use specific resistance as it is used by Weingarten et al. to optimize gaits). • A tuning algorithm which coordinates changing the robot's gait parameters with values of the cost function in order to find gait parameters which minimize costs. • A means of storing the gaits generated by the tuning algorithm • A means of mathematically interpolating the gaits stored in order to produce a continuum of efficient gaits • A suitably long stretch of (roughly) homogeneous terrain on which to test the gaits and their transitions • The existing, naive set of gaits to serve as a comparison