On the Effectiveness of Silly Walks as Initial Guesses for Optimal Legged Locomotion Problems

Trajectory optimization is a popular method of generating high-level plans for legged locomotion tasks, but convergence, and the quality of the solutions achieved, are dependent on the guess trajectory used to initialize the solver. Because the results are locally optimal at best, finding a good solution to a poorly-defined problem necessitates an unbiased initialization technique that facilitates broad exploration of the solution space over multiple attempts, but the problem is unlikely to solve at all if the guess is too far from feasible. In this paper, we attempt to navigate this trade-off between randomness and reliability using ‘silly walks': stochastically-generated gaits that satisfy some of the problem's feasibility constraints. We present a simple method of generating these motions, and compare the performance of this type of guess to various random sampling approaches. Through tests on a pendulum, hopper and quadrupedal model, we demonstrate that the silly walk offers a favourable balance of reliability, convergence time and solution diversity for legged locomotion problems.

I. Introduction

Trajectory optimization is a useful tool for motion planning in robotics. Because the forward and reverse kinematics are solved simultaneously using this method, it allows actions to be simulated without precise prior knowledge of how they should be performed. This is especially valuable in legged robotics applications: before a motion can be executed by a platform, it must be specified at least in terms of a footfall sequence or series of key postures. While slow, constant-speed locomotion might not require a more complicated strategy than “put one foot in front of the other”, there is no one, well-defined motion pattern associated with challenging tasks such as sharp turns or sudden stops.