Gait Optimization for Legged Systems Through Mixed Distribution Cross-Entropy Optimization

TL;DR

CrEGOpt is proposed, a bi-level optimization method that combines traditional trajectory optimization with a black-box optimization scheme and can find solutions for biped, quadruped, and hexapod robots in under 10 seconds.

Abstract

Legged robotic systems can play an important role in real-world applications due to their superior load-bearing capabilities, enhanced autonomy, and effective navigation on uneven terrain. They offer an optimal trade-off between mobility and payload capacity, excelling in diverse environments while maintaining efficiency in transporting heavy loads. However, planning and optimizing gaits and gait sequences for these robots presents significant challenges due to the complexity of their dynamic motion and the numerous optimization variables involved. Traditional trajectory optimization methods address these challenges by formulating the problem as an optimization task, aiming to minimize cost functions, and to automatically discover contact sequences. Despite their structured approach, optimization-based methods face substantial difficulties, particularly because such formulations result in highly nonlinear and difficult to solve problems. To address these limitations, we propose CrEGOpt, a bi-level optimization method that combines traditional trajectory optimization with a black-box optimization scheme. CrEGOpt at the higher level employs the Mixed Distribution Cross-Entropy Method to optimize both the gait sequence and the phase durations, thus simplifying the lower level trajectory optimization problem. This approach allows for fast solutions of complex gait optimization problems. Extensive evaluation in simulated environments demonstrates that CrEGOpt can find solutions for biped, quadruped, and hexapod robots in under 10 seconds. This novel bi-level optimization scheme offers a promising direction for future research in automatic contact scheduling.

Figures (7)

• Figure 1: Overview of CrEGOpt method.
• Figure 2: Single rigid body dynamics model with contacts. Image from chatzilygeroudis2023evolving.
• Figure 3: Wall-time performance for experiments of Sec. \ref{['sec:simple_exps']}. Contact-Implicit Optimization always maxed out the maximum wall-time. The box plots show the median (black line) and the interquartile range (25th and 75th percentiles) over 20 replicates; the whiskers extend to the most extreme data points not considered outliers, and outliers are plotted individually.
• Figure 4: Scaling experiments (Sec. \ref{['sec:scaling']}, 20 replicates). CrEGOpt is able to keep similar wall-times performances ($\approx$7 s) even when increasing the number of legs. On the contrary, CrEGOpt without the proposed heuristic sampling fails to find effective gaits as the number of legs increases.
• Figure 5: CrEGOpt optimization results (Sec. \ref{['sec:go_exps']}). Solid lines are the median over 10 replicates and the shaded regions are the regions between the 25-th and 75-th percentiles.