Adaptive Gait Modeling and Optimization for Principally Kinematic Systems

TL;DR

The paper addresses robust locomotion under unanticipated environments by coupling adaptive system identification with geometric mechanics to produce real-time, locally valid motion models for principally kinematic systems. It introduces online Recursive Least Squares filters operating in phase space, paired with a real-time confidence metric, and an SDE-based perturbation generator to gather diverse data around nominal gaits. The method enables rapid in-situ gait refinement, achieving up to a 10× improvement in sample efficiency for the nine-link Purcell swimmer and demonstrating fast adaptation to substrate changes. The approach offers practical impact for in-field gait optimization, injury recovery, and terrain adaptation in soft, nano, medical, and bio-hybrid robots, where simulations alone are insufficient.

Abstract

Robotic adaptation to unanticipated operating conditions is crucial to achieving persistence and robustness in complex real world settings. For a wide range of cutting-edge robotic systems, such as micro- and nano-scale robots, soft robots, medical robots, and bio-hybrid robots, it is infeasible to anticipate the operating environment a priori due to complexities that arise from numerous factors including imprecision in manufacturing, chemo-mechanical forces, and poorly understood contact mechanics. Drawing inspiration from data-driven modeling, geometric mechanics (or gauge theory), and adaptive control, we employ an adaptive system identification framework and demonstrate its efficacy in enhancing the performance of principally kinematic locomotors (those governed by Rayleigh dissipation or zero momentum conservation). We showcase the capability of the adaptive model to efficiently accommodate varying terrains and iteratively modified behaviors within a behavior optimization framework. This provides both the ability to improve fundamental behaviors and perform motion tracking to precision. Notably, we are capable of optimizing the gaits of the Purcell swimmer using approximately 10 cycles per link, which for the nine-link Purcell swimmer provides a factor of ten improvement in optimization speed over the state of the art. Beyond simply a computational speed up, this ten-fold improvement may enable this method to be successfully deployed for in-situ behavior refinement, injury recovery, and terrain adaptation, particularly in domains where simulations provide poor guides for the real world.

Figures (4)

• Figure 1: The Purcell swimmer incrementally experiences more stochastically perturbed cycles in a new operating environment. Model metrics of the batch model (green) and adaptive model (red) are evaluated for their predictive performance at that point in the experiment on a hold-out test set of 40 cycles (for 100 pairs of training and testing trials). The model metrics for both methods are shown in boxplots where each box corresponds to $5,25,50,75,95$ percentiles of a model trained with the first $n \in [5,10,15,20,25,30,35,40]$ cycles of data experienced.
• Figure 2: The predictive quality of the adaptive models (blue, $\lambda_{RLS}=0.99$, and orange, ($\lambda_{RLS}=0.7$)) and batch model (green) are compared throughout environmental changes experienced by the Purcell swimmer. Each model is trained with 40 cycles of data collected in 'Env 1'. In this test, the system is unknowingly exposed to two other environments, where each environment consists of 40 cycles of data. We changed the drag coefficient ratio experienced on the links for the environment changes, where this ratio is $2.0, 3.0, 4.0$, respectively for environments 1, 2, and 3. The batch model (which is never recomputed during the trial) has constant large predictive errors on new substrates. The adaptive model is refined each time a sample is collected and can adapt to the new environments relatively quickly. We note that the forgetful model has a faster adaptation rate but achieves lower, less stable prediction quality throughout the trial.
• Figure 3: Above we lay out an optimization architecture for behavior refinement. (Top Level) The optimization will attempt to improve behaviors only when it receives a high enough prediction confidence from the adaptive model. (Middle Level) The adaptive model recursively updates from real-world interactions, also producing an estimate of its model confidence in real-time (quantified as $\Gamma$). (Bottom Level) A nominal gait, parameterized as p, is given to the Command Gen module, which generates stochastic perturbations around the nominal gait.
• Figure 4: Gait optimization results for Purcell swimmers using the adaptive model optimizer. (A) The three-link Purcell swimmer can refine its gaits from grey to black, optimizing in 40 cycles of experience. 50 trials of the (B) three-link Purcell, (C) five-link Purcell swimmer, and (D) nine-link Purcell swimmer optimization for extremality, with current progress plotted throughout the experience of the trial. Relative performance in displacement per cycle is shown compared to the initial behavior, with [5,50,95] percentiles of performance plotted throughout and [5,25,50,75,95] percentile boxplots provided for the end of the run. The width of the boxplot indicates the number of cycles executed before reaching the final performance value.