Game-theoretic models are effective tools for modeling multi-agent interactions, especially when robots need to coordinate with humans. However, applying these models requires inferring their specifications from observed behaviors—a challenging task known as the inverse game problem. Existing inverse game approaches often struggle to account for behavioral uncertainty and measurement noise, and leverage both offline and online data. To address these limitations, we propose an inverse game method that integrates a generative trajectory model into a differentiable mixed-strategy game framework. By representing the mixed strategy with a conditional variational autoencoder (CVAE), our method can infer high-dimensional, multi-modal behavior distributions from noisy measurements while adapting in real-time to new observations. We extensively evaluate our method in a simulated navigation benchmark, where the observations are generated by an unknown game model. Despite the model mismatch, our method can infer Nash-optimal actions comparable to those of the ground-truth model and the oracle inverse game baseline, even in the presence of uncertain agent objectives and noisy measurements.

Ergodic search enables optimal exploration of an information distribution with guaranteed asymptotic coverage of the search space. However, current methods typically have exponential computational complexity and are limited to Euclidean space. We introduce a computationally efficient ergodic search method. Our contributions are two-fold as follows: First, we develop a kernel-based ergodic metric, generalizing it from Euclidean space to Lie groups. We prove this metric is consistent with the exact ergodic metric and ensures linear complexity. Second, we derive an iterative optimal control algorithm for trajectory optimization with the kernel metric. Numerical benchmarks show our method is two orders of magnitude faster than the state-of-the-art method. Finally, we demonstrate the proposed algorithm with a peg-in-hole insertion task. We formulate the problem as a coverage task in the space of SE(3) and use a 30-s-long human demonstration as the prior distribution for ergodic coverage. Ergodicity guarantees the asymptotic solution of the peg-in-hole problem so long as the solution resides within the prior information distribution, which is seen in the 100% success rate.

Gait generation for soft robots is challenging due to the nonlinear dynamics and high dimensional input spaces of soft actuators. Limitations in soft robotic control and perception force researchers to hand-craft open loop controllers for gait sequences, which is a non-trivial process. Moreover, short soft actuator lifespans and natural variations in actuator behavior limit machine learning techniques to settings that can be learned on the same time scales as robot deployment. Lastly, simulation is not always possible, due to heterogeneity and nonlinearity in soft robotic materials and their dynamics change due to wear. We present a sample-efficient, simulation free, method for self-generating soft robot gaits, using very minimal computation. This technique is demonstrated on a motorized soft robotic quadruped that walks using four legs constructed from 16 “handed shearing auxetic” (HSA) actuators. To manage the dimension of the search space, gaits are composed of two sequential sets of leg motions selected from 7 possible primitives. Pairs of primitives are executed on one leg at a time; we then select the best-performing pair to execute while moving on to subsequent legs. This method-which uses no simulation, sophisticated computation, or user input-consistently generates good translation and rotation gaits in as low as 4 minutes of hardware experimentation, outperforming hand-crafted gaits. This is the first demonstration of completely autonomous gait generation in a soft robot.