Set-Valued Rigid Body Dynamics for Simultaneous, Inelastic, Frictional Impacts
This addresses a critical issue in robotics simulation for model-based controllers and learned policies, improving accuracy when transferring from simulation to real robots.
The paper tackles the problem of accurately simulating simultaneous, inelastic, frictional impacts in robotics, which is crucial for tasks like manipulation and locomotion where outcomes are sensitive to impact order. It introduces a set-valued rigid-body model that generates a broad set of physically reasonable outcomes, with an algorithm providing tight approximations and probabilistic guarantees.
Robotic manipulation and locomotion often entail nearly-simultaneous collisions -- such as heel and toe strikes during a foot step -- with outcomes that are extremely sensitive to the order in which impacts occur. Robotic simulators commonly lack the accuracy to predict this ordering, and instead pick one with a heuristic. This discrepancy degrades performance when model-based controllers and policies learned in simulation are placed on a real robot. We reconcile this issue with a set-valued rigid-body model which generates a broad set of physically reasonable outcomes of simultaneous frictional impacts. We first extend Routh's impact model to multiple impacts by reformulating it as a differential inclusion (DI), and show that any solution will resolve all impacts in finite time. By considering time as a state, we embed this model into another DI which captures the continuous-time evolution of rigid body dynamics, and guarantee existence of solutions. We finally cast simulation of simultaneous impacts as a linear complementarity problem (LCP), and develop an algorithm for tight approximation of the post-impact velocity set with probabilistic guarantees. We demonstrate our approach on several examples drawn from manipulation and legged locomotion.