Optimal Steering of Stochastic Mobile Robots that Undergo Collisions with their Environment

The paper introduces a state-feedback closed-loop control approach with integrated collision exploitation. We represent the system's kinematics in the form of a drift-diffusion stochastic differential equation, and follow a stochastic switching framework to model the transition between states of free motion and in collision with the environment. We formulate an optimal steering problem and compute the control input related to state feedback. Collisions are found beneficial in terms of increasing task success probability when steering a robot from an initial to a target spatial distribution. In certain cases, collisions may help reduce the control energy for the task when compared to optimal steering with collision avoidance. We provide a mathematical basis to explain this finding, perform several parametric analyses in simulation to validate the theoretical analysis, and conduct realistic physics simulations to quantify the impact of realistic constraints (bounded control input, physical impact of collision, and friction) on control energy and success probability. Further, we validate the proposed approach experimentally with an omni-directional collision-resilient wheeled robot.