Optimal Steering of Stochastic Mobile Robots that Undergo Collisions with their Environment The paper introduces a statefeedback closedloop control approach with integrated collision exploitation. We represent the systemxe2x80x99s kinematics in the form of a driftdiffusion 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 omnidirectional collisionresilient wheeled robot.

ContinuousTime Collision Avoidance for Trajectory Optimization in Dynamic Environments Common formulations to consider collision avoidance in trajectory optimization often use either preprocessed environments or only check and penalize collisions at discrete time steps. However, when only checking at discrete states, this requires either large margins that prevent manipulation close to obstacles or dense time discretization increasing the dimensionality of the optimization problem in complex environments. Nonetheless, collisions may still occur in the interpolationtransition between two valid states or in environments with thin obstacles. In this work, we introduce a computationally inexpensive continuoustime collision avoidance term in presence of static and moving obstacles. Our penalty is based on conservative advancement and harmonic potential fields and can be used as either a cost or constraint in offtheshelf nonlinear programming solvers. Due to the use of conservative advancement (collision checks) rather than distance computations, our method outperforms discrete collision avoidance based on signed distance constraints resulting in smooth motions with continuoustime safety while planning in discrete time. We evaluate our proposed continuous collision avoidance on scenarios including manipulation of moving targets, locomanipulation on mobile robots, manipulation trajectories for humanoids, and quadrotor path planning and compare penalty terms based on harmonic potential fields with ones derived from contact normals.