PIVO: Probabilistic Inverse Velocity Obstacle for Navigation under Uncertainty In this paper, we present an algorithmic framework which computes the collisionfree velocities for the robot in a human shared dynamic and uncertain environment. We extend the concept of Inverse Velocity Obstacle (IVO) to a probabilistic variant to handle the state estimation and motion uncertainties that arise due to the other participants of the environment. These uncertainties are modeled as nonparametric probability distributions. In our PIVO: Probabilistic Inverse Velocity Obstacle, we propose the collisionfree navigation as an optimization problem by reformulating the velocity conditions of IVO as chance constraints that takes the uncertainty into account. The space of collisionfree velocities that result from the presented optimization scheme are associated to a confidence measure as a specified probability. We demonstrate the efficacy of our PIVO through numerical simulations and demonstrating its ability to generate safe trajectories under highly uncertain environments.

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.