  This paper introduces Probabilistic Chekov (p-Chekov), a chance-constrained
motion planning system that can be applied to high degree-of-freedom (DOF)
robots under motion uncertainty and imperfect state information. Given process
and observation noise models, it can find feasible trajectories which satisfy a
user-specified bound over the probability of collision. Leveraging our previous
work in deterministic motion planning which integrated trajectory optimization
into a sparse roadmap framework, p-Chekov shows superiority in its planning
speed for high-dimensional tasks. P-Chekov incorporates a linear-quadratic
Gaussian motion planning approach into the estimation of the robot state
probability distribution, applies quadrature theories to waypoint collision
risk estimation, and adapts risk allocation approaches to assign allowable
probabilities of failure among waypoints. Unlike other existing risk-aware
planners, p-Chekov can be applied to high-DOF robotic planning tasks without
the convexification of the environment. The experiment results in this paper
show that this p-Chekov system can effectively reduce collision risk and
satisfy user-specified chance constraints in typical real-world planning
scenarios for high-DOF robots.
