  This paper introduces Chance Constrained Gaussian Process-Motion Planning
(CCGP-MP), a motion planning algorithm for robotic systems under motion and
state estimate uncertainties. The paper's key idea is to capture the variations
in the distance-to-collision measurements caused by the uncertainty in state
estimation techniques using a Gaussian Process (GP) model. We formulate the
planning problem as a chance constraint problem and propose a deterministic
constraint that uses the modeled distance function to verify the
chance-constraints. We apply Simplicial Homology Global Optimization (SHGO)
approach to find the global minimum of the deterministic constraint function
along the trajectory and use the minimum value to verify the
chance-constraints. Under this formulation, we can show that the optimization
function is smooth under certain conditions and that SHGO converges to the
global minimum. Therefore, CCGP-MP will always guarantee that all points on a
planned trajectory satisfy the given chance-constraints. The experiments in
this paper show that CCGP-MP can generate paths that reduce collisions and meet
optimality criteria under motion and state uncertainties. The implementation of
our robot models and path planning algorithm can be found on GitHub.
