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

Chance-Constrained Motion Planning using Modeled Distance-to-Collision Functions