Chance-Constrained Rollover-Free Manipulation Planning with Uncertain Payload Mass

This paper presents a chance-constrained rollover-free manipulation planning method for robotic arms under payload mass uncertainty. The corresponding motion planning problem is stated as a chance-constrained nonlinear optimal control problem (NOCP) subject to kinematics and rollover stability constraints. The latter takes the form of a chance constraint that ensures a certain probability of the robot maintaining dynamic rollover stability in the presence of payload mass uncertainty. To achieve efficient solutions to the NOCP, a novel geometric bound for the stability region is derived. The novel bound is then utilized to modify the rollover-stability constraint. To showcase its benefit, comparisons between the proposed bound of probabilistic rollover stability measure and the naive noise model are provided through statistical analysis. The formulation's practicality is demonstrated through experiments with a Kinova Jaco 2 arm mounted on a free-to-roll platform. Results demonstrate greater robustness of the robot's motion plan to mass uncertainty and computational efficiency of the trajectory generation.