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.Â

In this paper, a computationally efficient chance-constrained rollover-free motion planning method is presented. Specifically, the method is developed to plan motions for reconfigurable vehicles with the knowledge of a 3-D terrain model that has limited accuracy. The overall motion planning problem is formulated as a nonlinear optimal control problem (NOCP) that employs a constraint in the form of a bound on the probability of rollover under terrain-induced vehicle orientation uncertainty. To increase the computational efficiency of the NOCP, a geometric interpretation of the chance constraint is derived based on the characteristics of SO(3), the 3-D rotation group. Monte Carlo simulations are provided to demonstrate the usefulness of the geometric interpretation through comparisons with other methods. Experimental data gathered from driving a mobile robot through real forests are also used to validate the proposed model. Finally, path and trajectory generation results obtained with the proposed planning method for a feller-buncher machine traversing through uncertain 3-D terrain are presented to showcase the method’s overall performance and efficiency.