Real-Time-Feasible Collision-Free Motion Planning For Ellipsoidal Objects

Online planning of collision-free trajectories is a fundamental task for robotics and self-driving car applications. This paper revisits collision avoidance between ellipsoidal objects using differentiable constraints. Two ellipsoids do not overlap if and only if the endpoint of the vector between the center points of the ellipsoids does not lie in the interior of the Minkowski sum of the ellipsoids. This condition is formulated using a parametric over-approximation of the Minkowski sum, which can be made tight in any given direction. The resulting collision avoidance constraint is included in an optimal control problem (OCP) and evaluated in comparison to the separating-hyperplane approach. Not only do we observe that the Minkowski-sum formulation is computationally more efficient in our experiments, but also that using pre-determined over-approximation parameters based on warm-start trajectories leads to a very limited increase in suboptimality. This gives rise to a novel real-time scheme for collision-free motion planning with model predictive control (MPC). Both the real-time feasibility and the effectiveness of the constraint formulation are demonstrated in challenging real-world experiments.

Stochastic Model Predictive Control with Optimal Linear Feedback for Mobile Robots in Dynamic Environments

Robot navigation around humans can be a challenging problem since human movements are hard to predict. Stochastic model predictive control (MPC) can account for such uncertainties and approximately bound the probability of a collision to take place. In this paper, to counteract the rapidly growing human motion uncertainty over time, we incorporate state feedback in the stochastic MPC. This allows the robot to more closely track reference trajectories. To this end the feedback policy is left as a degree of freedom in the optimal control problem. The stochastic MPC with feedback is validated in simulation experiments and is compared against nominal MPC and stochastic MPC without feedback. The added computation time can be limited by reducing the number of additional variables for the feedback law with a small compromise in control performance.