Convex risk-bounded continuous-time trajectory planning and tube design in uncertain nonconvex environments

In this paper, we address the trajectory planning problem in uncertain nonconvex static and dynamic environments that contain obstacles with probabilistic location, size, geometry. To problem, provide a risk-bounded method looks for continuous-time trajectories guaranteed bounded risk over time horizon. Risk is defined as probability of collision obstacles. Existing approaches to problems either are limited Gaussian uncertainties convex or rely on sampling-based methods need uncertainty samples discretization. leverage notion contours transform into deterministic optimization problem. set all points environment risk. The obtained is, general, nonlinear time-varying optimization. We based sum-of-squares efficiently solve obtain without provided approach deals arbitrary (and known) uncertainties, nonlinear, obstacles, suitable online problems. addition, build max-sized tube respect its parameterization along so any state inside have