Optimally Convergent Trajectories for Navigation

Abstract

This paper investigates optimization-based planning methods for generating trajectories which are robust to state uncertainty in undersensed and underactuated systems. Specifically, these methods are applied to an undersensed robotic hill climbing system. In previous work, divergence metrics based on contraction analysis were used to quantify robustness of a trajectory to state uncertainty in conjunction with a kinodynamic RRT planner to guide the planner towards more convergent directions. Resulting trajectories were sub-optimal or needed to be smoothed prior to implementation. This work proposes an optimization framework to plan optimally robust and smooth trajectories which can also be readily implemented on the robotic hill climbing problem. A new hill climbing controller is also presented which can guarantee for the first time the strongest result of contraction analysis, global asymptotic convergence, where possible. Trajectories created using the new trajectory optimization framework and hill controller are shown to be smoother and more robust than previous methods as well as an asymptotically optimal versions of previous methods.