IIIT Hyderabad Publications |
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Towards Efficient Trajectory Optimization for Non-Holonomic RobotsAuthor: Mithun Babu Nallana Date: 2021-02-20 Report no: IIIT/TH/2021/12 Advisor:Madhava Krishna,Arun Kumar Singh AbstractAutonomous cars and fixed-wing aerial vehicles (FWV) have the so-called non-holonomic kinematics which non-linearly maps control input to states. As a result, trajectory optimization using such a motion model becomes highly non-linear and non-convex. In this work, we present two alternate methods to efficiently solve this trajectory optimization problem. The first approach is based on the path velocity decomposition paradigm. The optimization underlying this approach has a two layer structure wherein first, an appropriate path is computed for the vehicle followed by the computation of optimal forward velocity along it. A key feature of this approach is that it offloads most of the responsibility of collision avoidance to the velocity optimization layer for which computationally efficient formulations can be derived. In particular, we extend our previously developed concept of time scaled collision cone (TSCC) constraints and formulate the forward velocity optimization layer as a convex quadratic programming problem. In the second approach, we improve the computational tractability of the problem by reformulating trajectory optimization in terms of a set of bi-convex cost and constraint functions along with a non-linear penalty. The bi-convex part acts as a relaxation for the non-holonomic trajectory optimization while the residual of the penalty dictates how well its output obeys the non-holonomic behavior. We adopt an alternating minimization approach for solving the reformulated problem and show that it naturally leads to the replacement of the challenging non-linear penalty with a globally valid convex surrogate. Along with the common cost functions modeling goal-reaching, trajectory smoothness, etc., the proposed optimizer can also accommodate a class of non-linear costs for modeling goal-sets, while retaining the bi-convex structure. We perform validation of first approach on autonomous driving scenarios to compute lane change, overtaking and merging maneuvers among multiple dynamic obstacles. We later benchmark the second approach against those based on sequential quadratic programming (SQP) and interior-point methods on common examples from autonomous driving and FWV navigation and show that it produces solutions with similar cost as the former while significantly outperforming the latter. Furthermore, as compared to both SQP and interior-point optimizers, it achieves more than 20x reduction in computation time. Full thesis: pdf Centre for Robotics |
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