发表机构
University of California at Berkeley（加州大学伯克利分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对具有状态约束和状态相关不确定输入的鲁棒轨迹规划问题，通过拉格朗日对偶推导有限非光滑约束，并提出两步凸启发式方法，在交会场景中计算时间较Gurobi减少13.8倍且保持鲁棒性。
AI 中文摘要
我们处理具有状态约束以及控制/状态相关的不确定输入和测量的鲁棒轨迹规划问题。不确定输入和测量满足具有秩2不定乘子的二次不等式；测量依赖于不确定状态实现和不确定输入。通过拉格朗日对偶，我们推导出有限非光滑约束，以保证状态约束的鲁棒满足，从而得到一种无需双层求解器即可处理的公式。我们针对所得非凸非光滑公式开发了一种两步凸启发式方法，使用凸松弛后接凸可行性恢复步骤。我们在具有状态相关导航不确定性的交会场景中测试了该两步方法，与商业求解器Gurobi相比，计算时间减少了13.8倍，同时保持了约束的鲁棒满足。
英文摘要
We address robust trajectory-planning problems with state constraints and with control/state-dependent uncertain inputs and measurements. Uncertain inputs and measurements satisfy quadratic inequalities with rank-2 indefinite multipliers; measurements depend on the uncertain-state realization and on the uncertain inputs. By means of Lagrangian duality, we derive finite nonsmooth constraints that guarantee robust satisfaction of the state constraints, yielding a formulation that can be addressed without bilevel solvers. We develop a two-step convex heuristic for the resulting nonconvex nonsmooth formulation, using a convex relaxation followed by a convex feasibility-recovery step. We test the two-step approach on a rendezvous scenario with state-dependent navigation uncertainty, and we reduce by a factor 13.8 the computation time with respect to the commercial solver Gurobi, while maintaining robust satisfaction of constraints.
