轨迹优化的凸策略：应用于多胞形轨迹问题
Convex strategies for trajectory optimisation: application to the Polytope Traversal Problem
摘要：
非线性轨迹优化（TO）方法需要良好的初始猜测来收敛到局部最优解。一个可行的猜测通常可以通过分配大量的时间来完成轨迹来获得。然而，对于不稳定的动态系统，如人形机器人，这种准静态假设并不总是成立。我们提出了一个保守的制定的TO问题，同时计算一个可行的路径和时间分配。该问题作为一个有效的凸优化问题，保证收敛到局部最优解。该方法的兴趣与遍历顺序的多面体序列的可行轨迹的计算说明。我们证明，在准静态解决方案是不允许的问题的情况下，我们的方法是能够找到一个可行的解决方案，在所有考虑的情况下，成功率高于$80 \%$，在不到10毫秒的问题涉及遍历少于5个多面体和少于1秒的问题，涉及20个多面体，从而证明了其可靠地向高级非线性求解器提供初始猜测的能力。
英文摘要：
Non-linear Trajectory Optimisation (TO) methods require good initial guesses to converge to a locally optimal solution. A feasible guess can often be obtained by allocating a large amount of time for the trajectory to complete. However for unstable dynamical systems such as humanoid robots, this quasi-static assumption does not always hold. We propose a conservative formulation of the TO problem that simultaneously computes a feasible path and its time allocation. The problem is solved as an efficient convex optimisation problem guaranteed to converge to a locally optimal solution. The interest of the approach is illustrated with the computation of feasible trajectories that traverse sequentially a sequence of polytopes. We demonstrate that on instances of the problem where the quasi static solutions are not admissible, our approach is able to find a feasible solution with a success rate above $80 \%$ in all the scenarios considered, in less than 10ms for problems involving traversing less than 5 polytopes and less than 1s for problems involving 20 polytopes, thus demonstrating its ability to reliably provide initial guesses to advanced non linear solvers.
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