用支持向量机线性化非凸避障约束，显著提升运动规划效率
Decoupling Collision Avoidance in and for Optimal Control using Least-Squares Support Vector Machines
- 将分离超平面定理转为分类问题，消除优化变量中的超平面
- 在复杂环境中使轨迹计算时间减少50%至90%
- 适合需高效避障的机器人路径规划场景
本文提出一种方法，将针对凸形体的可微但非凸避障约束线性化。通过重新利用分离超平面定理，将微分避障约束引入最优控制问题（OCP）。将该定理视为分类问题，从而从OCP中移除超平面作为优化变量，有效将非凸约束转化为线性约束。采用双层算法，在优化求解器迭代间计算超平面，并将其作为参数嵌入OCP。实验表明，该方法在复杂环境中有良好可扩展性，适用于多种运动规划方法。相比将超平面直接作为变量的先进方法，轨迹计算时间减少50%至90%。
原文摘要 · Abstract (English)
This paper details an approach to linearise differentiable but non-convex collision avoidance constraints tailored to convex shapes. It revisits introducing differential collision avoidance constraints for convex objects into an optimal control problem (OCP) using the separating hyperplane theorem. By framing this theorem as a classification problem, the hyperplanes are eliminated as optimisation variables from the OCP. This effectively transforms non-convex constraints into linear constraints. A bi-level algorithm computes the hyperplanes between the iterations of an optimisation solver and subsequently embeds them as parameters into the OCP. Experiments demonstrate the approach's favourable scalability towards cluttered environments and its applicability to various motion planning approaches. It decreases trajectory computation times between 50\% and 90\% compared to a state-of-the-art approach that directly includes the hyperplanes as variables in the optimal control problem.
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