用凸优化实现多边形机器人避障，实时性与安全性兼得。
Iterative Convex Optimization with Control Barrier Functions for Obstacle Avoidance among Polytopes
- 通过精确最近点计算构造线性控制屏障函数，保证凸性。
- 在复杂迷宫中实现毫秒级求解，全程无碰撞。
- 适用于非线性系统、多机器人及三维场景，适合实时控制。
基于优化的控制与轨迹规划中，多边形机器人避障多边形障碍物是一个挑战性问题。现有方法常依赖光滑几何近似（如超球体或椭球体），虽具可微距离表达，但扭曲真实几何并限制可行集；另一些方法将精确多面体距离集成至非线性模型预测控制（MPC），导致非凸规划，难以满足实时性要求。本文通过精确多面体间最近点计算导出支撑超平面，构建线性离散时间控制屏障函数（DCBF）约束。提出一种新颖的迭代凸MPC-DCBF框架，通过局部线性化系统动态与机器人几何，确保每轮迭代的有限时域优化为凸问题。该方法降低计算复杂度，支持安全关键控制与轨迹规划的快速在线实现，适用于多机器人及三维环境。数值实验表明，在复杂迷宫场景中可实现毫秒级求解的无碰撞导航。
原文摘要 · Abstract (English)
Obstacle avoidance of polytopic obstacles by polytopic robots is a challenging problem in optimization-based control and trajectory planning. Many existing methods rely on smooth geometric approximations, such as hyperspheres or ellipsoids, which allow differentiable distance expressions but distort the true geometry and restrict the feasible set. Other approaches integrate exact polytope distances into nonlinear model predictive control (MPC), resulting in nonconvex programs that limit real-time performance. In this paper, we construct linear discrete-time control barrier function (DCBF) constraints by deriving supporting hyperplanes from exact closest-point computations between convex polytopes. We then propose a novel iterative convex MPC-DCBF framework, where local linearization of system dynamics and robot geometry ensures convexity of the finite-horizon optimization at each iteration. The resulting formulation reduces computational complexity and enables fast online implementation for safety-critical control and trajectory planning of general nonlinear dynamics. The framework extends to multi-robot and three-dimensional environments. Numerical experiments demonstrate collision-free navigation in cluttered maze scenarios with millisecond-level solve times.
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