Obstacle avoidance between polytopes is a challenging topic for optimal control and optimization-based trajectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simplification of system dynamics, or through model predictive control with dual variables using distance constraints, requiring long horizons for obstacle avoidance. In either case, the solution can only be applied as an offline planning algorithm. In this paper, we exploit the property that a smaller horizon is sufficient for obstacle avoidance by using discrete-time control barrier function (DCBF) constraints and we propose a novel optimization formulation with dual variables based on DCBFs to generate a collision-free dynamically-feasible trajectory. The proposed optimization formulation has lower computational complexity compared to existing work and can be used as a fast online algorithm for control and planning for general nonlinear dynamical systems. We validate our algorithm on different robot shapes using numerical simulations with a kinematic bicycle model, resulting in successful navigation through maze environments with polytopic obstacles.
翻译:在顶端之间避免障碍是最佳控制和优化轨迹规划问题的一个具有挑战性的议题。 现有的工作要么通过混合整数优化,依靠简化系统动态,或者通过模型预测控制,同时使用距离限制的双重变量,需要较长的视野来避免障碍。 在这两种情况下,解决方案只能作为一种离线规划算法来应用。 在本文中,我们利用较小的地平线足以通过使用离散时间控制屏障功能(DCBF)限制来避免障碍的属性,我们提议一种基于DCBF的双重变量的新优化配方,以生成一个无碰撞的动态可行轨迹。 与现有工作相比,拟议的优化配方与现有工作相比,计算复杂程度较低,可以用作用于一般非线性动态系统控制和规划的快速在线算法。 我们用动态自行车模型进行数字模拟,验证了不同机器人形状的算法,从而成功通过多位障碍的磁带环境进行导航。