Abstract
Optimization-based approaches are widely employed to generate optimal robot motions while considering various constraints, such as robot dynamics, collision avoidance, and physical limitations. It is crucial to efficiently solve the optimization problems in practice, yet achieving rapid computations remains a great challenge for optimization-based approaches with nonlinear constraints. In this paper, we propose a geometric projector for dynamic obstacle avoidance based on velocity obstacle (GeoPro-VO) by leveraging the projection feature of the velocity cone set represented by VO. Furthermore, with the proposed GeoPro-VO and the augmented Lagrangian spectral projected gradient descent (ALSPG) algorithm, we transform an initial mixed integer nonlinear programming problem (MINLP) in the form of constrained model predictive control (MPC) into a sub-optimization problem and solve it efficiently. Numerical simulations are conducted to validate the fast computing speed of our approach and its capability for reliable dynamic obstacle avoidance.
Abstract (translated)
基于优化的方法广泛应用于生成最优机器人运动，同时考虑各种约束，如机器人动力学、避障和物理限制。在实践中有效地解决优化问题至关重要，然而，对于基于非线性约束的优化方法来说，实现快速计算仍然是一个巨大的挑战。在本文中，我们提出了一种基于速度障碍物（GeoPro-VO）的运动障碍物避障几何投影方法，通过利用速度锥集的代表VO的速度锥的投影特征。此外，基于GeoPro-VO和提出的增强拉格朗日光谱投影梯度下降（ALSPG）算法，我们将初始混合整数非线性规划问题（MINLP）形式为约束模型预测控制（MPC）的问题转化为子优化问题并求解它，从而实现高效计算。为了验证我们方法的高速计算速度和可靠的运动障碍物避障能力，进行了一系列数值仿真。
URL
https://arxiv.org/abs/2403.10043
