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.

翻译：基于优化的方法被广泛用于在考虑机器人动力学、碰撞避免及物理限制等多种约束条件下生成最优机器人运动。如何在实践中高效求解优化问题至关重要，但对于含有非线性约束的优化方法而言，实现快速计算仍是一大挑战。本文通过利用速度障碍（VO）所表征的速度锥集的投影特性，提出了一种基于速度障碍的几何投影器动态避障方法（GeoPro-VO）。进一步地，结合所提出的GeoPro-VO与增广拉格朗日谱投影梯度下降算法（ALSPG），我们将形式为约束模型预测控制（MPC）的初始混合整数非线性规划问题（MINLP）转化为子优化问题并高效求解。数值仿真验证了该方法在快速计算能力及可靠动态避障性能方面的有效性。