论文标题
CPC：时间 - 最佳四轨轨迹的互补进度限制
CPC: Complementary Progress Constraints for Time-Optimal Quadrotor Trajectories
论文作者
论文摘要
在许多移动机器人方案（例如无人机赛车）中，目标是生成一个轨迹，该轨迹在最少的时间内通过多个航路点。这个问题称为时间优势。最先进的方法要么使用多项式轨迹公式，因此由于其平滑度或数值优化而是次优的，这需要将路点分配为成本或约束特定离散时间节点。对于时间最佳计划，这种时间分配是先验的未知，并且使传统方法无法产生真正的时间优势轨迹。我们介绍了一种新的进度表述，通过互补性约束绑定到航路点。虽然进度变量表示完成方向点的完成，但仅在局部接近路点的互补性约束中才允许更改此进度。这可以同时优化轨迹和时间点的时间分配。据我们所知，这是第一种允许针对四型和其他系统进行真正最佳时间的轨迹计划的方法。我们执行并讨论有关最优性和凸性的评估，与其他相关方法相比，并在质量上与专家人类的基线进行评估。
In many mobile robotics scenarios, such as drone racing, the goal is to generate a trajectory that passes through multiple waypoints in minimal time. This problem is referred to as time-optimal planning. State-of-the-art approaches either use polynomial trajectory formulations, which are suboptimal due to their smoothness, or numerical optimization, which requires waypoints to be allocated as costs or constraints to specific discrete-time nodes. For time-optimal planning, this time-allocation is a priori unknown and renders traditional approaches incapable of producing truly time-optimal trajectories. We introduce a novel formulation of progress bound to waypoints by a complementarity constraint. While the progress variables indicate the completion of a waypoint, change of this progress is only allowed in local proximity to the waypoint via complementarity constraints. This enables the simultaneous optimization of the trajectory and the time-allocation of the waypoints. To the best of our knowledge, this is the first approach allowing for truly time-optimal trajectory planning for quadrotors and other systems. We perform and discuss evaluations on optimality and convexity, compare to other related approaches, and qualitatively to an expert-human baseline.
