# CPC: Complementary Progress Constraints for Time-Optimal Quadrotor Trajectories

arXiv: https://arxiv.org/abs/2007.06255 · HTML: https://mlsanity.com/paper/2007.06255/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2020.

## Built on by (most cited first, 2 of 2)

- [Autonomous Drone Racing with Deep Reinforcement Learning](https://mlsanity.com/paper/2103.08624/) (2021)
- [AutoTune: Controller Tuning for High-Speed Flight](https://mlsanity.com/paper/2103.10698/) (2021)

## Abstract (arXiv)

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.