# The Convex Feasible Set Algorithm for Real Time Optimization in Motion Planning

arXiv: https://arxiv.org/abs/1709.00627 · HTML: https://mlsanity.com/paper/1709.00627/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2017.

## Built on by (most cited first, 9 of 9)

- [Safe Control with Neural Network Dynamic Models](https://mlsanity.com/paper/2110.01110/) (2021)
- [Safety-aware Motion Prediction with Unseen Vehicles for Autonomous Driving](https://mlsanity.com/paper/2109.01510/) (2021)
- [Provably Safe Tolerance Estimation for Robot Arms via Sum-of-Squares Programming](https://mlsanity.com/paper/2104.08896/) (2021)
- [Proactive Human-Robot Co-Assembly: Leveraging Human Intention Prediction and Robust Safe Control](https://mlsanity.com/paper/2306.11862/) (2023)
- [Learning Predictive Control with Deep Koopman Operators for Autonomous Vehicle Motion Planning](https://mlsanity.com/paper/2606.08136/) (2026)
- [Motion Planning with Model-Based Diffusion via Constraint Optimization and Adaptive Scheduling](https://mlsanity.com/paper/2607.14455/) (2026)
- [Reachable Sets-based Trajectory Planning Combining Reinforcement Learning and iLQR](https://mlsanity.com/paper/2503.17398/) (2025)
- [A highly maneuverable flying squirrel drone with agility-improving foldable wings](https://mlsanity.com/paper/2504.09609/) (2025)
- [ELMP: Efficient Learning for Motion Planning via Analytical Policy Gradients](https://mlsanity.com/paper/2607.00215/) (2026)

## Abstract (arXiv)

With the development of robotics, there are growing needs for real time motion planning. However, due to obstacles in the environment, the planning problem is highly non-convex, which makes it difficult to achieve real time computation using existing non-convex optimization algorithms. This paper introduces the convex feasible set algorithm (CFS) which is a fast algorithm for non-convex optimization problems that have convex costs and non-convex constraints. The idea is to find a convex feasible set for the original problem and iteratively solve a sequence of subproblems using the convex constraints. The feasibility and the convergence of the proposed algorithm are proved in the paper. The application of this method on motion planning for mobile robots is discussed. The simulations demonstrate the effectiveness of the proposed algorithm.