# Optimization-Based Collision Avoidance

arXiv: https://arxiv.org/abs/1711.03449 · HTML: https://mlsanity.com/paper/1711.03449/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2017.

## Built on by (most cited first, 29 of 29)

- [Deep Interactive Motion Prediction and Planning: Playing Games with Motion Prediction Models](https://mlsanity.com/paper/2204.02392/) (2022)
- [Active Uncertainty Reduction for Safe and Efficient Interaction Planning: A Shielding-Aware Dual Control Approach](https://mlsanity.com/paper/2302.00171/) (2023)
- [NeuPAN: Direct Point Robot Navigation with End-to-End Model-based Learning](https://mlsanity.com/paper/2403.06828/) (2024)
- [HOPE: A Reinforcement Learning-based Hybrid Policy Path Planner for Diverse Parking Scenarios](https://mlsanity.com/paper/2405.20579/) (2024)
- [Autonomous Navigation for Quadrupedal Robots with Optimized Jumping through Constrained Obstacles](https://mlsanity.com/paper/2107.00773/) (2021)
- [Blending Data-Driven Priors in Dynamic Games](https://mlsanity.com/paper/2402.14174/) (2024)
- [Adaptive Diffusion Terrain Generator for Autonomous Uneven Terrain Navigation](https://mlsanity.com/paper/2410.10766/) (2024)
- [Autonomous Vehicle Parking in Dynamic Environments: An Integrated System with Prediction and Motion Planning](https://mlsanity.com/paper/2204.10383/) (2022)
- [Real-Time Capable Decision Making for Autonomous Driving Using Reachable Sets](https://mlsanity.com/paper/2309.12289/) (2023)
- [LeTO: Learning Constrained Visuomotor Policy with Differentiable Trajectory Optimization](https://mlsanity.com/paper/2401.17500/) (2024)
- [A Cooperation-Aware Lane Change Method for Autonomous Vehicles](https://mlsanity.com/paper/2201.10746/) (2022)
- [Proactive Emergency Collision Avoidance for Automated Driving in Highway Scenarios](https://mlsanity.com/paper/2310.17381/) (2023)
- [Learning Maximal Safe Sets Using Hypernetworks for MPC-based Local Trajectory Planning in Unknown Environments](https://mlsanity.com/paper/2410.20267/) (2024)
- [Residual Neural Terminal Constraint for MPC-based Collision Avoidance in Dynamic Environments](https://mlsanity.com/paper/2508.03428/) (2025)
- [Collaborative Navigation and Manipulation of a Cable-towed Load by Multiple Quadrupedal Robots](https://mlsanity.com/paper/2206.14424/) (2022)
- [SAFER: Safe Collision Avoidance using Focused and Efficient Trajectory Search with Reinforcement Learning](https://mlsanity.com/paper/2209.11789/) (2022)
- [A Multi-Heuristic Search-based Motion Planning for Automated Parking](https://mlsanity.com/paper/2307.07857/) (2023)
- [Embodied Escaping: End-to-End Reinforcement Learning for Robot Navigation in Narrow Environment](https://mlsanity.com/paper/2503.03208/) (2025)
- [When Environments Shift: Safe Planning with Generative Priors and Robust Conformal Prediction](https://mlsanity.com/paper/2602.12616/) (2026)
- [Agentic Self-Evolutionary Replanning for Embodied Navigation](https://mlsanity.com/paper/2603.02772/) (2026)
- [Unified Multimodal Vessel Trajectory Prediction with Explainable Navigation Intention](https://mlsanity.com/paper/2511.14265/) (2025)
- [CN-CBF: Composite Neural Control Barrier Function for Robot Navigation in Dynamic Environments](https://mlsanity.com/paper/2603.06921/) (2026)
- [iCOIL: Scenario Aware Autonomous Parking Via Integrated Constrained Optimization and Imitation Learning](https://mlsanity.com/paper/2305.13663/) (2023)
- [Automated Parking Planning with Vision-Based BEV Approach](https://mlsanity.com/paper/2406.15430/) (2024)
- [ADEPT: Adaptive Diffusion Environment for Policy Transfer Sim-to-Real](https://mlsanity.com/paper/2506.01759/) (2025)
- [Spatial Envelope MPC: High Performance Driving without a Reference](https://mlsanity.com/paper/2509.18506/) (2025)
- [LLM-Driven Scenario-Aware Planning for Autonomous Driving](https://mlsanity.com/paper/2601.21876/) (2026)
- [SRL-MPC: Shape-Aware Reinforcement Learned Model Predictive Control](https://mlsanity.com/paper/2608.21175/) (2026)
- [From Semantic Decisions to Feasible Trajectories: Self-Evolving LLM-Guided Optimal Control for Narrow-Space Parking](https://mlsanity.com/paper/2609.24631/) (2026)

## Abstract (arXiv)

This paper presents a novel method for reformulating non-differentiable collision avoidance constraints into smooth nonlinear constraints using strong duality of convex optimization. We focus on a controlled object whose goal is to avoid obstacles while moving in an n-dimensional space. The proposed reformulation does not introduce approximations, and applies to general obstacles and controlled objects that can be represented in an n-dimensional space as the finite union of convex sets. Furthermore, we connect our results with the notion of signed distance, which is widely used in traditional trajectory generation algorithms. Our method can be used in generic navigation and trajectory planning tasks, and the smoothness property allows the use of general-purpose gradient- and Hessian-based optimization algorithms. Finally, in case a collision cannot be avoided, our framework allows us to find "least-intrusive" trajectories, measured in terms of penetration. We demonstrate the efficacy of our framework on a quadcopter navigation and automated parking problem, and our numerical experiments suggest that the proposed methods enable real-time optimization-based trajectory planning problems in tight environments. Source code of our implementation is provided at https://github.com/XiaojingGeorgeZhang/OBCA.