Journal
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY
Volume 29, Issue 3, Pages 972-983Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCST.2019.2949540
Keywords
Collision avoidance; Trajectory; Optimization; Planning; Aerospace electronics; Robots; Navigation; Autonomous driving; collision avoidance; model predictive control (MPC); navigation in tight environments; nonlinear optimization; obstacle avoidance; path planning; trajectory optimization
Funding
- Hyundai Center of Excellence, UC Berkeley
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This article presents a novel method that exactly reformulates nondifferentiable collision avoidance constraints into smooth, differentiable constraints using convex optimization. The proposed reformulation is exact and applicable to general obstacles and controlled objects. By connecting the results with signed distance concept, the method can be applied to generic navigation and trajectory planning tasks, enabling real-time optimization-based trajectory planning.
This article presents a novel method for exactly reformulating nondifferentiable collision avoidance constraints into smooth, differentiable 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 is exact, does not introduce any approximations, and applies to general obstacles and controlled objects that can be represented as the union of convex sets. We connect our results with the notion of signed distance, which is widely used in traditional trajectory generation algorithms. Our method can be applied to 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 an automated parking problem, where our numerical experiments suggest that the proposed method is robust and enables real-time optimization-based trajectory planning in tight environments. Sample code of our example is provided at https://github.com/XiaojingGeorgeZhang/OBCA.
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