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Semi-Infinite Programming for Collision Avoidance in Optimal and Model-Predictive Control
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AI
DOI：10.1109/TRO.2026.3686181.png)
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Abstract
En 中文
This article presents a novel approach for collision avoidance in optimal and model-predictive control, in which the environment is represented by a large number of points and the robot as a union of padded polygons. The conditions that none of the points shall collide with the robot can be written in terms of an infinite number of constraints per obstacle point. We show that the resulting semi-infinite programming optimal control problem can be efficiently tackled through a combination of two methods: local reduction and an external active-set method. Specifically, this involves iteratively identifying the closest point obstacles, determining the lower level distance minimizer among all feasible robot shape parameters, and solving the upper level finitely constrained subproblems. In addition, this article addresses robust collision avoidance in the presence of ellipsoidal state uncertainties. Enforcing constraint satisfaction over all possible uncertainty realizations extends the dimension of constraint infiniteness. The infinitely many constraints arising from translational uncertainty are handled by local reduction together with the robot shape parameterization, while rotational uncertainty is addressed via a backoff reformulation. A controller implemented based on the proposed method is demonstrated on a real-world robot running at 20 Hz, enabling fast and collision-free navigation in tight spaces. An application to 3-D collision avoidance is also demonstrated in simulation.
Keywords:
Collision avoidance
mobile robots
motion and path planning
optimization and optimal control
Journal
IF:
10.5
Papers:
3.3K
Citations:
2.8W
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