Semi-Infinite Programming for Collision-Avoidance in Optimal and Model Predictive Control

2025-08-17

AI Summary

This work addresses collision avoidance for polygonal robots in high-density point-cloud environments within optimal control and model predictive control (MPC). Methodologically, the robot is modeled as a buffered polygonal union, while obstacles are represented as large-scale point clouds; semi-infinite programming (SIP) is introduced to uniformly encode the infinite set of collision-avoidance constraints, and an efficient solver is developed combining local constraint reduction with an outer-level active-set algorithm; to handle state uncertainty modeled as ellipsoidal sets, uncertainty propagation analysis is integrated with a fallback reconstruction mechanism to ensure rotational robustness. The key contributions are: (i) the first systematic application of SIP to real-time MPC-based obstacle avoidance; (ii) demonstration of 20-Hz closed-loop control on physical robots; (iii) successful high-speed, collision-free navigation in confined spaces; and (iv) validation of extensibility to 3D environments.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Security and Privacy: Large-scale security measurements
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

This paper 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 (SIP) optimal control problem (OCP) 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 paper 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 20Hz, enabling fast and collision-free navigation in tight spaces. An application to 3D collision avoidance is also demonstrated in simulation.

Problem

• Semi-infinite programming for collision avoidance in optimal control
• Handling infinite constraints from obstacle points and uncertainties
• Efficiently solving SIP OCP via local reduction and active-set methods

Innovation

• Semi-infinite programming for collision avoidance
• Local reduction with active-set method
• Robust handling of ellipsoidal state uncertainties