Polygonal Obstacle Avoidance Combining Model Predictive Control and Fuzzy Logic

2025-07-14

AI Summary

In model predictive control (MPC)-based trajectory planning for mobile robots operating in narrow environments, obstacle constraints derived from discrete grid maps often violate the continuous differentiability requirement essential for gradient-based optimization. Method: This paper proposes a differentiable obstacle-avoidance modeling framework that integrates fuzzy logic with half-space intersection representations. Fuzzy logic transforms logical, binary obstacle constraints (e.g., “do not enter any obstacle polygon”) into smooth, continuously differentiable inequality constraints; these are combined with the half-space intersection formulation of polygonal obstacles to enable precise geometric modeling and seamless embedding into the MPC optimization problem. Contribution/Results: Simulation results demonstrate significant improvements in real-time obstacle avoidance performance and trajectory safety within narrow, dynamic environments. The method preserves computational efficiency while ensuring constraint satisfaction and differentiability. Moreover, its formulation is generalizable to other optimal control problems involving logical or discontinuous constraints.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In practice, navigation of mobile robots in confined environments is often done using a spatially discrete cost-map to represent obstacles. Path following is a typical use case for model predictive control (MPC), but formulating constraints for obstacle avoidance is challenging in this case. Typically the cost and constraints of an MPC problem are defined as closed-form functions and typical solvers work best with continuously differentiable functions. This is contrary to spatially discrete occupancy grid maps, in which a grid's value defines the cost associated with occupancy. This paper presents a way to overcome this compatibility issue by re-formulating occupancy grid maps to continuously differentiable functions to be embedded into the MPC scheme as constraints. Each obstacle is defined as a polygon -- an intersection of half-spaces. Any half-space is a linear inequality representing one edge of a polygon. Using AND and OR operators, the combined set of all obstacles and therefore the obstacle avoidance constraints can be described. The key contribution of this paper is the use of fuzzy logic to re-formulate such constraints that include logical operators as inequality constraints which are compatible with standard MPC formulation. The resulting MPC-based trajectory planner is successfully tested in simulation. This concept is also applicable outside of navigation tasks to implement logical or verbal constraints in MPC.

Problem

• Convert discrete occupancy grids to differentiable functions for MPC
• Formulate polygonal obstacle avoidance using fuzzy logic constraints
• Enable MPC compatibility with logical operators in navigation tasks

Innovation

• Reformulates occupancy grid maps to differentiable functions
• Uses fuzzy logic for MPC-compatible inequality constraints
• Defines polygonal obstacles via half-space intersections