Polygonal Obstacle Avoidance Combining Model Predictive Control and Fuzzy Logic

TL;DR

This paper introduces a novel method combining fuzzy logic with model predictive control to enable obstacle avoidance in mobile robot navigation using polygonal representations of obstacles, overcoming the challenge of integrating discrete maps into MPC.

Contribution

It presents a new approach to reformulate obstacle avoidance constraints from polygonal maps into differentiable functions compatible with MPC, utilizing fuzzy logic to handle logical operators.

Findings

Successfully tested in simulation

Compatible with standard MPC formulations

Applicable to logical and verbal constraints

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.