Allowing larger deviation from the reference path while guaranteeing convergence in dynamic or unknown environments

Determine how to modify the MPC-based motion planning scheme that uses a reference path so that it permits greater deviation from the reference path in dynamic environments or with unknown obstacles while still guaranteeing convergence to the target; in particular, characterize how obstacle size, prediction horizon length, and the presence of local minima affect this guarantee.

Background

The proposed MPC approach relies on a reference path to ensure convergence, which the authors argue is necessary but can be restrictive in dynamic or partially unknown environments. They wish to relax the tight dependence on the path while preserving guarantees, pointing to a need for theoretical characterization of factors like obstacle size, horizon length, and local minima.

They explicitly identify this as an open problem and suggest that resolving the relationship among these factors could enable such an extension.