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.

References

Furthermore, while we argue it is necessary, the strong dependence on the reference path is a limitation in dynamic environments or with unknown obstacles. In these cases, it becomes desirable to allow further deviation from the reference path, while still guaranteeing convergence to the target. This is an open question and important topic for future research. It could probably be solved, if an answer is found on how obstacle size, length of the prediction horizon and existence of local minima are related.

— MPC-based motion planning for non-holonomic systems in non-convex domains  (2510.18402 - Lorenzen et al., 21 Oct 2025) in Section 5 (Conclusions and Future Work)

This avoidance is reactive, inherited from Falco. It suffices for low-density motion, but fast obstacles on random trajectories are hard to evade; moreover, evasive detours can steer the robot off the planned path and trigger relocalization, lowering success. Handling such cases requires velocity-level reasoning and trajectory prediction, left to future work.

— EgoNav: Bridging Learned Waypoints and Geometry-Aware Local Control for Robust Indoor Navigation  (2608.25642 - Wang et al., 26 Aug 2026) in Section 4.4, “Robustness to Dynamic Obstacles”