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Rigorous extension of MPC scheme to handle unknown and dynamic obstacles

Develop a rigorous extension of the MPC-based motion planning scheme that employs an artificial steady state tied to a reference path so that it formally handles scenarios with (i) obstacles that are unknown a priori and discovered at runtime, (ii) global reference paths that intersect obstacles, and (iii) dynamic obstacles ignored by the global planner.

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Background

The paper presents an MPC formulation for non-holonomic robots in non-convex environments that guarantees convergence to a target under static, known obstacles, using an artificial steady state tied to a global reference path. The authors note that, in practice, the environment may include unknown or dynamic obstacles, and even global paths that cross obstacles.

They report that simulations often succeed in these settings (e.g., with sufficiently long prediction horizons), but emphasize that a formal, rigorous extension of the algorithm or MPC more broadly to provably handle such cases has not been established.

References

We highlight that it is not strictly necessary for all obstacles to be known beforehand, provided that the path p can be re-computed at runtime, if needed. Furthermore, in our simulations, often a solution could be found even if the global path went through obstacles, as long as the MPC prediction horizon was sufficiently long and similarly if dynamic obstacles - ignored by the path planner - were present. This behavior is expected, as standard MPC formulations have generally been shown to perform well in such scenarios. Nevertheless, we note that a rigorous extension of the algorithm, or of MPC in general, to handle these cases remains a relevant open question.

— MPC-based motion planning for non-holonomic systems in non-convex domains (2510.18402 - Lorenzen et al., 21 Oct 2025) in Section 3 (Main Results), paragraph following Theorem 1