SCU‐T‐MPC: Risk‐Aware and Socially Compliant Topological Motion Planning Under Uncertainty

Topology‐driven model predictive control (T‐MPC) has demonstrated significant performance in navigating dynamic environments by planning trajectories in distinct homotopy classes in parallel. However, its performance is limited by deterministic assumptions about obstacle motions and a cost function that ignores social norms. This paper presents a unified framework, socially compliant topology‐driven model predictive control under uncertainty (SCU‐T‐MPC) that addresses these limitations. First, we introduce the concept of probabilistic homotopy classes by integrating multi‐modal uncertainty into the topological guidance planner, enabling robustness to various potential futures. Second, we formulate a risk‐aware parallel optimisation scheme where each local planner incorporates chance constraints and a risk‐adjusted cost. Finally, we learn a social preference model from human demonstration data that map topological features to a social cost, biasing the trajectory selection towards socially compliant behaviours. We provide theoretical guarantees on the robustness of our approach. Extensive simulation experiments with a mobile robot navigating among pedestrians show that SCU‐T‐MPC outperforms existing planners in terms of safety, efficiency and social acceptability.