Constrained Motion Planning

Constrained motion planning studies how robots can reach goals while respecting obstacles, dynamics, joint or contact limits, and task requirements, which is essential for safe, executable behavior. Methods include sampling and graph search, trajectory optimization and model predictive control, and planning directly on constraint manifolds; control barrier functions, reachability analysis, and signal temporal logic encode safety and task conditions. Learning-based trajectory proposals, including diffusion models, are increasingly paired with optimization, projection, or safety certificates to improve speed and handle complex environments. A central challenge is balancing formal feasibility and robustness to uncertainty with real-time computation, especially in high-dimensional, dynamic, and multi-robot settings.