How do you formulate and solve constrained motion planning for autonomous vehicles?

Constrained motion planning formulation: 1) State space - vehicle pose, velocity, acceleration, steering angle; 2) Constraints - vehicle dynamics (maximum steering angle, acceleration limits), collision avoidance (static and dynamic obstacles), road boundaries, traffic rules, comfort bounds (jerk limits); 3) Objective function - progress toward goal, safety margins, comfort, efficiency; 4) Solution methods - optimization-based (convex relaxation, sequential quadratic programming), sampling-based with constraint checking, or MPC with receding horizon. Handling dynamic environments: Prediction integration, contingency planning, reactive adjustments. Real-time requirements (~100ms cycle) demand efficient algorithms. Constraint tightening provides robustness margins for uncertainty. Tuning balances performance metrics while ensuring constraint satisfaction.