motion-planning

When grids fail in high dimensions, random sampling saves you. Understand why PRM builds reusable roadmaps, how RRT grows a tree toward the goal, what probabilistic completeness really means, and how RRT* achieves asymptotic optimality.

Discretise C-space into a grid, then search it intelligently. Understand Dijkstra's optimality guarantee, how A* accelerates it with admissible heuristics ($f=g+h$), why consistency matters, and where greedy search goes wrong.

Understand why every motion planner secretly works in configuration space: how robots become points, obstacles inflate, and why high-dimensional C-spaces make naive search intractable.

Trace the full perceive-plan-act loop on a mobile robot: AMCL localization feeds a global costmap, a global planner (A*/NavFn) sets the course, and DWA or TEB local planners execute it — with recovery behaviors when things go wrong.

Learn how to generate smooth robot trajectories — trapezoidal velocity profiles, cubic and quintic polynomials — and how to combine feedforward and feedback to track them with minimal error on real arms and mobile robots.