This open-access educational module presents the configuration space theory, discrete graph search algorithms, high-dimensional sampling frameworks, and continuous trajectory optimization techniques foundational to autonomous robotic motion planning.
Core Technical Topics
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Configuration Space (C-Space): Manifold formulations in SE(2) and SE(3), C-obstacle computation via Minkowski sums (C_obs = O ⊕ (-R)), and distance metrics.
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Graph-Based Search: Dijkstra's algorithm and A* search, evaluation of admissible and consistent heuristics (h(n) ≤ h*(n)), and grid traversal complexity.
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Sampling-Based Motion Planning: Rapidly-exploring Random Trees (RRT), asymptotic optimality via RRT* local parent selection and tree rewiring (lim_{n→∞} c_n = c*), and solving the narrow passage challenge.
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Kinodynamic Trajectory Optimization: Arc-length time parameterization (q(t) = q(s(t))), motor velocity/acceleration constraints, nonholonomic vehicle constraints (Dubins/Reeds-Shepp curves), and objective cost functionals.
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Multi-Robot Planning & Obstacle Avoidance: Combined configuration space scaling (dim(C) = ∑ dim(C_i)), Dynamic Window Approach (DWA), and hierarchical collision detection.
Pedagogical Assets
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12 fully worked numerical engineering problems with complete mathematical derivations and step-by-step solutions.
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Dedicated engineering challenges analysis covering narrow passages, dynamic obstacles, nonholonomic feasibility, and trajectory smoothing.
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Interactive conceptual quick reviews and self-assessment checkpoints.
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Standardized cross-platform layout designed for university coursework adoption and offline reference.
Target Audience & Level
Designed for upper-division undergraduate engineering courses (Robotics, Autonomous Systems, Mechatronics, and Computer Science), advanced university-preparatory STEM programs, and autonomous navigation systems engineers.
