Resources

Here are some learning resources that I created. This includes teaching notes, motion planning lecture slides (created jointly with Wolfgang Hönig), and code libraries which you might find helpful.

Teaching Notes

• Introduction to Configuration Spaces and Homeomorphisms (April 2025) Introduction to robot configuration spaces and homeomorphisms
• Your Thesis Journey: From Vision to Success (February 2025) A guide to writing a bachelor's or master's thesis
• Probabilistic Completeness Proofs for Sampling-Based Motion Planning (August 2024) A guide on constructing probabilistic completeness proofs for sampling-based motion planners
• On the Principle of Maximum Entropy (February 2024) Explanation of the principle of maximum entropy and its definition
• From Homotopy to Local Minima: Efficient Path Space Partitioning (November 2023) Proposes local minima as an efficient alternative to homotopy for path space partitioning
• Curvature-Based Rejection Sampling for Arbitrary Parameterized Surfaces (June 2023) A way to conduct uniform sampling on arbitrary parameterized surfaces
• Asymptotic Optimality of AO-x (June 2022) A proof that the kinodynamic motion planner AO-x is asymptotically optimal
• Monte Carlo Tree Search (March 2021) A very brief introduction to the Monte Carlo tree search algorithm
• Policy Gradients (January 2021) Details policy gradient methods in reinforcement learning
• Markov Decision Processes (February 2020) Brief introduction to Markov decision processes used in reinforcement learning
• Riemannian Center of Mass (April 2018) Describes the Riemannian center of mass, a generalization of the center of mass to manifolds
• Projection of an N Dimensional Polytope Onto an N-1 Dimensional Polytope (April 2015) Ways of how the projection of a polytope onto another polytope changes its topology
• Geometry of Quaders on Top of Surface Elements of Polytopes (November 2014) How to formulate geometric quaders above the surface of a polytope
• Maximum Ball on a Surface Element of a Polytope (September 2014) Shows how to find the maximum ball inside a polytope using convex optimization
• Convexity Constraints in Optimization over Functional Spaces (April 2014) Brief introduction to applying convex constraints on functional spaces
• Geometrical Visualization of the Projection of a Point Onto a Hyperplane (July 2013) Shows how to project a point onto a hyperplane using geometric arguments

Motion Planning Lecture Slides

Please check here for an up-to-date version and videos.

• Lecture 1 Organization, Introduction, Problem Formulation
• Lecture 2 Transformations, Angular Representations, Metrics, Efficient Collision Checking
• Lecture 3 Graph-based Planning: Representations, A*, Admissible Heuristics
• Lecture 4 Advanced Search-Based Motion Planning
• Lecture 5 Sampling-Based Geometric Motion Planning: PRMs
• Lecture 6 Introduction to the Open Motion Planning Library (OMPL)
• Lecture 7 RRT, RRT*, Kinodynamic RRT
• Lecture 8 Kinodynamic Planning: SST*, AO-x, Geometric Planning: Informed RRT*, BIT*
• Lecture 9 Sampling-Based Motion Planning: Theory and Advanced Planners; Intro to Optimization
• Lecture 10 Optimization-Based Motion Planning
• Lecture 11 Optimization-Based Motion Planning: Differential Flatness and SCP
• Lecture 12 Advanced Optimization, Comparison, and Hybrid Approaches
• Lecture 13 Multi-robot Motion Planning

Code

• Motion Explorer A framework to visualize the structure of planning problems using local-minima trees
• OMPL Benchmark Plotter Plot benchmarks from the Open Motion Planning Library (OMPL)
• Configuration Space Visualizer A visualization tool to visualize 2D configuration spaces for point robots.
• CPP Util Several handy C/C++ utility functions
• FFmpeg Video Manipulation Interface to create and edit videos in python using ffmpeg-python.
• Vim Snippets Additional Vim snippets to optimize my workflow
• BPY Scripting Blender python bpy scripts