Kinematics grounded motion planning for robots

Course Overview:

 

Most people assume that planning a path from A to B is a solved problem, and that the only remaining challenge is collecting enough data to make robots do household chores. But this is far from the truth. Anyone who has worked on pick-and-place tasks in cluttered environments knows that, despite many available planners, finding and quickly replanning a safe path, especially when objects are unexpectedly moved, is still a complex and challenging problem. This is mostly due to the fact that robot motion are inherently limited by their kinematics. 
Have you ever been astonished to see that year after year, new robot arms enter the market and yet they all  look almost identical to existing models? Yet, despite their similar appearance, these robot arms can differ significantly in their kinematic structure. As a result, tasks carefully programmed or learned on one robot often cannot be directly transferred to another. These differences have real consequences and will hinder large-scale deployment of controllers for industrial and household manipulation tasks.
This course will teach you how to analyze and understand robot kinematics, identify which designs are easier to control, and recognize potential limitations. With this knowledge, you will not only be able to program robots more effectively, but also advise industry on selecting the right robotic platform for their specific needs.
Specifically, this course will allow you to develop an analytical, intuition-driven understanding of forward and inverse kinematics, singularity visualization, and constraint-aware motion planning (joint limits, collision avoidance, and singularity robustness). We will evaluate this on a variety of platform, from robotic arms doing complex pick and place, to multiple robot arms manipulating objects in synchronization. At this end of the class, you should be able to confidently explain and predict robot ability to perform a given task, a growing need as modern robots increasingly execute learning-based policies that must still obey geometry.

 

Content:

 

The course focuses on analytical treatments of kinematics, forward/inverse kinematics and singularity structure, supported by differential kinematics when needed for interpretation and visualization. Students build models from D–H parameters and URDF, study the multiplicity of IK solutions and their continuation along a path, and learn how singularities shape reachable motions and planner robustness. Constraint-aware motion planning is treated as a kinematics problem: selecting consistent IK branches while respecting joint limits, avoiding collisions via robot geometry, and staying away from ill-conditioned regions. Practical sessions emphasize implementation and validation in realistic robot simulations, culminating in a final project that integrates the full pipeline.

1. Robot modeling for planning: frames, D–H parameters, URDF; joint limits and collision geometry
2. Analytical forward and inverse kinematics; multiple IK solutions and solution continuation along a path
3. Singularity analysis and visualization; interpreting “what motions are possible” near singular configurations
4. Differential kinematics (Jacobian) as a tool for interpretation, conditioning metrics, and robustness analysis
5. Constraint-aware motion planning: joint limits, collision checking, singularity-aware planning and execution in simulation
6. Advanced glimpses: screw-theory formulation for compact motion description; an introduction-level view of Conformal Geometric Algebra (CGA) as a modern geometric language
7. Final project: end-to-end kinematics-grounded motion planning pipeline deployed on realistic robot simulations, with evaluation and a concise report