A mathematical motivation for industrial robotic motion planning

A mathematical motivation for industrial robotic motion planning

In this talk, I will give rigorous definitions of concepts in robotics using real analysis and differential geometry as my tools. I will define configuration space, cartesian space, forward kinematics and collision for an abstract robot at a configuration. I will then illustrate some basic algorithms used in collision detection and if time permits I will also discuss methods used in solving 6R inverse kinematics and method used in the industry when solving the inverse kinematics of manipulators with more than 6 joints. I will discuss kinematic singularities and talk about singularity avoidance and path optimization using a specific measure. The main objective of this talk is collision-free path planning which I will define and illustrate using a specific algorithm (RRT – Rapidly growing random Tree). I will then show and discuss application used for path planning specifically : bin-picking and coverage planning. Finally I will show videos and demonstration of solutions used by the industry when solving bin-picking and coverage planning problems.