Regularization of the movement of a material point along a flat trajectory: application to robotics problems
This addresses trajectory optimization for robotics applications, but it appears incremental as it applies known regularization techniques to specific planar cases.
The paper tackles the control problem of moving a tool along a predefined flat trajectory by minimizing a cost functional based on kinetic energy and inertia forces, reducing it to a fourth-order ODE system and providing numerical solutions for straight, circular, and elliptical paths.
The control problem of the working tool movement along a predefined trajectory is considered. The integral of kinetic energy and weighted inertia forces for the whole period of motion is considered as a cost functional. The trajectory is assumed to be planar and defined in advance. The problem is reduced to a system of ordinary differential equations of the fourth order. Numerical examples of solving the problem for movement along straight, circular and elliptical trajectories are given.