Robot Path Planning Using Spline Functions

Abstract

we studied the problem of robot path planning, which determines how the robot’s degrees of freedom change over time. The robot moves by passing through specified points, either with its joints (when points are given in joint space) or with its end-effector (when points are given in Cartesian space). We constructed smooth paths using interpolation polynomials, which produce simple linear systems that are easy to solve. We also explored using multiple polynomials connected in sequence to generate smooth paths.
We found that specifying joint positions, velocities, and accelerations at the start and end points can make the linear system degenerate, preventing a solution from existing. Increasing the number of intermediate points requires higher-degree polynomials, which significantly increases the computational load when calculating values at each point. We addressed this issue by using spline functions, which guarantee that the system of equations has a solution and can be efficiently solved using the sweep method.