A Scope of Convex Optimization in Path Planning of Robot in Constrained Space

A fascinating problem in robotics is path planning. In this paper, an alternate method for the end-effector of robot path planning based on the Convex Optimization (CO) based algorithm is proposed. This task aims to minimise the path length of the robot figuring out the robots' trajectory of motion from priory known initial point to fixed destination point in the global map. Using the CO algorithm, a local trajectory planning scheme has been created to determine robot's optimal position going forward in the world map from its current position. This ensures that the paths that need to be developed locally for robot is small enough and have the least amount of space with any type of obstacles that may be present. The optimized path is further refined using cubic splines (using
$L_2,\boldsymbol{L}_\infty$
) to smooth out each turning/way point effectively. This refinement step enhances the path's continuity and ensures a more seamless trajectory. Ultimately, the proposed algorithm is crafted utilizing MATLAB CVX and it is employed to plan the trajectory of the Epson Robot T3 end-effector's path when polygonal multi-obstacles are present in its operational space. Simulation results are provided to validate the effectiveness of the proposed algorithm in navigating through complex environments while avoiding obstacles.