Trajectory Optimization of Industrial Robots with a Feasible Direction Interior Point Algorithm

Trajectory planning is considered a fundamental concern in robotics. In this paper, we discuss the use of optimization techniques to obtain optimum trajectories of industrial robots. We use the flexibility of optimization techniques to address different formulations and solve them using the Feasible Direction Interior Point Algorithm (FDIPA). This method essentially solves two linear systems in each iteration to compute a descent and feasible direction of the problem, then performs a line search procedure that assures global convergence and feasibility of all iterates. Initially, it will be presented the physical description of the tasks to be executed by the serial robotic manipulator. At first, we discuss point-to-point collision-free paths, that is, given an initial pose of the robot and a final target point, find an optimum trajectory that minimizes time, total displacement, energy or other performance index while avoiding collision with an obstacle. Then we discuss the path-following cases, where, given the desired trajectory of the end-effector, optimum joint trajectories are calculated, such that velocity or acceleration peaks are minimum. Further, both cases are formulated as optimization problems, which we also deal with joint mechanical limits (maximum displacements, velocities and accelerations) as constraints. Finally, we use a 4 degrees-of-freedom (DOF) planar manipulator to present numerical examples. Our results prove the effectiveness of the proposed approach and ensure robustness and applicability of the optimization method in the context of robotics.