Optimal Trajectory Planning for an Industrial Mobile Robot using Optimal Control Theory

Optimal path planning with optimal journey time and the motor saturation limit are two main challenges in mobile industrial robot design. The motion speed and motor saturation limit are important factors determining the required torque. Calculating the optimal torque value reduces the construction and motor selection costs. This paper proposes the theory of optimal control open-loop base model for path planning by simultaneously minimizing the journey time, wheels’ torque for industrial robots. In this study, nonlinear equations of robot motion were considered as a constraint in optimal control problems. Next, the cost function was proposed, including the torque of the left and right wheels and time-related terminal conditions and disturbance, in which the nonlinear equations of the industrial robot motion are assumed as constraints. The final equations were numerically solved, and the effectiveness of the proposed method was demonstrated by simulating and path design for industrial robots' motions along with considering motor saturation limit.