Trajectory Planning for a Spraying Robotic Arm Using a Digital Twin and an Improved SAC Algorithm

This paper proposes a trajectory planning method for a four-degree-of-freedom (4-DOF) spraying robotic arm based on a digital twin platform and an improved soft actor–critic (SAC) algorithm. The method addresses the complex environment of underground shotcrete spraying operations, the high cost and risk of physical robotic arm training, and the difficulty of incorporating spraying process constraints into traditional path planning methods. To enable unified modeling of the virtual prototype, operating scenario, reference trajectory, joint constraints, and spraying process proxy indicators, a digital twin platform for the spraying robotic arm was built using Unity Editor 2022.3.14f1c1.A composite reward function was designed to incorporate trajectory tracking, spray distance, nozzle normal, spraying speed, safety, and motion smoothness, and a prioritized experience replay (PER) mechanism based on double-critic temporal difference (TD) error was introduced to the conventional SAC algorithm. Simulation results show that, under the current digital twin environment and two-dimensional S-shaped reference trajectory, the Improved SAC algorithm reduces trajectory tracking root mean square error (RMSE) from 24.0 ± 2.0 mm to 8.0 ± 0.7 mm, corresponding to a 66.7% reduction compared with standard SAC. In addition, the spray distance error, nozzle normal error, spraying speed error, and motion smoothness index are reduced by 43.5%, 49.1%, 47.3%, and 48.7%, respectively.