Trajectory Optimisation of a Robotic Manipulator Using a Novel Evolutionary Intelligence Algorithm

In this paper, we present a novel approach for Proportional–Integral–Derivative (PID) tuning of a robotic manipulator, modeled using the Lagrange method and validated through comprehensive modeling and simulation. To optimize the PID gains, we developed a hybrid algorithm that combines Greylag Goose Optimization (GGO) with the Sine Cosine Algorithm (SCA), leveraging the strengths of both optimization techniques. The proposed hybrid algorithm, termed GGOSCA, was tested against GGO and Particle Swarm Optimization (PSO) using three objective functions: Lyapunov Based Function (LBF), Integral of Absolute Error (IAE), and Integral of Time-weighted Absolute Error (ITAE). The results demonstrated that GGOSCA outperforms both GGO and PSO across all objective functions. Specifically, GGOSCA achieved the lowest costs of 0.1018, 0.2484, and 0.6601 for LBF, IAE, and ITAE, respectively, compared to 0.1022, 0.2580, and 0.6939 for GGO, and 0.1023, 0.2660, and 0.7273 for PSO. The superior performance of GGOSCA highlights its effectiveness in balancing exploration and exploitation, making it well-suited for complex control tasks such as PID tuning in robotic systems. This novel combination of GGO and SCA provides a robust and efficient solution for optimizing control parameters in dynamic environments, demonstrating its potential through rigorous modeling and simulation.