This paper focuses primarily on adaptive dynamic programming (ADP)-based tracking control of the hydraulic-driven flexible robotic manipulator system (HDFRMS) with varying payloads and uncertainties via singular perturbation theory (SPT). Firstly, the dynamics is derived using a driven Jacobin matrix, which represents the coupling between the hydraulic servo-driven system and rigid–flexible manipulator established using the assumed mode method and Lagrange principle. Furthermore, the whole dynamic model of the manipulator system is decoupled into a second slow subsystem (SSS), a second fast subsystem (SFS) and a first fast subsystem (FFS). The three subsystems can describe a large range of movement, flexible vibration and electro-hydraulic servo control, respectively. Hereafter, an adaptive dynamic programming trajectory tracking control law with a critic-only policy iteration algorithm is presented in the second slow timescale, while both robust optimal control (ROC) in the second first timescale and adaptive sliding mode control (ASMC) in the first fast timescale are also designed using the Lyapunov stability theory. Finally, the numerical simulations are carried out to illustrate the rightness and robustness of the singular perturbation decomposition and proposed composite control algorithm.

The accuracy and precision of the inverse kinematics solution is the key to determine the performance of the robotic arm motion. Aiming at the Particle Swarm Optimization(PSO) algorithm’s low accuracy in solving inverse kinematics of 2-link flexible macro robotic arms with 2-link rigid micro robotic arms(2F2R macro-micro robotic arm), this paper proposes the Multiple Genetic Particle Swarm Optimization algorithm (MGAPSO), which employs a hybrid inertia weight updating strategy and integrates the multiple parallel swarm search mode and the genetic mutation operation to increase the diversity of the populations and the search accuracy. In order to verify the effectiveness of MGAPSO algorithm , two sets of experiments are conducted with six test functions and 2F2R macro-micro robotic arm, respectively. Simulation results show the optimal solution accuracy of improved MGAPSO is 1.19*10-14 , which is better than other algorithms of 3.45*10-7. This paper provides a new algorithm for the inverse kinematics problem.