This paper presents a trajectory planning method based on multi-objective optimization, including time optimal and jerk optimal for the manipulators in the presence of obstacles. The proposed method generates a trajectory configuration in the joint space with kinematic and obstacle constraints using quintic B-spline. Gilbert–Johnson–Keerthi detecting algorithm is utilized to detect whether there is a collision and obtain the minimum distance between the manipulator and obstacles. The degree of constraint violations is introduced to redefine the Pareto domination, and the constrained multi-objective particle swarm algorithm (CMOPSO) is adopted to solve the time-jerk optimization problem. Finally, the Z-type fuzzy membership function is proposed to select the best optimal solution in the Pareto front obtained by CMOPSO. Test results show the effectiveness of the proposed method.

This article presents a composite adaptive control method to improve the position-tracking performance of an electro-hydraulic system driven by dual constant displacement pump and dual servo motor named as a novel electro-hydraulic system with unknown disturbance. A composite adaptive controller based on backstepping method is designed to estimate the uncertainties of electro-hydraulic control system, including the damping coefficient and elastic modulus. In order to release the persistent excitation condition of conventional adaptive control, which is often infeasible in practice, a prediction error based on the online historical data is used to update the estimated parameters. Furthermore, a disturbance observer is used to estimate the disturbance including the unmeasurable load force, friction and other unmodeled disturbance. The experiment results are provided and compared with other methods to verify the effectiveness of the proposed method, and the results have indicated that the proposed method has a better position-tracking performance with the convergent estimated parameters.

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