This brief presents the real-time dynamic Dubins-Helix (RDDH) method for trajectory smoothing, which consists of Dubins-Helix trajectory generation and pitch angle smoothing. The generated 3-D trajectory is called the RDDH trajectory. On one hand, the projection of 3-D trajectory on the horizontal plane is partially generated by Dubins path planner such that the curvature radius constraint is satisfied. On the other hand, the Helix curve is constructed to satisfy the pitch angle constraint, even in the case that the initial and final poses are close. Furthermore, by analyzing the relationship between the parameters and the effectiveness of the RDDH trajectory, the smoothing algorithm is designed to obtain appropriate parameters for a shorter and smoother trajectory. In the end, the numerical results show the proposed method can generate an effective trajectory under diverse initial conditions and achieve real-time computation.

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Vibration has a great influence on the working accuracy of flexible-link manipulators. In this paper, an online trajectory planning method for the flexible-link manipulator is proposed to suppress the vibration. Firstly, the vibration dynamic model of planar flexible-link manipulator is established, and the actual vibration trajectory of manipulator is solved by reasonable simplification. Then, taking residual energy of vibration as an objective function, the optimizer based on Particle Swarm Optimization(PSO) intelligent search algorithm is employed to search the motion trajectory of the manipulator with the best vibration suppression effect. Finally, the optimizer based on back propagation neural networks(BPNN) is employed instead of PSO optimizer to generate manipulator motion trajectory rapidly, and the optimal trajectory database searched by PSO optimizer is used to train BPNN. Simulation results show that this method can generate the trajectory rapidly and suppress the vibration effectively, and can be applied to the online trajectory planning of flexible manipulator.