The problems of a 7-degree of freedom (DOF) manipulator with rapid and continuous response to uncertain fast-flying objects are addressed: 1) how to effectively solve trajectory planning of the 7-DOF manipulator with multiple criteria; and 2) how to make the 7-DOF manipulator realize the rapid and continuous response to uncertain fast-flying objects. In the proposed approach, based on the trajectory parameterization of the 7-DOF manipulator, a multiobjective teaching-learning-based optimization (MOTLBO) algorithm is adopted to find a close representation of the Pareto optimal set rather than a single solution. As such, an optimal solution can be chosen as digital knowledge information. A new methodology based on a knowledge base representing and learning the operation environment, that is, skill digitization, is presented, which enables the 7-DOF manipulator to realize the rapid and continuous response skill. Simulation and practical testing results of a ping-pong robot validate the feasibility and effectiveness of the proposed approach, in which the online trajectory generation spends only around 1 ms.

The redundant humanoid manipulator has characteristics of multiple degrees of freedom and complex joint structure, and it is not easy to obtain its inverse kinematics solution. The inverse kinematics problem of a humanoid manipulator can be formulated as an equivalent minimization problem, and thus it can be solved using some numerical optimization methods. Biogeography-based optimization (BBO) is a new biogeography inspired optimization algorithm, and it can be adopted to solve the inverse kinematics problem of a humanoid manipulator. The standard BBO algorithm that uses traditional migration and mutation operators suffers from slow convergence and prematurity. A hybrid biogeography-based optimization (HBBO) algorithm, which is based on BBO and differential evolution (DE), is presented. In this hybrid algorithm, new habitats in the ecosystem are produced through a hybrid migration operator, that is, the BBO migration strategy and DE/best/1/bin differential strategy, to alleviate slow convergence at the later evolution stage of the algorithm. In addition, a Gaussian mutation operator is adopted to enhance the exploration ability and improve the diversity of the population. Based on these, an 8-DOF (degree of freedom) redundant humanoid manipulator is employed as an example. The end-effector error (position and orientation) and the ‘away limitation level’ value of the 8-DOF humanoid manipulator constitute the fitness function of HBBO. The proposed HBBO algorithm has been used to solve the inverse kinematics problem of the 8-DOF redundant humanoid manipulator. Numerical simulation results demonstrate the effectiveness of this method.