Designing Consensus Algorithms for Three-Link Manipulators

We deal with a consensus control problem for a group of three-link manipulators which are networked by digraphs. Assuming that the control inputs of each manipulator are the torques on its links and they are constructed based on weighted difference between its states and those of its neighbor agents, we aim to propose an algorithm on computing the weighting coefficients in the control inputs, so that full consensus is achieved among the manipulators. The control problem is reduced to designing Hurwitz polynomials with complex coefficients. We show that by using Hurwitz polynomials with complex coefficients, a necessary and sufficient condition is obtained for designing the consensus algorithm. Moreover, the discussion is extended to the case of designing convergence rate of consensus. Numerical examples are provided to illustrate the condition and the design algorithms.