This paper investigates the efficiency of a 2-period limit-cycle gait from the kinetic energy viewpoint. First, we formulate a steady 2-period gait by using simple recurrence formulas for the kinetic energy of an asymmetric rimless wheel. Second, we theoretically show that, in the case that the mean value of the hip angle is constant, the generated 2-period steady gait is less efficient than a 1-period symmetric one in terms of kinetic energy. Furthermore, we show that the symmetric gait is not always optimal from another viewpoint. Finally, we investigate the validity of the derived theory through numerical simulations of virtual passive dynamic walking using a compass-like biped robot.
This paper is devoted to control of nonholonomic Hamiltonian systems with affine constraints (NHSAC). We first sum up some concepts on nonholonomic affine constraints and the HNSAC. Next, we derive two versions of generalized canonical transformations for the NHSAC; the one transforms the NHSAC into a simpler system that has the structure of the extended chained form, the other changes the Hamiltonian of the NHSAC in order to make the NHSAC satisfy passivity. We then design a control algorithm based on passivity for a physical example, a coin on a rotating table. Finally, some simulations are carried out to verify the proposed method.
Several meta-heuristic methods such as genetic algorithms and particle swarm optimization (PSO) have been applied for solving multi-objective optimization problems, and have been observed to be useful for generating the whole Pareto optimal solutions. In this research, we propose a new method of multi-objective particle swarm optimization by using generalized data envelopment analysis (GDEA) in order to improve the convergence and the diversity when searching for the solutions as well as to decide easily parameters in PSO. In addition, we investigate the effectiveness of the proposed PSO method using GDEA through some numerical examples.