The paper deals with modeling and design of energy-optimal motion of mechatronic system having less number of actuators than degrees of freedom. Such mechatronic system is termed underactuated. We consider an underactuated mechatronic system modeled a bipedal locomotion robot with 11 degrees of freedom. The system comprises nine links and is used to represent the bipeds planar dynamics in sagittal plane. The bodies are connected by friction-free hinge joints. Its assumed that the control inputs are torque actuators acting only at hip and knee joints. The ankle and the metatarsal joints of the feet are spanned with springs al-lowing discrete switching of their stiffness parameters in accordance to varying constraints imposed on the systems motion. The algorithm has been developed for synthesizing the energy-optimal anthropomorphic motion of the bipedal locomotion system with passively controlled feet and discrete switching of their joint stiffness parameters. Algorithm uses the smoothing cubic splines for approximation of variable functions, inverse dynamics approach, extern penalty functions method, and minimization of the nonsmooth objective function in orthogonal directions. The efficiency of the developed algorithm has been confirmed by simulation of human gait like motions for considered underactuated system. Applications of the results obtained can be found in robotics, bioengineering (prosthetics, orthotics), others
