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In this paper a hopping robot motion with offset mass is discussed. A mathematical model has been considered and an efficient single layered neural network has been developed to suit to the dynamics of the hopping robot, which ensures guaranteed tracking performance leading to the stability of the otherwise unstable system. The neural network takes advantage of the robot regressor dynamics that expresses the highly nonlinear robot dynamics in a linear form in terms of the known and unknown robot parameters. Time delays in the control mechanism play a vital role in the motion of hopping robots. The present work also enables us to estimate the maximum time delay admissible with out losing the guaranteed tracking performance. Further this neural network does not require offline training procedures. The salient features are highlighted by appropriate simulations.

This paper explores the vertical upward jumping of a planar biped. There are two stance phases and one flight phase in the jump. One stance phase takes place before the flight phase, another one after the flight phase. The stance phase before the flight phase is decomposed into several parts: A crouching, a thrust at the knees, a rotation of both feet (massless) around their toes. The second stance phase (after the flight phase) starts with a touchdown of the toes. It consists of a feet rotation, a touchdown of the whole soles and finally of a straightening up movement of the biped. A mathematical model for this kind of jump is developed. Torques are applied at the hip, knee and ankle joints. The control algorithm is designed to ensure the jump of the biped. The synthesis of the jumping process is supported by simulation, which gives consistent results with human data from biomechanical literature. The stick diagram of the jump derived from simulation results seems natural for the human jumping.