An optimization model is developed in this paper for the joint trajectories of a hopping robot with a four-bar linkage leg. The dynamic behaviour of the one-legged robot is investigated during the stance and swing phases, and their impacts on gait planning are analysed. Certain constraints characterizing the continuous and cyclic motion of the robot are obtained. The optimization model is solved for the minimum torque and maximum velocity objective functions separately, and the results are compared with those in nature.

Increasing the energy autonomy of a hopping one-legged robot is studied in this paper. For a particular passive gait, of all those possible, the energy dissipated per unit length of travel is shown to be less than for any other gait. This optimal gait is identified analytically, by exploiting the commonly used SLIP model to simplify real robot dynamics. Both mechanical and electrical losses are considered. The accuracy of the optimal gait analytical prediction is evaluated by a numerical analysis of a realistic robot model. Finally, restrictions imposed on executing the optimal gait due to motor limitations are studied.