A Control Algorithm for a 3D Hopping Machine

The paper addresses several control problems for a three-dimensional hopping machine. The machine consists of a ponderable torso and an imponderable leg. The leg is a kinematic chain with joints allowing rotation and translation. The leg is attached at the torso's center of mass. The force in the leg is developed by a linear spring. A control system is synthesized within the framework of a periodic linear quadratic problem. The efficiency of the controller is exemplified by a case where the hopper changes the direction of its motion