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We describe a technique to generate motion segments, for a Luxo hopping robot by solving an optimal control problem using exact analytic gradients of the cost function. Analytic gradients are required to solve the optimal control problem reliably; obtaining them is made possible by a hybrid recursive algorithm that calculates the system dynamics and its exact derivatives. Each motion segment, or primitive, is determined by a unique cost function, so that a complete movement is created from the robot model, the customized optimal control problem, and the objective function, without need for detailed path planning by a person. Once the primitives are generated, they are used to control an experimental robot as it performs the motion in the primitive. The problem formulation takes into account limitations such as torque and velocity limits of the motors on the experimental robot.