The use of free vibration in elastic structure can lead to energy efficient robot locomotion, since it significantly reduces the energy expenditure if properly designed and controlled. However, it is not well understood how to harness the dynamics of free vibration for the robot locomotion, because of the complex dynamics originated in discrete events and energy dissipation during locomotion. From this perspective, the goal of this paper is to propose a design strategy of hopping robot based on elastic curved beams and actuated rotating masses, and identify the minimalistic model that can characterize the basic principle of robot locomotion. Since the robot mainly exhibits vertical hopping, three one-dimensional models are examined that contain different configurations of simple spring-damper-mass components. The real-world and simulation experiments show that one of the models best characterizes the robot hopping, through analyzing the basic kinematics and negative works in actuation. Based on this model, the self-stability of hopping motion under disturbances is investigated and design and control parameters are analyzed for the energy efficient hopping. Additionally, further analyses show that this robot can achieve the energy efficient hopping with the variation in payload, and the source of energy dissipation of the robot hopping is investigated.
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This paper presents the application of operational space control based on hierarchical task optimization for quadrupedal locomotion. We show how the behavior of a complex robotic machine can be described by a simple set of least squares problems with different priorities for motion, torque, and force optimization. Using projected dynamics of floating base systems with multiple contact points, the optimization dimensionality can be reduced or decoupled such that the formulation is purely based on the inversion of kinematic system properties. The present controller is extensively tested in various experiments using the fully torque controllable quadrupedal robot StarlETH. The load distribution is optimized for static walking gaits to improve contact stability and/or actuator efficiency under various terrain conditions. This is augmented with simultaneous joint position and torque limitations as well as with an interpolation method to ensure smooth contact transitions. The same control structure is further used to stabilize dynamic trotting gaits under significant external disturbances such as uneven ground or pushes. To the best of our knowledge, this work is the first documentation of static and dynamic locomotion with pure task-space inverse dynamics (no joint position feedback) control.