Analysis and Control of a Dissipative Spring-Mass Hopper with Torque Actuation

It has long been established that simple spring-mass models can accurately represent the dynamics of legged locomotion. Existing work in this domain, however, almost exclusively focuses on the idealized Spring-Loaded Inverted Pendulum (SLIP) model and neglects passive dissipative effects unavoidable in any physical robot or animal. In this paper, we extend on a recently proposed analytic approximation to the stance trajectories of a dissipative SLIP model to analyze stability properties of a planar hopper with a single rotary actuator at the hip. We first describe how a suitably chosen torque controller can compensate for damping losses, maintaining the same energy level across strides and hence reducing the return map to a single dimension. We then identify and characterize equilibrium points for this return map under a fixed leg placement policy and show that "uncontrolled" asymptotic stability is feasible for this energy-regulated system. Subsequent presentation of simulation evidence establishes that the predictions of this approximate model are consistent with the exact plant model. The paper concludes with the application of our energy-regulation scheme to the design of a task-level gait controller that uses explicit leg placement commands in conjunction with the hip torque.


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There are limitations on the extent to which manually constructed mathematical models can capture relevant aspects of legged locomotion. Even simple models for basic behaviours such as running involve non-integrable dynamics, requiring the use of possibly inaccurate approximations in the design of model-based controllers. In this study, we show how data-driven frequency domain system identification methods can be used to obtain input–output characteristics for a class of dynamical systems around their limit...
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In the literature, spring-loaded inverted pendulum (SLIP) model with damping has been used to represent the dynamics of legged locomotion. Based on a planar version of the model, a group of existing work focus on controlling the hip torque (between body and leg) in stance and in flight phases to generate stable planar locomotion (the SLIP-T model). Most of these studies assume an infinite body inertia such that the applied hip torque does not affect the attitude of the robot body. In practice, for any finit...
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© 2022 IOP Publishing Ltd.The spring-loaded inverted pendulum model has been one of the most studied conceptual models in the locomotion community. Even though it can adequately explain the center of mass trajectories of numerous legged animals, it remains insufficient in template-based control of complex robot platforms, being unable to capture additional dynamic characteristics of locomotion exhibited in additional degrees of freedom such as trunk pitch oscillations. In fact, analysis of trunk behavior du...
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Legged robots have complex architecture because of their nonlinear dynamics and unpredictable ground contact characteristics. They can be also dynamically stable and exhibit dynamically dexterous behaviors like running, jumping, flipping which require complex plant models that may sometimes be difficult to build. In this thesis, we focused on half circular compliant legged monopod that can be considered as a reduced-order dynamical model for the hexapod robot, called RHex. The main objective of this thesis ...
Citation Formats
M. M. Ankaralı and U. Saranlı, “Analysis and Control of a Dissipative Spring-Mass Hopper with Torque Actuation,” ROBOTICS: SCIENCE AND SYSTEMS VI, pp. 41–48, 2011, Accessed: 00, 2020. [Online]. Available: