Control of underactuated planar pronking through an embedded spring-mass Hopper template

Autonomous use of legged robots in unstructured, outdoor settings requires dynamically dexterous behaviors to achieve sufficient speed and agility without overly complex and fragile mechanics and actuation. Among such behaviors is the relatively under-studied pronking (aka. stotting), a dynamic gait in which all legs are used in synchrony, usually resulting in relatively slow speeds but long flight phases and large jumping heights. Instantiations of this gait for robotic systems have been mostly limited to open-loop strategies, suffering from severe pitch instability for underactuated designs due to the lack of active feedback. However, both the kinematic simplicity of this gait and its dynamic nature suggest that the Spring-Loaded Inverted Pendulum model (SLIP) would be a good basis for the implementation of a more robust feedback controller for pronking. In this paper, we describe how template-based control, a controller structure based on the embedding of a simple dynamical "template" within a more complex "anchor" system, can be used to achieve very stable pronking for a planar, underactuated hexapod robot. In this context, high-level control of the gait is regulated through speed and height commands to the SLIP template, while the embedding controller ensures the stability of the remaining degrees of freedom. We use simulation studies to show that unlike existing open-loop alternatives, the resulting control structure provides explicit gait control authority and significant robustness against sensor and actuator noise. © 2010 Springer Science+Business Media, LLC

Parametric Identification of Hybrid Linear-Time-Periodic Systems

In this paper, we present a state-space system identification technique for a class of hybrid LTP systems, formulated in the frequency domain based on input-output data. Other than a few notable exceptions, the majority of studies in the state-space system identification literature (e.g. subspace methods) focus only on LTI systems. Our goal in this study is to develop a technique for estimating time-periodic system and input matrices for a hybrid LTP system, assuming that full state measurements are available. To this end, we formulate our problem in a linear regression framework using Fourier transformations, and estimate Fourier series coefficients of the time-periodic system and input matrices using a least-squares solution. We illustrate the estimation accuracy of our method for LTP system dynamics using a hybrid damped Mathieu function as an example. © 201