Browsing by Subject "Spring-Loaded Inverted Pendulum (SLIP)"

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Open Access
Adaptive control of a one-legged hopping robot through dynamically embedded spring-loaded inverted pendulum template
(2011) Uyanık, İsmail
Practical realization of model-based dynamic legged behaviors is substantially more challenging than statically stable behaviors due to their heavy dependence on second-order system dynamics. This problem is further aggravated by the dif- ficulty of accurately measuring or estimating dynamic parameters such as spring and damping constants for associated models and the fact that such parameters are prone to change in time due to heavy use and associated material fatigue. In the first part of this thesis, we present an on-line, model-based adaptive control method for running with a planar spring-mass hopper based on a once-per-step parameter correction scheme. Our method can be used both as a system identifi- cation tool to determine possibly time-varying spring and damping constants of a miscalibrated system, or as an adaptive controller that can eliminate steady-state tracking errors through appropriate adjustments on dynamic system parameters. We use Spring-Loaded Inverted Pendulum (SLIP) model, which is the mostly used, effective and accurate descriptive tool for running animals of different sizes and morphologies, to evaluate our algorithm. We present systematic simulation studies to show that our method can successfully accomplish both accurate tracking and system identification tasks on this model. Additionally, we extend our simulations to Torque-Actuated Dissipative Spring-Loaded Inverted Pendulum (TD-SLIP) model towards its implementation on an actual robot platform. In the second part of the thesis, we present the design and construction of a onelegged hopping robot we built to test the practical applicability of our adaptive control algorithm. We summarize the mechanical, electronics and software design of our robot as well as the performed system identification studies to calibrate the unknown system parameters. Finally, we investigate the robot’s motion achieved by a simple torque-actuated open loop controller.
Open Access
Identification and stability analysis of periodic motions for a planar legged runner with a rigid body and a compliant leg
(2013) Bayır, Güneş
The Spring-Loaded Inverted Pendulum (SLIP) model is an extensively used and fundamental template for modeling human and animal locomotion. Despite its wide use, the SLIP is a very simple model and considering the effects of body dynamics only as a point mass. Although the assumption of a point mass for the upper body simplifies system dynamics, it prevents us from performing detailed analysis for more realistic robot platforms with upper trunks. Hence, we consider an extension to the classic SLIP model to include the upper body dynamics in order to better understand human and animal locomotion. Due to its coupled rotational dynamics, extending the SLIP model to the Body-Attached Spring-Loaded Inverted Pendulum (BA-SLIP) brings additional difficulties in the analysis process, making it more difficult to obtain analytical solutions. Consequently, simulations have been used to reveal the periodic structure behind locomotion with this model, and to find fixed points of discretized system dynamics. These fixed points correspond to periodic motions of the system and are important in designing controllers since they are used as steady-state control targets for most applications. The main concern of this thesis is to find fixed points of the BA-SLIP model and to investigate the dimension of the fixed point manifold. We performed extensive simulation studies to find fixed points of the system and the properties of the underlying space with a PD controller. Our simulations revealed the existence of periodic gaits, in which the upper body should be downward oriented for stable locomotion. Additionally, a region of stability is found such that the model sustains periodic gaits when it stays inside this region. Finally, we show that fixed points for running with upright body orientation are unstable when system dynamics are regulated with a constant parameter controller. We also present some simulation results which indicate the existence of stable periodic motions when controllers with time varying parameters, that use current state information, are used.