Browsing by Subject "SLIP"

Now showing 1 - 3 of 3

Open Access
An analytical solution to the stance dynamics of passive spring-loaded inverted pendulum with damping
(World Scientific, 2009-09) Ankaralı, M. M.; Arslan, Ömür; Saranlı, Uluç
The Spring-Loaded Inverted Pendulum (SLIP) model has been established both as a very accurate descriptive tool as well as a good basis for the design and control of running robots. In particular, approximate analytic solutions to the otherwise non integrable dynamics of t his model provide principled ways in which gait controllers can be built, yielding invaluable insight into their stability properties. However, most existing work on the SLIP model completely disregards the effects of damping, which often cannot be neglected for physical robot platforms. In this paper, we introduce a new approximate analytical solution to the dynamics of this system that also takes into account viscous damping in the leg. We compare both the predictive performance of our approximation as well as the tracking performance of an associated deadbeat gait controller to similar existing methods in the literature and show t hat it significantly outperforms them in the presence of damping in the leg.
Open Access
Neural network based estimator and controller for SLIP and TD-SLIP monopod robots
(2020-12) Öztürk, Ahmet Safa
Using spring loaded inverted pendulum models for legged locomotion, a wide range of applications can be developed for mobile robots. Spring loaded inverted pendulum model brings new challenges of solving the forward and inverse kinematic maps. Although exact solutions of SLIP model cannot be obtained analytically due to nonintegrability of stance dynamics, approximate analytical solutions are proposed to overcome these challenges in many of the previous studies. An alternative to approximate analytical solutions, neural network based forward and inverse kinematic map predictions can also be used. We used neural networks to design estimators and controllers, as forward and inverse kinematic map predictors. Required datasets are generated with existing simulations for spring loaded inverted pendulum models and datasets are constructed by including the determined inputs and outputs for the neural networks. Neural networks are designed by using different architectures and properties. Training results of estimators for predicting the goal state in the apex return map are reported for different configurations. Trained controllers are verified using the simulation and verified controllers are tested under the different run scenarios. By comparing all of the results, potential of the neural network based estimators and controllers is discussed.
Open Access
On the periodic gait stability of a multi-actuated spring-mass hopper model via partial feedback linearization
(Springer Netherlands, 2017) Hamzaçebi, H.; Morgül, Ö.
Spring-loaded inverted pendulum (SLIP) template (and its various derivatives) could be considered as the mostly used and widely accepted models for describing legged locomotion. Despite their simple nature, as being a simple spring-mass model in dynamics perspective, the SLIP model and its derivatives are formulated as restricted three-body problem, whose non-integrability has been proved long before. Thus, researchers proceed with approximate analytical solutions or use partial feedback linearization when numerical integration is not preferred in their analysis. The key contributions of this paper can be divided into two parts. First, we propose a dissipative SLIP model, which we call as multi-actuated dissipative SLIP (MD-SLIP), with two extended actuators: one linear actuator attached serially to the leg spring and one rotary actuator attached to hip. The second contribution of this paper is a partial feedback linearization strategy by which we can cancel some nonlinear dynamics of the proposed model and obtain exact analytical solution for the equations of motion. This allows us to investigate stability characteristics of the hopping gait obtained from the MD-SLIP model. We illustrate the applicability of our solutions with open-loop and closed-loop hopping performances on rough terrain simulations. © 2017, Springer Science+Business Media Dordrecht.