An analytical solution to the stance dynamics of passive spring-loaded inverted pendulum with damping

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

Approximate analytic solutions to non-symmetric stance trajectories of the passive Spring-Loaded Inverted Pendulum with damping

This paper introduces an accurate yet analytically simple approximation to the stance dynamics of the Spring-Loaded Inverted Pendulum (SLIP) model in the presence of non-negligible damping and non-symmetric stance trajectories. Since the SLIP model has long been established as an accurate descriptive model for running behaviors, its careful analysis is instrumental in the design of successful locomotion controllers. Unfortunately, none of the existing analytic methods in the literature explicitly take damping into account, resulting in degraded predictive accuracy when they are used for dissipative runners. We show that the methods we propose not only yield average predictive errors below 2% in the presence of significant damping, but also outperform existing alternatives to approximate the trajectories of a lossless model. Finally, we exploit both the predictive performance and analytic simplicity of our approximations in the design of a gait-level running controller, demonstrating their practical utility and performance benefits. © 2010 Springer Science+Business Media B.V

Independent estimation of input and measurement delays for a hybrid vertical spring-mass-damper via harmonic transfer functions

System identification of rhythmic locomotor systems is challenging due to the time-varying nature of their dynamics. Even though important aspects of these systems can be captured via explicit mechanics-based models, it is unclear how accurate such models can be while still being analytically tractable. An alternative approach for rhythmic locomotor systems is the use of data-driven system identification in the frequency domain via harmonic transfer functions (HTFs). To this end, the input-output dynamics of a locomotor behavior can be linearized around a stable limit cycle, yielding a linear, time-periodic system. However, few if any model-based or data-driven identification methods for time-periodic systems address the problem of input and measurement delays in the system. In this paper, we focus on data-driven system identification for a simple mechanical system and analyze its dynamics in the presence of input and measurement delays using HTFs. By exploiting the way input delays are modulated by the periodic dynamics, our results enable the separate, independent estimation of input and measurement delays, which would be indistinguishable were the system linear and time invariant. © 2015, IFAG

Control of underactuated planar hexapedal pronking through a dynamically embedded SLIP monopod

Pronking (aka. stotting) is a gait in which all legs are used in synchrony, resulting in long flight phases and large jumping heights that may potentially be useful for mobile robots on rough terrain. Robotic instantiations of this gait suffer from severe pitch instability either due to underactuation, or the lack of sufficient feedback. Nevertheless, the dynamic nature of this gait suggests that the Spring-Loaded Inverted Pendulum Model (SLIP), a very successful predictive model for both natural and robotic runners, would be a good basis for more robust and maneuverable robotic 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 stable and controllable pronking for a planar, underactuated hexapod model. In this context, high-level control of the gait is regulated through speed and height commands to the SLIP template, while the embedding controller based on approximate inverse-dynamics and carefully designed passive dynamics ensures the stability of the remaining degrees of freedom. We show through extensive simulation experiments that unlike existing open-loop alternatives, the resulting control structure provides stability, explicit maneuverability and significant robustness against sensor and actuator noise. ©2010 IEEE

Body mass index and complications following major gastrointestinal surgery: A prospective, international cohort study and meta-analysis

Aim Previous studies reported conflicting evidence on the effects of obesity on outcomes after gastrointestinal surgery. The aims of this study were to explore the relationship of obesity with major postoperative complications in an international cohort and to present a metaanalysis of all available prospective data. Methods This prospective, multicentre study included adults undergoing both elective and emergency gastrointestinal resection, reversal of stoma or formation of stoma. The primary end-point was 30-day major complications (Clavien–Dindo Grades III–V). A systematic search was undertaken for studies assessing the relationship between obesity and major complications after gastrointestinal surgery. Individual patient meta-analysis was used to analyse pooled results. Results This study included 2519 patients across 127 centres, of whom 560 (22.2%) were obese. Unadjusted major complication rates were lower in obese vs normal weight patients (13.0% vs 16.2%, respectively), but this did not reach statistical significance (P = 0.863) on multivariate analysis for patients having surgery for either malignant or benign conditions. Individual patient meta-analysis demonstrated that obese patients undergoing surgery formalignancy were at increased risk of major complications (OR 2.10, 95% CI 1.49–2.96, P < 0.001), whereas obese patients undergoing surgery for benign indications were at decreased risk (OR 0.59, 95% CI 0.46–0.75, P < 0.001) compared to normal weight patients. Conclusions In our international data, obesity was not found to be associated with major complications following gastrointestinal surgery. Meta-analysis of available prospective data made a novel finding of obesity being associated with different outcomes depending on whether patients were undergoing surgery for benign or malignant disease