Browsing by Subject "Legged locomotion"

Now showing 1 - 11 of 11

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
Approximate analytic solutions to non-symmetric stance trajectories of the passive Spring-Loaded Inverted Pendulum with damping
(Springer Netherlands, 2010) Saranlı U.; Arslan, Ö.; Ankaralı, M. M.; Morgül, Ö.
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.
Open Access
An approximate stance map of the spring mass hopper with gravity correction for nonsymmetric locomotions
(IEEE, 2009) Arslan, Ömür; Saranlı, Uluç; Morgül, Ömer
The Spring-Loaded Inverted Pendulum (SLIP) model has long been established as an effective and accurate descriptive model for running animals of widely differing sizes and morphologies, while also serving as a basis for several hopping robot designs. Further research on this model led to the discovery of several analytic approximations to its normally nonintegrable dynamics. However, these approximations mostly focus on steady-state running with symmetric trajectories due to their linearization of gravitational effects, an assumption that is quickly violated for locomotion on more complex terrain wherein transient, non-symmetric trajectories dominate. In this paper, we introduce a novel gravity correction scheme that extends on one of the more recent analytic approximations to the SLIP dynamics and achieves good accuracy even for highly non-symmetric trajectories. Our approach is based on incorporating the total effect of gravity on the angular momentum throughout a single stance phase and allows us to preserve the analytic simplicity of the approximation to support our longer term research on reactive footstep planning for dynamic legged locomotion. We compare the performance of our method in simulation to two other existing analytic approximations and show that it outperforms them for most physically realistic non-symmetric SLIP trajectories while maintaining the same accuracy for symmetric trajectories. © 2009 IEEE.
Open Access
Control and system identification of legged locomotion with recurrent neural networks
(2022-06) Çatalbaş, Bahadır
In recent years, robotic systems have gained massive popularity in the industry, military, and daily use for various purposes, thanks to advancements in artificial intelligence and control theory. As an exciting sub-branch of robotics with their differences and opportunities, legged robots have the potential to diversify and spread the use of robotic systems to new fields. Especially, legged locomotion is a desirable ability for mechanical systems where agile mobility and a wide range of motions are required to fulfill the designated task. On the other hand, unlike wheeled robots, legged robot platforms have a hybrid dynamical structure consisting of the flight and contact phases of the legs. Since the hybrid dynamical structure and nonlinear dynamics in the robot model make it challenging to apply control and perform system identification for them, various methods are proposed to solve these problems in the literature. This thesis focuses on developing new neural network-based techniques to apply control and system identification to legged locomotion so that robotic platforms can be designed to move efficiently as animal counterparts do in nature. In the first part of this thesis, we present our works on neural network-based controller development and evaluation studies for bipedal locomotion. In detail, neural controllers, in which long short-term memory (LSTM) type of neuron models are employed at recurrent layers, are utilized in the feedback and feedforward paths. Supervised learning data sets are produced using a biped robot platform controlled by a central pattern generator to train these neural networks. Then, the ability of the neural networks to perform stable gait by controlling the robot platform is assessed under various ground conditions in the simulation environment. After that, the stable walking generation capacity of the neural networks and the central pattern generators are compared with each other. It is shown that the proposed neural networks are more successful gait controllers than the central pattern generator, which is employed to generate data sets used in training. In the second part, we present our studies on the end-to-end usage of neural networks in system identification for bipedal locomotion. To this end, supervised learning data sets are produced using a biped robot model controlled by a central pattern generator. After that, neural networks are trained under series-parallel and parallel system identification schemes to approximate the input-output relations of the biped robot model. In detail, different neural models and neural network architectures are trained and tested in an end-to-end manner. Among neuron models, LeakyReLU and LSTM are found as the most suitable feedforward and recurrent neuron types for system identification, respectively. Moreover, neural network architecture consisting of recurrent and feedforward layers is found to be efficient in terms of learnable parameter numbers for system identification of the biped robot model. The last part discusses the results obtained in the control and system identification studies using neural networks. In the light of acquired results, neural networks with recurrent layers can apply control and systems identification in an end-to-end manner. Finally, the thesis is completed by discussing possible future research directions with the obtained results.
Open Access
Identification of a vertical hopping robot model via harmonic transfer functions
(Sage Publications Ltd., 2016) Uyanık, İ.; Ankaralı, M. M.; Cowan, N. J.; Saranlı U.; Morgül, Ö.
A common approach to understanding and controlling robotic legged locomotion is the construction and analysis of simplified mathematical models that capture essential features of locomotor behaviours. However, the representational power of such simple mathematical models is inevitably limited due to the non-linear and complex nature of biological locomotor systems. Attempting to identify and explicitly incorporate key non-linearities into the model is challenging, increases complexity, and decreases the analytic utility of the resulting models. In this paper, we adopt a data-driven approach, with the goal of furnishing an input–output representation of a locomotor system. Our method is based on approximating the hybrid dynamics of a legged locomotion model around its limit cycle as a Linear Time Periodic (LTP) system. Perturbing inputs to the locomotor system with small chirp signals yield the input–output data necessary for the application of LTP system identification techniques, allowing us to estimate harmonic transfer functions (HTFs) associated with the local LTP approximation to the system dynamics around the limit cycle. We compare actual system responses with responses predicted by the HTF, providing evidence that data-driven system identification methods can be used to construct models for locomotor behaviours.
Open Access
Identification of legged locomotion via model-based and data-driven approaches
(2017-05) Uyanık, İsmail
Robotics is one of the core areas where the bioinspiration is frequently used to design various engineered morphologies and to develop novel behavioral controllers comparable to the humans and animals. Biopinspiration requires a solid understanding of the functions and concepts in nature and developing practical engineering applications. However, understanding these concepts, especially from a human or animal point of view, requires the signi cant use of mathematical modeling and system identi cation methods. In this thesis, we focus on developing new system identi cation methods for understanding legged locomotion models towards building better legged robot platforms that can locomote e ectively as their animal counterparts do in nature. In the rst part of this thesis, we present our e orts on experimental validation of the predictive performance of mechanics-based mathematical models on a physical one-legged hopping robot platform. We extend upon a recently proposed approximate analytical solution developed for the lossy spring{mass models for a real robotic system and perform a parametric system identi cation to carefully identify the system parameters in the proposed model. We also present our assessments on the predictive performance of the proposed approximate analytical solution on our one-legged hopping robot data. Experiments with di erent leg springs and cross validation of results yield that our approximate analytical solutions provide a su ciently accurate representation of the physical robot platform. In the second part, we adopt a data-driven approach to obtain an input{output representation of legged locomotion models around a stable periodic orbit (a.k.a. limit cycle). To this end, we rst linearize the hybrid dynamics of legged locomotor systems around a limit cycle to obtain a linear time periodic (LTP) system representation. Hence, we utilize the frequency domain analysis and identi cation methods for LTP systems towards the identi cation of input{output models (harmonic transfer functions) of legged locomotion. We propose simulation experiments on simple legged locomotion models to illustrate the prediction performance of the estimated input{output models. Finally, the third part considers estimating state space models of legged locomotion using input{output data. To accomplish this, we rst propose a state space identi cation method to estimate time periodic state and input matrices of a hybrid LTP system under full state measurement assumption. We then release this assumption and proceed with subspace identi cation methods to estimate LTP state space realizations for unknown stable LTP systems. We utilize bilinear (Tustin) transformation and frequency domain lifting methods to generalize our solutions to di erent LTP system models. Our results provide a basis towards identi cation of state space models for legged locomotion.
Open Access
Independent estimation of input and measurement delays for a hybrid vertical spring-mass-damper via harmonic transfer functions
(IFAC, 2015-06) Uyanık, İsmail; Ankaralı, M. M.; Cowan, N. J.; Saranlı, U.; Morgül, Ömer; Özbay, Hitay
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.
Open Access
Model-based identification and control of a one-legged hopping robot
(2018-01) Orhon, Hasan Eftun
Spring-mass models are well established tools for the analysis and control of legged locomotion. Among the alternatives, spring-loaded inverted pendulum (SLIP) model has shown to be a very accurate descriptor of animal locomotion. Despite its wide use, the SLIP model includes non-integrable stance dynamics that prevent analytical solutions for its equations of motion. Fortunately, there are approximate analytical solutions for different SLIP variants. However, the practicality of such approximations are mostly tested on simulation studies with a few notable exceptions. This thesis extends upon a recent approximation to a hip torque actuated dissipative SLIP (TD-SLIP) model that uses torque actuation to compensate for energy losses. Systematic experiments for careful assessment of the predictive performance of the approximate analytical solution is presented on a well-instrumented one-legged hopping robot which is revised to enhance compatibility and accuracy of the system. Electronic structure of the robot is modified according to TD-SLIP model such that robot uses a real-time operating system to increase processing speed. Using the parameters and results generated by the predictive performance of the approximate analytical solution, a model-based controller is designed and implemented on the robot platform to generate a stable closed-loop running behaviour on the one legged hoping robot platform. In addition, ground reaction forces during the stance phase on the experimental platform is investigated and compared with the human running and the traditional SLIP model data to understand if torque-actuated models approximate natural locomotion better than traditional model.
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
A new footstep planning for SLIP and TD-SLIP models
(2020-12) İslamoğlu, Serkan
Spring Loaded Inverted Pendulum (SLIP) is a well-known model and an accurate descriptive tool, which can scientifically represent the dynamics of the legged locomotion. Torque actuated Dissipative SLIP (TD-SLIP), on the other hand, is fundamentally an enhanced version of the SLIP model. Inclusion of more realistic damping model and the hip torque actuation has led the researchers to develop a sufficiently better analytic approximation. This thesis proposes a new methodology to achieve footstep planning on the SLIP and TD-SLIP models, distinctly. It contributes a novel planning algorithm by utilising the constructed touchdown-totouchdown map, and a novel recursive function to plan and execute the planning. The thesis provides a background information about the modelling and simulation of both of the used models, and an auxiliary function, which administers a derivative-free method to calculate the minimum of an input function. After defining the problems and the corresponding proposed solutions, the foundations of the preparation phase is established. This phase is fundamentally constructed to accumulate required information for the algorithm implementation and simulation phase. The main phase consists of subsections, which can be composed of the combination of following properties; planning type, as online and offline, policy type; as forward and backwards and output type; as based on distance or based on minimum step count. According to the stated problem, the planning is successfully realised not only for a single desired distance, but also an array of waypoints. In addition to this, the presented illustrations of different initial states show that the planning can also be constructed via any different initial touchdown state. Therefore, the obtained results are quite promising, since all of the cases and their combinations successfully reach the destinations with a negligible error value, which is less than 1%. Although, the offline planning type provides the results in a rapid way, the obtained data to use the plan requires much more space, which also increases dramatically when the step count (level) is incremented. In addition to this, the forward planning is faster than the backwards one, but they both generate very similar results.
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.