The Fluid Field SLIP Model: Terrestrial-Aquatic Dynamic Legged Locomotion

2021 ◽  
Author(s):  
Max P. Austin ◽  
Jonathan E. Clark
Keyword(s):  
Legged Locomotion ◽  
Slip Model ◽  
Fluid Field

A Simple Analytical Tool for Legged Robot Design

2012 ◽  
Author(s):  
Zhuohua Shen ◽  
Justin Seipel
Keyword(s):  
Analytical Solutions ◽  
Inverted Pendulum ◽  
Legged Locomotion ◽  
Robot Design ◽  
Slip Model ◽  
Legged Robot ◽  
Biologically Relevant ◽  
Analytical Approximations ◽  
Energy Conserving ◽  
Spring Loaded Inverted Pendulum

Although legged locomotion is better at tackling complicated terrains compared with wheeled locomotion, legged robots are rare, in part, because of the lack of simple design tools. The dynamics governing legged locomotion are generally nonlinear and hybrid (piecewise-continuous) and so require numerical simulation for analysis and are not easily applied to robot designs. During the past decade, a few approximated analytical solutions of Spring-Loaded Inverted Pendulum (SLIP), a canonical model in legged locomotion, have been developed. However, SLIP is energy conserving and cannot predict the dynamical stability of real-world legged locomotion. To develop new analytical tools for legged robot designs, we first analytically solved SLIP in a new way. Then based on SLIP solution, we developed an analytical solution of a hip-actuated Spring-Loaded Inverted Pendulum (hip-actuated-SLIP) model, which is more biologically relevant and stable than the canonical energy conserving SLIP model. The analytical approximations offered here for SLIP and the hip actuated-SLIP solutions compare well with the numerical simulations of each. The analytical solutions presented here are simpler in form than those resulting from existing analytical approximations. The analytical solutions of SLIP and the hip actuated-SLIP can be used as tools for robot design or for generating biological hypotheses.

Modeling, Analysis, and Control of SLIP Running on Dynamic Platforms

2020 ◽  
Vol 1 (2) ◽  
Author(s):  
Amir Iqbal ◽  
Zhu Mao ◽  
Yan Gu
Keyword(s):  
Rigid Body ◽  
Dynamic Model ◽  
Control Strategy ◽  
Initial Conditions ◽  
Legged Locomotion ◽  
Force Model ◽  
Slip Model ◽  
Modeling Analysis ◽  
And Control ◽  
Slip Motion

Abstract The complex dynamic behaviors of legged locomotion on stationary terrain have been extensively analyzed using a simplified dynamic model called the spring-loaded inverted pendulum (SLIP) model. However, legged locomotion on dynamic platforms has not been thoroughly investigated even by using a simplified dynamic model such as SLIP. In this paper, we present the modeling, analysis, and control of a SLIP model running on dynamic platforms. Three types of dynamic platforms are considered: (a) a sinusoidally excited rigid-body platform; (b) a spring-supported rigid-body platform; and (c) an Euler–Bernoulli beam. These platforms capture some important domains of real-world locomotion terrain (e.g., harmonically excited platforms, suspended floors, and bridges). The interaction force model and the equations of motion of the SLIP-platform systems are derived. Numerical simulations of SLIP running on the three types of dynamic platforms reveal that the platform movement can destabilize the SLIP even when the initial conditions of the SLIP motion are within the domain of attraction of its motion on flat, stationary platforms. A simple control strategy that can sustain the forward motion of a SLIP on dynamic platforms is then synthesized. The effectiveness of the proposed control strategy in sustaining SLIP motion on dynamic platforms is validated through simulations.

A Spring-Mass Model of Locomotion With Full Asymptotic Stability

2011 ◽  
Author(s):  
Zhuohua Shen ◽  
Justin Seipel
Keyword(s):  
Mass Velocity ◽  
Inverted Pendulum ◽  
Center Of Mass ◽  
Legged Locomotion ◽  
Reduced Model ◽  
Asymptotically Stable ◽  
Slip Model ◽  
Mass Model ◽  
Improved Stability ◽  
Spring Loaded Inverted Pendulum

A reduced model of legged locomotion, called the Spring Loaded Inverted Pendulum (SLIP) has previously been developed to predict the dynamics of locomotion. However, due to energy conservation, the SLIP model can only be partially asymptotically stable in the center-of-mass velocity. The more recently developed Clock-Torqued Spring Loaded Inverted Pendulum (CT-SLIP) model is fully asymptotically stable, and has a significantly larger stability basin than SLIP, but requires more than twice as many parameters. To more completely explore the parameter space and understand the reason for improved stability, we develop and analyze a further reduced model called the Forced-Damped Spring Loaded Inverted Pendulum (FD-SLIP) model.

A Spring-Mass Model of Locomotion With Full Asymptotic Stability

2011 ◽  
Author(s):  
Zhuohua Shen ◽  
Justin Seipel
Keyword(s):  
Inverted Pendulum ◽  
Center Of Mass ◽  
Legged Locomotion ◽  
Human Locomotion ◽  
Whole Body ◽  
Slip Model ◽  
Mass Model ◽  
Energy Conserving ◽  
Spring Loaded Inverted Pendulum ◽  
Passive Model

The concept of passive dynamic walking and running [5] has demonstrated that a simple passive model can represent the dynamics of whole-body human locomotion. Since then, many passive models were developed and studied: [3,1,2,11]. The later developed Spring-Loaded Inverted Pendulum (SLIP) [1, 4, 11, 2] exhibits stable center of mass (CoM) motions just by resetting the landing angle at each touch down. Also, compared to SLIP, a SLIP-like model with simple flight leg control is better at resisting perturbations of the angle of velocity but not the magnitude [11, 2, 7]. Energy conserving models explain much about whole-body locomotion. Recently, there has been investigations of modified spring-mass models capable of greater stability, like that of animals and robots [9, 10, 8, 12]. Inspired by RHex [6], the Clock-Torqued Spring-Loaded Inverted Pendulum (CT-SLIP) model [9] was developed, and has been used to explain the robust stability of animal locomotion [12]. Here we present a model (mechanism) simpler than CT-SLIP called Forced-Damped SLIP (FD-SLIP) that can attain full asymptotically stability of the CoM during locomotion, and is capable of both walking and running motions. The FD-SLIP model, having fewer parameters, is more accessible and easier to analyze for the exploration and discovery of principles of legged locomotion.

A Simple Model for Body Pitching Stabilization

2013 ◽  
Author(s):  
Yuhang Che ◽  
Zhuohua Shen ◽  
Justin Seipel
Keyword(s):  
Asymptotic Stability ◽  
Energy Efficient ◽  
Time Delays ◽  
Inertial Frame ◽  
Legged Locomotion ◽  
Stable Region ◽  
Model Parameters ◽  
Slip Model ◽  
Robotic Control ◽  
Body Frame

Pitching dynamics are an important component of the dynamics of legged locomotion. We develop an energy-open pitching stabilization model to achieve full asymptotic stability of locomotion. This model is called the pitched-actuated Spring-Loaded Inverted Pendulum (pitched-actuated SLIP) model. It extends the conservative SLIP model to include a trunk as well as net nonzero hip torque and leg damping. The hip torque is governed by a proportional and derivative controller which uses only the angle between body and leg as feedback during stance. During the swing phase of the leg, inertial frame feedback is used to reset the leg to a fixed angle in space. The use of body-frame feedback in stance is thought to be relevant to biology and robotic control, as time delays and uncertainty in inertial frame feedback could be challenging in stance. Further, this method of control during stance could be implemented in a neural feedforward manner using antagonistic pairs of muscle or muscle-like actuators around the hip joint. This model of pitching dynamics exhibits full asymptotic stability over a range of model parameters. Further, derivative control significantly impacts disturbance mitigation. Periodic locomotion solutions of the model with large energy cost tend to be unstable. Whereas, the most energy efficient locomotion solutions found tend to be within the stable region of the parameter space. The correlation between energy efficiency and stability found in this model may have significant implications for locomotion with pitching.

A Piecewise-Linear Approximation of the Canonical Spring-Loaded Inverted Pendulum Model of Legged Locomotion

2016 ◽  
Vol 11 (1) ◽  
Author(s):  
Zhuohua Shen ◽  
Justin Seipel
Keyword(s):  
Closed Form ◽  
Inverted Pendulum ◽  
Piecewise Linear ◽  
Closed Form Solution ◽  
Legged Locomotion ◽  
Form Solution ◽  
Piecewise Linear Approximation ◽  
Computational Time ◽  
Slip Model ◽  
Spring Loaded Inverted Pendulum

Here, we introduce and analyze a novel approximation of the well-established and widely used spring-loaded inverted pendulum (SLIP) model of legged locomotion, which has made several validated predictions of the center-of-mass (CoM) or point-mass motions of animal and robot running. Due to nonlinear stance equations in the existing SLIP model, many linear-based systems theories, analytical tools, and corresponding control strategies cannot be readily applied. In order to provide a significant simplification in the use and analysis of the SLIP model of locomotion, here we develop a novel piecewise-linear, time-invariant approximation. We show that a piecewise-linear system, with the only nonlinearity due to the switching event between stance and flight phases, can predict all the bifurcation features of the established nonlinear SLIP model over the entire three-dimensional model parameter space. Rather than precisely fitting only one particular solution, this approximation is made to quantitatively approximate the entire solution space of the SLIP model and capture all key aspects of solution bifurcation behavior and parametric sensitivity of the original SLIP model. Further, we provide an entirely closed-form solution for the stance trajectory as well as the system states at the end of stance, in terms of common functions that are easy to code and compute. Overall, the closed-form solution is found to be significantly faster than numerical integration when implemented using both matlab and c++. We also provide a closed-form analytical stride map, which is a Poincaré return section from touchdown (TD) to next TD event. This is the simplest closed-form approximate stride mapping yet developed for the SLIP model, enabling ease of analysis and numerical coding, and reducing computational time. The approximate piecewise-linear SLIP model presented here is a significant simplification over previous SLIP-based models and could enable more rapid development of legged locomotion theory, numerical simulations, and controllers.

Decoupled Stabilization of Spring-Mass Rigid-Body Locomotion

2011 ◽  
Author(s):  
Huan Hu ◽  
Justin Seipel
Keyword(s):  
Legged Locomotion ◽  
Humanoid Robots ◽  
The Body ◽  
Point Mass ◽  
Slip Model ◽  
In Series ◽  
General Force ◽  
Trunk Stabilization ◽  
Simple Models

Stable and reliable legged locomotion is critical for humans and humanoid robots. In the study of legged locomotion, simple models consisting of point-mass bodies and massless legs with telescoping actuators have been insightful. Several variants have been used, including the telescoping leg as a general force actuator [1], a simple passive linear or nonlinear spring [2], and a spring in series with a general force actuator [3]. These models serve as analogs that simplify the problem of understanding the mechanics of legged locomotion of real animals. One of defects of these simple models is the representation of the body by a point mass. Hence, trunk stabilization is not addressed. Nevertheless, this is a major problem in human and humanoid locomotion. In this study we propose a novel decoupled strategy to stabilize the trunk. First, we describe how this decoupled strategy works theoretically. Then, we present a case study based on the CT-SLIP model. Finally, we summarize the work and its expected impacts.

A Spring-Loaded Inverted Pendulum Locomotion Model With Radial Forcing

2012 ◽  
Author(s):  
Peter Larson ◽  
Justin Seipel
Keyword(s):  
Parameter Space ◽  
Inverted Pendulum ◽  
Legged Locomotion ◽  
Radial Force ◽  
Slip Model ◽  
Forcing Function ◽  
Spring Loaded Inverted Pendulum ◽  
The Stability

Recent locomotion models have demonstrated the benefits of hip torques on legged locomotion stability. Here, a simple constant radial forcing function along the leg of the Spring-Loaded Inverted Pendulum (SLIP) model is added. This model is analyzed in order to determine what effect such a radial force might have on the stability of locomotion versus the more commonly used hip-torque forcing. The model is found to be unstable for the vast majority of the parameter space studied, for any amount of added forcing and damping constants. This suggests that simple constant forcing along the leg does not produce stable locomotion, unlike the case where forcing happens via hip torque.

Stress fields in granular material and implications for performance of robot locomotion over granular media

2015 ◽  
Vol 8 (1) ◽  
pp. 2005-2009
Author(s):  
Diandong Ren ◽  
Lance M. Leslie ◽  
Congbin Fu
Keyword(s):  
Mechanical Properties ◽  
Granular Material ◽  
Granular Media ◽  
Rotation Frequency ◽  
Legged Locomotion ◽  
Working Environment ◽  
Navier Stokes ◽  
Maximum Speed ◽  
Sigmoid Curve ◽  
Multi Body

 Legged locomotion of robots has advantages in reducing payload in contexts such as travel over deserts or in planet surfaces. A recent study (Li et al. 2013) partially addresses this issue by examining legged locomotion over granular media (GM). However, they miss one extremely significant fact. When the robot’s wheels (legs) run over GM, the granules are set into motion. Hence, unlike the study of Li et al. (2013), the viscosity of the GM must be included to simulate the kinematic energy loss in striking and passing through the GM. Here the locomotion in their experiments is re-examined using an advanced Navier-Stokes framework with a parameterized granular viscosity. It is found that the performance efficiency of a robot, measured by the maximum speed attainable, follows a six-parameter sigmoid curve when plotted against rotating frequency. A correct scaling for the turning point of the sigmoid curve involves the footprint size, rotation frequency and weight of the robot. Our proposed granular response to a load, or the ‘influencing domain’ concept points out that there is no hydrostatic balance within granular material. The balance is a synergic action of multi-body solids. A solid (of whatever density) may stay in equilibrium at an arbitrary depth inside the GM. It is shown that there exists only a minimum set-in depth and there is no maximum or optimal depth. The set-in depth of a moving robot is a combination of its weight, footprint, thrusting/stroking frequency, surface property of the legs against GM with which it has direct contact, and internal mechanical properties of the GM. If the vehicle’s working environment is known, the wheel-granular interaction and the granular mechanical properties can be grouped together. The unitless combination of the other three can form invariants to scale the performance of various designs of wheels/legs. Wider wheel/leg widths increase the maximum achievable speed if all other parameters are unchanged.

scholarly journals Getting grip in changing environments: the effect of friction anisotropy inversion on robot locomotion

2021 ◽  
Vol 127 (5) ◽  
Author(s):  
Halvor T. Tramsen ◽  
Lars Heepe ◽  
Jettanan Homchanthanakul ◽  
Florentin Wörgötter ◽  
Stanislav N. Gorb ◽  
...  
Keyword(s):  
Energy Efficient ◽  
Legged Locomotion ◽  
Hexapod Robot ◽  
Friction Anisotropy ◽  
Anisotropic Friction ◽  
Walking Behavior ◽  
Robot Locomotion ◽  
Computational Morphology ◽  
Anisotropic Structures ◽  
Walking Environment

AbstractLegged locomotion of robots can be greatly improved by bioinspired tribological structures and by applying the principles of computational morphology to achieve fast and energy-efficient walking. In a previous research, we mounted shark skin on the belly of a hexapod robot to show that the passive anisotropic friction properties of this structure enhance locomotion efficiency, resulting in a stronger grip on varying walking surfaces. This study builds upon these results by using a previously investigated sawtooth structure as a model surface on a legged robot to systematically examine the influences of different material and surface properties on the resulting friction coefficients and the walking behavior of the robot. By employing different surfaces and by varying the stiffness and orientation of the anisotropic structures, we conclude that with having prior knowledge about the walking environment in combination with the tribological properties of these structures, we can greatly improve the robot’s locomotion efficiency.

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