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.

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.

Asymptotic stability of fractional difference equations with bounded time delays

2020 ◽  
Vol 23 (2) ◽  
pp. 571-590
Author(s):  
Mei Wang ◽  
Baoguo Jia ◽  
Feifei Du ◽  
Xiang Liu
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Difference Equations ◽  
Integral Inequality ◽  
Time Delays ◽  
Asymptotical Stability ◽  
Stability Conditions ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
Fractional Difference Equation

AbstractIn this paper, an integral inequality and the fractional Halanay inequalities with bounded time delays in fractional difference are investigated. By these inequalities, the asymptotical stability conditions of Caputo and Riemann-Liouville fractional difference equation with bounded time delays are obtained. Several examples are presented to illustrate the results.

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.

scholarly journals Effectiveness of Information from Vehicles beyond Nearest Vehicle Ahead for Traffic Flow

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
Hikaru Shimizu ◽  
Sho Nishiyama ◽  
Yukiko Wakita ◽  
Eisuke Kita
Keyword(s):  
Stability Analysis ◽  
Traffic Flow ◽  
Flow Simulation ◽  
The Other ◽  
Stable Region ◽  
Model Parameters ◽  
Model Stability ◽  
Acceleration Rate ◽  
Traffic Flow Simulation ◽  
Vehicle Acceleration

A driver usually controls the vehicle according to only the information from the nearest leader vehicle. If the information from the other leader vehicles is also available, the driver can control the vehicle more adequately. The aim of this study is to discuss the effectiveness of the information from the other leader vehicles than the nearest one for the traffic flow. For this purpose, the traffic flow is modeled by using the Chandler-type multi-vehicle-following model. This model changes the vehicle acceleration rate according to the velocity differences between the vehicle and its multileader vehicles. After the model stability analysis, the traffic flow simulation is performed. The results reveal that the stable region of the model parameters expands according to the increase of the number of the leader vehicles.

Asymptotic Stability of Controlled Nonlinear Stochastic Systems Considering the Dynamics of Sensors and Actuators

2021 ◽  
pp. 2150180
Author(s):  
Jiaojiao Sun ◽  
Zuguang Ying ◽  
Ronghua Huan ◽  
Weiqiu Zhu
Keyword(s):  
Asymptotic Stability ◽  
Stochastic Systems ◽  
Stochastic Averaging ◽  
Stochastic Averaging Method ◽  
Stable Region ◽  
High Dimensional ◽  
Nonlinear Stochastic System ◽  
Dimensional System ◽  
Sensors And Actuators ◽  
Controlled System

A closed-loop controlled system usually consists of the main structure, sensors, and actuators. In this paper, asymptotic stability of trivial solutions of a controlled nonlinear stochastic system considering the dynamics of sensors and actuators is investigated. Considering the inherent and intentional nonlinearities and random loadings, the coupled dynamic equations of the controlled system with sensors and actuators are given, which are further formulated by a controlled, randomly excited, dissipated Hamiltonian system. The Hamiltonian of the controlled system is introduced, and, based on the stochastic averaging method, the original high-dimensional system is reduced to a one-dimensional averaged system. The analytical expression of Lyapunov exponent of the averaged system is derived, which gives the approximately necessary and sufficient condition of the asymptotic stability of trivial solutions of the original high-dimensional system. The validation of the proposed method is demonstrated by a four-degree-of-freedom controlled system under pure stochastically parametric excitations in detail. A comparative analysis, which is related to the stochastic asymptotic stability of the system with and without considering the dynamics of sensors and actuators, is carried out to investigate the effect of their dynamics on the motion of the controlled system. Results show that ignoring the dynamics of sensors and actuators will get a shrink stable region of the controlled system.

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