Using Energy Shaping and Regulation for Limit Cycle Stabilization, Generation, and Transition in Simple Locomotive Systems

2021 ◽  
Author(s):  
Mark Yeatman ◽  
Robert D. Gregg
Keyword(s):  
Limit Cycles ◽  
Energy Function ◽  
Inverted Pendulum ◽  
Control Parameters ◽  
Energy Shaping ◽  
Constant Energy ◽  
Gait Characteristics ◽  
Hopping Robot ◽  
Control Framework ◽  
Globally Stable

Abstract This paper explores new ways to use energy shaping and regulation methods in walking systems to generate new passive-like gaits and dynamically transition between them. We recapitulate a control framework for Lagrangian hybrid systems, and show that regulating a state varying energy function is equivalent to applying energy shaping and regulating the system to a constant energy value. We then consider a simple 1-dimensional hopping robot and show how energy shaping and regulation control can be used to generate and transition between nearly globally stable hopping limit cycles. The principles from this example are then applied on two canonical walking models, the spring loaded inverted pendulum (SLIP) and compass gait biped, to generate and transition between locomotive gaits. These examples show that piecewise jumps in control parameters can be used to achieve stable changes in desired gait characteristics dynamically/online.

Investigating the Nonlinear Dynamics of Human Balance Using Topological Data Analysis

2020 ◽  
Vol 15 (9) ◽  
Author(s):  
Kyle W. Siegrist ◽  
Ryan M. Kramer ◽  
James R. Chagdes
Keyword(s):  
Time Series ◽  
Postural Stability ◽  
Inverted Pendulum ◽  
Balance Control ◽  
Neuromuscular Diseases ◽  
Neuromuscular Control ◽  
Topological Data Analysis ◽  
Control Parameters ◽  
Human Balance ◽  
Neuromuscular Impairment

Abstract Understanding the mechanisms behind human balance has been a subject of interest as various postural instabilities have been linked to neuromuscular diseases (e.g., Parkinson's, multiple sclerosis, and concussion). This paper presents a method to characterize an individual's postural stability and estimate of their neuromuscular feedback control parameters. The method uses a generated topological mapping between a subject's experimental data and a dataset consisting of time-series realizations generated using an inverted pendulum mathematical model of upright balance. The performance of the method is quantified using a set of validation time-series realizations with known stability and neuromuscular control parameters. The method was found to have an overall sensitivity of 85.1% and a specificity of 91.9%. Furthermore, the method was most accurate when identifying limit cycle oscillations (LCOs) with a sensitivity of 91.1% and a specificity of 97.6%. Such a method has the capability of classifying an individual's stability and revealing possible neuromuscular impairment related to balance control, ultimately providing useful information to clinicians for diagnostic and rehabilitation purposes.

Gait Optimization for Quadruped Rovers

Robotica ◽  
2019 ◽  
Vol 38 (7) ◽  
pp. 1263-1287
Author(s):  
Lukas Zhornyak ◽  
M. Reza Emami
Keyword(s):  
Three Dimensional ◽  
Inequality Constraints ◽  
Maximum Speed ◽  
Control Parameters ◽  
Domestic Cats ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Gait Characteristics ◽  
Equality And Inequality Constraints ◽  
Gait Optimization

SUMMARYThis paper studies the gait characteristics of a quadruped rover that mimics domestic cats, and attempts to optimize these characteristics. The kinematics and dynamics formulation of the rover’s three-dimensional model is developed, and its gait, pose and corresponding control parameters are computed to minimize torque or maximize speed, using a genetic algorithm. The optimization model consists of a set of equality and inequality constraints that ensure the feasibility and stability of the gaits, while considering the entire gait spectrum that feline species exhibit. The optimal gaits for minimizing the torque closely resemble lateral sequence gaiting, with a trotting behaviour as speed increases. A running gait is obtained at the maximum speed. The optimization results appear to conform to the biological observations of feline species, suggesting the tendency of conserving energy in biological gaiting.

Control and Stability Analysis of Limit Cycles in a Hopping Robot

2007 ◽  
Vol 23 (3) ◽  
pp. 553-563 ◽  
Author(s):  
M. Ahmadi ◽  
H. Michalska ◽  
M. Buehler
Keyword(s):  
Stability Analysis ◽  
Limit Cycles ◽  
Hopping Robot

scholarly journals Robust Passivity Cascade Technique-Based Control Using RBFN Approximators for the Stabilization of a Cart Inverted Pendulum

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1229
Author(s):  
Reza Rahmani ◽  
Saleh Mobayen ◽  
Afef Fekih ◽  
Jong-Suk Ro
Keyword(s):  
Inverted Pendulum ◽  
Angular Position ◽  
Parametric Uncertainty ◽  
Closed Loop System ◽  
External Disturbances ◽  
Pendulum System ◽  
State Variable ◽  
Inverted Pendulum System ◽  
Control Framework ◽  
Exogenous Disturbances

This paper proposes a novel passivity cascade technique (PCT)-based control for nonlinear inverted pendulum systems. Its main objective is to stabilize the pendulum’s upward states despite uncertainties and exogenous disturbances. The proposed framework combines the estimation properties of radial basis function neural networks (RBFNs) with the passivity attributes of the cascade control framework. The unknown terms of the nonlinear system are estimated using an RBFN approximator. The performance of the closed-loop system is further enhanced by using the integral of angular position as a virtual state variable. The lumped uncertainties (NN—Neural Network approximation, external disturbances and parametric uncertainty) are compensated for by adding a robustifying adaptive rule-based signal to the PCT-based control. The boundedness of the states is confirmed using the passivity theorem. The performance of the proposed approach was assessed using a nonlinear inverted pendulum system under both nominal and disturbed conditions.

scholarly journals Experimental Assimilation of Various Tuning Rules with Fractional Order Controller in Inverted Pendulum

2019 ◽  
Vol 8 (6S2) ◽  
pp. 753-757
Keyword(s):  
Fractional Order ◽  
Pid Control ◽  
Pid Controller ◽  
Inverted Pendulum ◽  
Control Parameters ◽  
Controller Tuning ◽  
Tuning Methods ◽  
Fractional Order Controller ◽  
Two Parameters ◽  
Tuning Rules

Modified pendulum is a commonplace trial territory for the investigation of control hypotheses. The adjusting of a reversed pendulum by moving a truck along a flat track is a commonplace issue in the zone of control. So as to improve the capacity of PID controller reacting for the heap unsettling influence, controller tuning guidelines assume fundamental job. This work engaged with enhancement of the PID control parameters for controlling the pendulum in upstanding position particularly with the best heartiness and contrasting it tentatively and ideal settings of a fragmentary PIλDμ controller which can satisfy five distinctive plan details for the shut circle framework, exploiting the fragmentary requests, λ and μ. Since these partial controllers have two parameters more than the customary PID controller improves the presentation of the framework. The pendulum has been adjusted in the upstanding position utilizing the two techniques and the exploratory outcomes are analyzed and announced. The recreation just as exploratory aftereffects of ordinary PID controller demonstrate that the arrangement of new and tuned controller parameters are furnishing the outcomes with better shut circle execution thought about than other tuning methods. And furthermore the control ability and the framework execution furnished by fragmentary request PID controller with the determined new arrangement of parameters has been tentatively demonstrated that the partial request PID controller gives controller execution relatively superior to the customary one along these lines it isn't just controlling the ongoing framework with better adjustment and following control yet additionally have heartiness to aggravations

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