In this paper, pole placement and two optimal control techniques which are the linear quadratic regulator and linear quadratic Gaussian are compared. A cart and inverted pendulum which is an ...inherently unstable dynamical system is used as a case study to analyze their performance and stability margins. Lagrangian equations defining the system dynamics are converted to linear state-space representation. The objective is to keep the pendulum in an upright position as the cart on which it is mounted moves from one position to another. MATLAB is used to solve the optimization problem and simulate the step response of the system. The robustness of both controllers is measured by giving uncertain model parameters to the system and observing the level of uncertainty these controllers can handle. The simulation results justify the relative advantages of these control schemes.
The neural control of balance during locomotion is currently not well understood, even in the light of considerable advances in research on balance during standing. In this paper, we lay out the ...control problem for this task and present a list of different strategies available to the central nervous system to solve this problem. We discuss the biomechanics of the walking body, using a simplified model that iteratively gains degrees of freedom and complexity. Each addition allows for different control strategies, which we introduce in turn: foot placement shift, ankle strategy, hip strategy, and push-off modulation. The dynamics of the biomechanical system are discussed using the phase space representation, which allows illustrating the mechanical effect of the different control mechanisms. This also enables us to demonstrate the effects of common general stability strategies, such as increasing step width and cadence.
This paper is concerned with the event-triggered fuzzy control design and its application to an inverted pendulum system. First, all of the introduced time-varying delay information from the inverted ...pendulum system and event-triggered mechanism is considered in the stability analysis. The interval of the time-varying delay is then divided into l nonuniform subintervals by utilizing an improved delay-partitioning technique. Information on each subinterval is processed by employing a reciprocally convex method. The proposed delay-dependent stability condition of the inverted pendulum system is determined to be considerably less conservative than the existing results in the literature, and the reduction in the conservativeness becomes progressively noticeable as the delay partitioning number l becomes progressively thinner. Moreover, by employing the parallel distributed compensation law, conditions sufficient for the resulting fuzzy controller and the event-triggering fuzzy controller are presented for the nonlinear inverted pendulum system. Finally, the advantages and effectiveness of the proposed design schemes are demonstrated by three simulation examples.
In this paper, a novel high-order disturbance observer (HODO) for the mobile wheeled inverted pendulum (MWIP) system is first proposed. Based on a choice method of optimal gain matrices, the ...estimation accuracy of the HODO can be improved. Combining the proposed HODO and sliding mode control (SMC), a new control strategy is designed for the balance and speed control of the MWIP system. The boundness of the estimation error of HODO is proved and the stability of the closed-loop control system is achieved through the appropriate selection of sliding surface coefficients. The effectiveness of all proposed methods is verified by experiments on a real MWIP system.
•This paper describes all the four control objectives of RIP and also provide a review of the recent (i.e. from the year 2011 to date).•Other types of RIP were reported along with their possible ...advantages.•Future research work was proposed, and limitations of the previous approaches in this area of research were presented.•The aim of this study is to summarize the state-of-the-art literature, point out unresolved problems, and then suggest future research. This is to prevent repetition of the study that has been conducted.
Rotary Inverted Pendulum (RIP) is an under-actuated mechanical system which is inherently nonlinear and unstable. For decades, it has been widely used as an experimental setup to explain and test different kinds of control algorithms. The main control objectives of RIP are: Swing-up control, stabilization control, switching control and trajectory tracking control. All these control objectives are described in this study. State-of-the art works proposed for each control objective have also been reviewed. These comprise the linear, nonlinear time invariant, self-learning and adaptive nonlinear controllers. Moreover, different kinds of nonlinear dynamic models of the RIP together with the developed linear models in the literature have been analyzed. This is because most of the proposed controllers applied on RIP are found to be model dependent since they are mainly based on integral and/or invariant motion. Other types of RIP are also reported along with their advantages. Future research opportunities and challenges of the previous approaches in this area of research are presented. We believe that expert researchers can use this paper as starting point for further advancement while graduate scholars can use it as an initial point.
In this article, we holistically present a hybrid-linear inverted pendulum (H-LIP) based approach for synthesizing and stabilizing 3-D foot-underactuated bipedal walking, with an emphasis on thorough ...hardware realization. The H-LIP is proposed to capture the essential components of the underactuated and actuated part of the robotic walking. The robot walking gait is then directly synthesized based on the H-LIP. We comprehensively characterize the periodic orbits of the H-LIP and provably derive the stepping stabilization via its step-to-step (S2S) dynamics, which is then utilized to approximate the S2S dynamics of the horizontal state of the center of mass of the robotic walking. The approximation facilities a H-LIP based stepping controller to provide desired step sizes to stabilize the robotic walking. By realizing the desired step sizes, the robot achieves dynamic and stable walking. The approach is fully evaluated in both simulation and experiment on the 3-D underactuated bipedal robot Cassie, which demonstrates dynamic walking behaviors with both high versatility and robustness.
The unicycle robot is an activated model with only one wheel, which ensures its safety. Researchers were particularly interested in the unicycle robot because of its great robustness, which allows it ...to travel around without colliding with the ground. The inverted pendulum having two arms is modelled using a mathematical representation based on the Lagrangian formulation in this work, which embodies our concept of the unicycle robot. The fuzzy logic control algorithm will then be used to produce a high level of solidity for this system.
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