Observer Design for an Inverted Pendulum with Biased Position Sensors

Abstract : Inverted pendulums can be considered as an approximation for the stabilization problem for legged robots. In this paper we design a linear observer for a reaction wheel inverted pendulum under biased angle measurements. The reaction wheel is a flywheel that allows the free spinning motor to apply the control torque on the pendulum. In this paper we consider the stabilization problem in the presence of a constant unknown bias in the pendulum angle measurements; this problem has important practical implications, allowing for less precise sensor placement as well as a closer approximation for the control of legged robots. This paper provides a theoretical and experimental basis for the estimation of the velocities and the bias in the system. INTRODUCTION Walking robotic systems are widely used for moving in difficult conditions such as overcoming of obstacles, turning in tight areas, moving over rough and/or unknown terrains [1]. Walking robots move by periodically lifting their legs, and, regardless of the number of legs and the gait used [2], the locomotion is characterized by the displacement of the center of mass with respect to the contact points. One of the approaches to modeling and stabilization of walking robots are the inverted pendulums [3, 4]. The center of mass of an inverted pendulum is located above the supporting points, it can be considered as an approximation of the mechanical configuration of bipedal walking robots in the problem of dynamic compensation for the deviation of the robot body from the equilibrium position that occurs when the device is walking. The analysis of the mathematical models of inverted pendulums and the design of control laws can be done with computational [5, 6] and imitational methods [7, 8] based on the equations of motion. The advantage of the control law design methods that use the differential equations of motion are high accuracy and numerical stability of the resulting solutions [9], ability to analyze the behavior of the system with varying physical parameters. Analytic solutions can also be used for a parametric identification of the system. In the same time, the computational power of control devices allow to implement fuzzy algorithms and artificial intelligence methods; it allows to use for the control tasks a large variety of methods heavy computational capabilities such as artificial neural networks [10], fuzzy and neuro-fuzzy control systems [11] based on evolutionary computations [12] and other heuristic methods. The disadvantages of these solutions include the dependence on the volume and quality of empirical samples of training data, as well as the inability to quickly compensate for significant variations in the operating conditions, leading to model inconsistencies with real data. The article covers the problem of stabilization of one-dimensional inverted pendulum equipped with a flywheel, under a systematic error in the position sensor readings. The stabilization is achieved with a LQR-controller. We use a linear observer to correct the bias of the position sensor and to estimate the velocities in the system. The advantages of this observer include the fact that it operates at arbitrary motion
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Contributor : Stanislav Aranovskiy <>
Submitted on : Friday, March 29, 2019 - 11:15:26 AM
Last modification on : Wednesday, June 12, 2019 - 11:36:21 AM

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Stanislav Aranovskiy, A Biryuk, E Nikulchev, I Ryadchikov, D Sokolov. Observer Design for an Inverted Pendulum with Biased Position Sensors. Izvestia Rossiiskoi Akademii Nauk.Teoriya i Systemy Upravleniya / Journal of Computer and Systems Sciences International, MAIK Nauka/Interperiodica, 2019, 58 (2), pp.145 - 153. ⟨10.1134/S1064230719020023⟩. ⟨hal-02083747⟩

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