Abstract
The development of controllers for underactuated systems with nonholonomic constraints has been a topic of significant interest for many researchers in recent years. These systems are hard to control because their linearization transform them into uncontrollable systems. The proposed approaches involve the use of a permanent excitation in the reference trajectory; coordinate transformation; discontinuities; or complex calculations. This paper proposes the design of the controller of the second-order chained form system for trajectory tracking by using a simpler approach based on linear algebra. Up to the present time, no controllers based on this approach have been designed for that system. The control problem is solved by setting two of the three systems variables as a reference, while the remaining variable is calculated imposing the condition that the equations system has an exact solution to ensure that tracking errors go to zero. The stability of the proposed controller is theoretically demonstrated, and simulations results show a suitable control system performance. Also, no coordinate transformation is necessary.
Highlights
In recent years, the interest in the control of underactuated systems with nonholonomic constraints has increased [1]
Underactuated systems are mechanical systems with fewer control inputs than degrees of freedom and nonintegrable acceleration constraints [2]. is paper considers the control for trajectory tracking and positioning of second-order chained form systems. ese are hard to control because their linearization transform them into uncontrollable systems. e well-known paper of Brockett highlights the difficulty of solving these problems [3]
Several articles addressed the control of underactuated systems with nonholonomic constraints
Summary
The interest in the control of underactuated systems with nonholonomic constraints has increased [1]. Is paper considers the control for trajectory tracking and positioning of second-order chained form systems. Several articles addressed the control of underactuated systems with nonholonomic constraints. Aneke et al [4, 5] resolved the problem of trajectory tracking by using a threestage method. They transformed the original system into an extended chained form system with a cascade arrangement. The second subsystem is exponentially stabilized by employing a backstepping procedure. They showed the closed-loop tracking dynamics stability of the system. Other authors used the backstepping procedure to develop control methodologies for trajectory tracking [6, 7]. A permanent excitation in the reference trajectory is necessary for system stability. is implies that the signals must not converge to zero, limiting their applications
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