Tracking control of an underactuated rigid body with a coupling input force

Abstract

This paper presents a set of basic problems concerning the control of an underactuated dynamic system. Exemplary system of a planar rigid body with a coupling input force is described. Lie brackets method is used to show accessibility of the system. A tracking problem is solved with computed torque algorithm. The coupling force makes the convergence to zero of all state variables errors impossible. After numerical simulation, stability of the system is mentioned.

Caster Car – underactuated ground vehicle with caster wheels

“…Position control presents good results of trajectory tracking with visible deviations from trajectory starting from the first 90 deg turning point around 38 second (Figure 14a). Full state control algorithm keeps All presented results of optimized selective control (Figures 8,10,14) give acceptable good results of position tracking and stable rotation errors with visible 360 degrees jumps. Results of optimized full state control (Figures 9,11,15) give stable behavior of position and rotation errors with more visible deviations.…”

“…The simplest method to describe the dynamics of the Caster Car is to use hovercraft mathematical model. The model described by [9] consist of a planar rigid body moving on a plane (Figure 3). The object has mass 𝑚 and inertia 𝐼 𝐶 respect to the center of mass (point 𝐶).…”

“…Many control problems are related to the input coupling effect visible in equations ( 1)-(3) -both inputs, ì 𝐹 (𝑡) and 𝛽(𝑡), presents in more than one equation. The new method of full configuration control with pseudoinverse operation was presented in [10].…”

“…Position and rotation of the Caster Car model could be controlled using full state control method based on the computed torque technique with the pseudoinverse operation and proportional-derivative feedback presented in [9]. Let's define the tracking problem of desired trajectory described by 𝑥 𝑑 (𝑡) and 𝑦 𝑑 (𝑡), with desired tangential orientation 𝜑 𝑑 (𝑡) with respect to trajectory.…”

Chaotic behaviors of an underactuated system in the trajectory tracking task

“…In this paper, one of the simplest underactuated models is described [6]. It can be used for a basic representation of a hovercraft, rocket or sliding vehicle.…”