Full-state Linearization Research Articles

Full state feedback linearization for a haulage trolley system: a novel differentiable manifold approach

The manuscript presents a manifold-based full-state linearization for a haulage trolley. The key result from the manifold approach is representing the linearized system as a function of the tangent vectors of the nonlinear system. The haulage trolley is linearized, and the system's performance is studied. Three case studies are interrogated; the nonlinear system, a regulator control problem, and a tracking control problem. A settling time of 2 s is set for the control problem, and a reference is set to 1 rad/s for the tracking problem. The results confirm that linear control methods work on the controllable linearized haulage trolley system.

Full-State Linearization and Stabilization of SISO Markovian Jump Nonlinear Systems

This paper investigates the linearization and stabilizing control design problems for a class of SISO Markovian jump nonlinear systems. According to the proposed relative degree set definition, the system can be transformed into the canonical form through the appropriate coordinate changes followed with the Markovian switchings; that is, the system can be full-state linearized in every jump mode with respect to the relative degree setn,…,n. Then, a stabilizing control is designed through applying the backstepping technique, which guarantees the asymptotic stability of Markovian jump nonlinear systems. A numerical example is presented to illustrate the effectiveness of our results.

Autonomous Stair Climbing of a Wheeled Double Inverted Pendulum

The described wheeled double inverted pendulum was built to serve as a stair-climbing device (SCD). It can negotiate steps autonomously. The overall SCD model is represented by a hybrid automaton. It consists of nonlinear situation-changing continuous-time properties. Depending on the situation, the SCD is either fully actuated or under-actuated. Furthermore, discontinuous phenomena exist due to wheel-to-ground unilateral constraints. Feedback linearization is used as a basis for the control design. Due to a different situation-changing relative degree a full-state linearization or a partial linearization is applied. The state transition “settling” is developed within the virtual constraints framework.

Load carrying capacity of flexible joint manipulators with feedback linearization

A computational technique for obtaining the maximum load carrying capacity of robotic manipulators with joint elasticity, subject to accuracy and actuators constraints, is described herein. A feedback linearization technique is used to minimize end-effector deflection. An inversion algorithm is employed for the synthesis of a dynamic feedback control law that provides input-output decoupling and full state linearization. The linearizing input transformations and the corresponding state diffeomorphisms are presented. The proposed technique is then applied to a flexible joint robot. Linearizing control law is been expressed in terms of different sets of model variables and their derivatives. As a result, different tracking errors and torques are introduced in the robot-given trajectory and different load carrying capacities are obtained.

Planning for dynamic multiagent planar manipulation with uncertainty: a game theoretic approach

This paper addresses the planning problem for multiagent dynamic manipulation in the plane. The objective of planning is to design the forces exerted on the object by agents with which the object can follow a given trajectory in spite of the uncertainty on pressure distribution. The main novelty of the proposed approach is the integration of noncooperative and cooperative games between agents in an hierarchical manner. Based on a dynamic model of the pushed object, the coordination problem is solved in two levels. In the lower control level, a fictitious force controller is designed by using a minimax technique to achieve the tracking performance. The design procedure is divided into two steps. First, a linear nominal controller is designed via full-state linearization with desired eigenvalues assignment. Next, a minimax control scheme is specified to optimally attenuate the worst-case effect of the uncertainty due to pressure distribution and achieve a minimax tracking performance. In the coordination level, a cooperative game is formulated between agents to distribute the fictitious force, and the objective of the game is to minimize the worst-case interaction force between agents and the object. Simulations are carried out for two-agent and three-agent manipulations, results demonstrate the effectiveness of the planning method.

Decoupling and feedback linearization of robots with mixed rigid/elastic joints

We consider some theoretical aspects of the control problem for rigid link robots having some joints rigid and some with non-negligible elasticity. We start from the reduced model of robots with all joints elastic introduced by Spong, which is linearizable by static feedback. For the mixed rigid/elastic joint case, we give structural necessary and sufficient conditions for input–output decoupling and full-state linearization via static state feedback. These turn out to be very restrictive. However, when a robot fails to satisfy these conditions, we show that a physically motivated dynamic state feedback will always guarantee the same result. The analysis is performed without resorting to the state-space equation format. As a result, the explicit form of the exact linearizing and input–output decoupling controllers is provided directly in terms of the robot dynamic model terms. © 1998 John Wiley & Sons, Ltd.

Linearizing the Ball and Beam System with a PD Control Law

Continuing the work of Hauser, Sastry and Kokotović’s (1992) about the Ball and Beam System where conditions for approximate full state linearization of nonlinear systems were presented. We present here a state linearization of the Ball and Beam System based on proportional and derivative feedback without neglecting any term.