**Output Track Controller with Gravitational Compensation**

for a Class of Hyper-Redundant Robot Arms

for a Class of Hyper-Redundant Robot Arms

**Mihaela FLORESCU, Van Dong Hai NGUYEN, Mircea IVANESCU**

University of Craiova, 13 Al. I. Cuza Street, Craiova, 200585, Romania

mihaelaflorescu@yahoo.com, florescu.mihaela@ucv.ro,

donghai.spkt@gmail.com, ivanescu@robotics.ucv.ro

**Abstract: **The paper studies the output tracking control problem of a class of hyper-redundant robotic arms described by hyperbolic equations. The stability analysis and the resulting controllers are obtained by using the concept of boundary geometric control and an output tracking technique. A conventional PD control is proposed and analysed. Then, for a dynamic model with uncertain components, a robust algorithm is discussed. The output stability is analysed. Numerical simulations are also provided to verify the effectiveness of the approach presented.

**Keywords: **Hyper-redundant arm, gravitational compensation, controller.

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**CITE THIS PAPER AS**:

Mihaela FLORESCU, Van Dong Hai NGUYEN, Mircea IVANESCU, **Output Track Controller with Gravitational Compensation for a Class of Hyper-Redundant Robot Arms**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 24 (3), pp. 309-316, 2015.

**Introduction**

The goal of this paper is to implement a control system for a class of hyper-redundant robots with continuum components. This class of robots represents one of the most attractive domains of robotics during the last decades. In [1-4], were analyzed the kinematic models by the “backbone curve”. The papers [5-7] derived a new kinematic model by using the differential geometry, [8, 12] studied the manipulability of continuum robots. Cable-driven continuum robot control with variable stiffness was studied in [13]. In [14-16] were studied the kinematics of multi-section continuum robots. Several biomimetic robotic prototypes with undulating actuation have been developed in [17, 18]. The differential kinematic models of a class of continuum micro-robot for endovascular surgery applications are treated in [19-24]. Other papers [26-28,33] use the assumption that the arm bends with constant curvature and propose new control strategies.

In our paper, the main parameter, the system state, is determined by the position generalised variables. The dynamic model is inferred and the constraints of the state variables and nonliner components are proved. The estimation of gravitational terms is very difficult in a complex motion. For this reason, the gravitational forces are treated as uncertain components that satisfy the inequality constraints. An essential part of designing feedback controllers for these models is designing practical controllers that are implementable. The inequality constraints on the gravitational components allow to introduce a decoupled control system. A PD boundary control algorithm is used in order to achieve a desired shape of the arm. The stability analysis and the resulting controllers are obtained using Liapunov techniques. The exponential stability of the system (error-observer) was proved. Numerical simulations and experimental tests verify the effectiveness of the presented techniques.

The paper is organized as follows. In Section 2, the dynamic model is presented. Section 3 concerns the formulation of the outputfeedback control and the design methodology of a PD output track controller. Section 4 presents the simulation results. Finally, a Conclusion Section ends the article.

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