This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS: SYSTEMS 1 Adaptive Algorithms for Performance Improvement of a Class of Continuum Manipulators Achille Melingui, Joseph Jean-Baptiste Mvogo Ahanda, Othman Lakhal, Jean Bosco Mbede, and Rochdi Merzouki Abstract—This paper addresses the position control of continuum manipulators. Their performances in terms of speed limitation and position accuracy are often mediocre compared with rigid body based robots. In regards to continuum manipu- lators control, nonadaptive kinematic schemes were shown poor performance in terms of tracking position accuracy, and exist- ing adaptive schemes were time-consuming. This paper presents a novel adaptive control scheme, namely the adaptive support vector regressor controller. The proposed approach exploits the optimization learning methods which yield global solutions of the training problem while keeping small size regressors. These characteristics make it possible to accelerate the convergence of the closed-loop system, thus reducing the execution time. The experimental results obtained using the compact bionic han- dling assistant robot demonstrate that nonadaptive kinematic architectures even in the presence of accurate learning models are not robust enough to deal with these challenging platforms and that adaptive control schemes can significantly improve the performance. Index Terms—Adaptive control, neural networks, robot kine- matics, support vector machines. I. I NTRODUCTION R ECENTLY, continuum robots [1]–[3] have gathered great interest in the robotics community, as regards the possi- bility of designing a class of bio-inspired manipulators with performances approaching in certain operational conditions the rigid industrial manipulators [4]–[9]. These robot proto- types are characterized by their lightweight structure, which can be built from the techniques of rapid prototyping and low costs of design. They are made of flexible materials, allowing them to maneuver in congested and unstructured environments. The property of hyper-redundancy [2], [10], [11] makes them suited for a large number of applications, including surgical interventions [3], rescue, exploration [12], and so on. Manuscript received August 9, 2016; revised November 6, 2016 and February 6, 2017; accepted February 19, 2017. This paper was recommended by Associate Editor Z. Li. A. Melingui and J. B. Mbede are with the Electrical and Telecommunications Engineering Department, Ecole Nationale Supérieure Polytechnique, University of Yaoundé 1, Yaoundé, Cameroon (e-mail: achillemelingui@gmail.com). J. J.-B. Mvogo Ahanda is with the Department of Physics, Faculty of Science, University of Yaoundé 1, Yaoundé, Cameroon. O. Lakhal and R. Merzouki are with the Polytech’Lille, CRIStAL, CNRS-UMR 9189, 59655 Villeneuve d’Ascq, France (e-mail: rochdi.merzouki@polytech-lille.fr). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSMC.2017.2678605 Robustness in control of continuum manipulators depends on the accuracy of their models, sensitive to the fluctuation of the kinematic and dynamic parameters, due to their hyper- redundancy, under-actuation, and the conditions of piloting. In the literature, different contributions exist on kinematic modeling of continuum robots [13]–[17]. However, few refer- ences are available in control of continuum manipulators such in [18]–[24]. Mahl et al. [22] proposed a variable curvature for the kinematics of multisection continuum manipulators. This is the improvement of the model accuracy regarding existing models of bending sections using the assumption of constant curvature. In this case, the authors implemented a kinematic controller to a bionic handling assistant (BHA) to validate the developed kinematic model. However, in the absence of an adaptive control algorithm, the tracking accuracy of the robot remains nonoptimal. Thus, Rolf and Steil [20] used a goal-directed exploration scheme, namely the online goal bab- bling in order to learn the optimal inverse kinematics of a BHA robot. Though performance during the learning process reaches a good level they remain isolated outlets. Therefore, the authors integrated a Cartesian feedback controller in the control scheme in order to improve the tracking accuracy. Braganza et al. [21] implemented a low-level joint controller in a soft extensible manipulator. They utilized neural networks (NNs) to compensate for the modeling uncertainties. The con- tributions proposed in [23] and [24] have allowed achievement of a good performance thanks to the type of the robot actua- tors. Knowing that experimented robots in [19], [20], and [22] are pneumatically actuated, and those used in [23] and [24] are controlled by wire cables. So, the type of the actuation can affect the performance of the global system in a closed loop, for example, the hysteresis phenomenon still acts in the pneumatic actuation. In addition, the flexible structure and the memory effect of the constitutive material of continuum manipulators cause this nonaccuracy in tracking of targets. These undesirable effects can strongly affect the positioning of the end effector of the manipulator, where it can reach dif- ferent positions inside the workspace, by only using the same controlled input of the pneumatic actuators [19]. Lakhal et al. [15], and Melingui et al. [18], [19] referred to the need to introduce adaptive algorithms to cope with undesirable effects. They also noted that the use of adaptive control laws is not sufficient as the robot model changes over time. Therefore, they were accorded to an update of the robot model and real-time adjustment of the controller’s parame- ters. The authors implemented NN technique [15], [18], [19] 2168-2216 c  2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.