This paper proposes a novel mathematical solution to solve the inverse kinematics (IK) of single section mobile continuum manipulators (SSMCMs). Thus, to achieve a given pose of the end-effector (EE), the proposed mathematical solution consists in determining the position and orientation parameters of the mobile platform and of a single section of the continuum manipulator. As advantages, the proposed mathematical solution eliminates the EE pose errors when the dynamic parameters are neglected and the continuum manipulator is cylindrical in shape. A simulation and an experiment validate the proposed approach.

The task space control of robot manipulators requires solving the thorny problem of stabilizing the compound system {outer controller - inner controller - robot manipulator}. To stabilize this compound system, both controllers must be designed by the user to achieve convergence of the tracking error. This problem is tricky to solve in the case of the control of an industrial robot manipulator because its internal controller is not accessible to users. In this work, we propose an adaptive neural network outer controller. The neural networks approximate the dynamics of the inner controller, the kinematic and dynamic parameters of the robot. Besides, the adaptive part finds parameters that achieve the stability of the global system. Since an adaptive approach is sensitive to errors in initial values, we have integrated into the controller a term that constrains the closed-loop system to maintain the prescribed performances. The effectiveness of the approach is demonstrated through Lyapunov's theory, simulation comparisons, and experimental studies.

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 manipulators control, nonadaptive kinematic schemes were shown poor performance in terms of tracking position accuracy, and existing 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 handling 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.