Soft continuum manipulators offer levels of compliance and inherent safety that can render them a superior alternative to conventional rigid robots for a variety of tasks, such as medical interventions or human–robot interaction. However, the ability of soft continuum manipulators to compensate for external disturbances needs to be further enhanced to meet the stringent requirements of many practical applications. In this paper, we investigate the control problem for soft continuum manipulators that consist of one inextensible segment of constant section, which bends under the effect of the internal pressure and is subject to unknown disturbances acting in the plane of bending. A rigid-link model of the manipulator with a single input pressure is employed for control purposes and an energy-shaping approach is proposed to derive the control law. A method for the adaptive estimation of disturbances is detailed and a disturbance compensation strategy is proposed. Finally, the effectiveness of the controller is demonstrated with simulations and with experiments on an inextensible soft continuum manipulator that employs pneumatic actuation.

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This article investigates the control problem for underactuated port-controlled Hamiltonian systems with multiple linearly parameterized additive disturbances including matched, unmatched, constant, and state-dependent components. The notion of algebraic solution of the matching equations is employed to design an extension of the interconnection and damping assignment passivity-based control methodology that does not rely on the solution of partial differential equations. The result is a dynamic state-feedback that includes a disturbance compensation term, where the unknown parameters are estimated adaptively. A simplified implementation of the proposed approach for underactuated mechanical systems is detailed. The effectiveness of the controller is demonstrated with numerical simulations for the magnetic-levitated-ball system and for the ball-on-beam system. K E Y W O R D Sadaptive control, disturbance rejection, mechanical systems, passivity-based control, underactuated systems 1 This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. 4112wileyonlinelibrary.com/journal/rnc Int J Robust Nonlinear Control. 2020;30:4112-4128.FRANCO et al. 4113A further aspect of energy shaping control that has been attracting increasing attention is robustness to disturbances, which are common to most practical application. Notable results in this area include the study of viscous friction within the controlled Lagrangians formulation, 12,13 and of continuous and smooth physical dissipation within the IDA-PBC framework, 14,15 while friction according to the Dahl model affecting the actuated part of the state was considered in Reference 16. Stability and robustness of disturbed PCH systems with dissipation were investigated in Reference 17. The robust energy shaping control of fully actuated mechanical systems with disturbances was presented in Reference 18, while disturbance attenuation for discrete-time systems was studied in Reference 19. More recently, integral IDA-PBC designs that rely on the classical solution of the PDE were proposed in References 20-22 for a class of underactuated mechanical systems with constant matched disturbances (ie, those affecting the actuated part of the state), and in Reference 23 for bounded matched disturbances. The result in Reference 21 was extended to unmatched constant disturbances in Reference 24, which, however, is only applicable to mechanical systems with constant inertia matrix. The case of nonconstant inertia matrix and variable but bounded disturbances was considered in Reference 25. In addition, the adaptive compensation of constant disturbances within energy shaping control was attempted in References 26,27: while the former still requires solving the PDE, the latter is confined to a limited class of mechanical systems. Besides energy shaping, a sliding mode control for a class of underactuated systems with dry friction was presented in Ref...

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This work investigates the control of nonlinear underactuated mechanical systems with matched and unmatched constant disturbances. To this end, a new control strategy is proposed, which builds upon the interconnection-anddamping-assignment passivity-based control, augmenting it with an additional term for the purpose of disturbance compensation. In particular, the disturbances are estimated adaptively and then accounted for in the control law employing a new matching condition of algebraic nature. Stability conditions are discussed, and for comparison purposes, an alternative controller based on partial feedback linearization is presented. The effectiveness of the proposed approach is demonstrated with numerical simulations for three motivating examples: the inertia wheel pendulum, the disk-on-disk system, and the pendulum-on-cart system. KEYWORDS adaptive control, matched and unmatched disturbances, nonlinear control, underactuated mechanical systems Int J Adapt Control Signal Process. 2019;33:1-15.wileyonlinelibrary.com/journal/acs

This work studies the balancing control problem for flexible inverted-pendulum systems and investigates the relationship between system parameters and robustness to disturbances. To this end, a new energy-shaping controller with adaptive disturbance-compensation for a class of underactuated mechanical systems is presented. Additionally, a method for the identification of key system parameters that affect the robustness of the closed-loop system is outlined. The proposed approach is applied to the flexible pendulum-on-cart system and a simulation study is conducted to demonstrate its effectiveness. Finally, the control problem for a classical pendulum-on-cart system with elastic joint is discussed to highlight the similarities with its flexible-link counterpart.

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This paper investigates the model-based nonlinear control of a class of soft continuum pneumatic manipulators that bend due to pressurization of their internal chambers and that operate in the presence of disturbances. A port-Hamiltonian formulation is employed to describe the closed loop system dynamics, which includes the pressure dynamics of the pneumatic actuation, and new nonlinear control laws are constructed with an energy-based approach. In particular, a multi-step design procedure is outlined for soft continuum manipulators operating on a plane and in 3D space. The resulting nonlinear control laws are combined with adaptive observers to compensate the effect of unknown disturbances and model uncertainties. Stability conditions are investigated with a Lyapunov approach, and the effect of the tuning parameters is discussed. For comparison purposes, a different control law constructed with a backstepping procedure is also presented. The effectiveness of the control strategy is demonstrated with simulations and with experiments on a prototype. To this end, a needle valve operated by a servo motor is employed instead of more sophisticated digital pressure regulators. The proposed controllers effectively regulate the tip rotation of the prototype, while preventing vibrations and compensating the effects of disturbances, and demonstrate improved performance compared to the backstepping alternative and to a PID algorithm.