Continuum robots have gained widespread popularity due to their inherent compliance and flexibility, particularly their adjustable levels of stiffness for various application scenarios. Despite efforts to dynamic modeling and control synthesis over the past decade, few studies have incorporated stiffness regulation into their feedback control design; however, this is one of the initial motivations to develop continuum robots. This paper addresses the crucial challenge of controlling both the position and stiffness of underactuated continuum robots actuated by antagonistic tendons. We begin by presenting a rigid-link dynamical model that can analyze the open-loop stiffening of tendon-driven continuum robots. Based on this model, we propose a novel passivity-based position-and-stiffness controller that adheres to the non-negative tension constraint. Comprehensive experiments on our continuum robot validate the theoretical results and demonstrate the efficacy and precision of this approach. Note to Practitioners—This paper is motivated by our experience and practical needs in building continuum robotic platforms. Stiffness, flexibility, and accurate configuration regulation are practically important properties for this class of robots. Even though simultaneous position-and-stiffness control is a mature topic for rigid and softly-actuated robots, it remains an open problem for continuum robots with theoretically guaranteed performance. The intention of this paper is to address this situation by proposing a model-based solution for a class of underactuated tendon-driven continuum robots. Hence, we propose an energy-based model and a passivity-based controller to regulate stiffness and configuration concurrently. We believe that this work can be beneficial for academic and industrial research in the context of control algorithms for continuum robots.

The automatic monitoring/tracking of environmental boundaries by multi-agent systems is a fundamental problem that has many practical applications. In this paper, we address this problem with formation control techniques based on parame tric curves that represent the boundary’s feedback shape. For that, we approximate the curve with truncated Fourier series, whose finite coefficients are utilized to characterize the curve’s shape and to automatically distribute the agents along it. These feedback Fourier coefficients are exploited to design a new type of formation controller that drives the agents to form desired curves. A detailed stability analysis is provided for the proposed control methodology, considering both fixed and switching multi-agent topologies. The reported numerical simulation and experimental studies demonstrate the performance and feasibility of our new method to track closed boundaries of different shapes.

In this paper we present a simple procedure to design fractional-PDμcontrollers for Single-Input-Single-Output-Linear Time Invariant (SISO-LTI) systems with constant time-delay. More precisely, based on a geometric approach, we present a methodology not only to design a stabilizing controller, but also to provide practical guidelines to design non-fragile PDμcontrollers. Finally, in order to illustrate the simplicity of the proposed approach as well as the efficiency of the PDμcontroller in a realistic scenario, we consider an experimental setup consisting of controlling a teleoperated system using two Phantom Omni haptic devices.

Two robust kinematic controllers for position trajectory tracking of a perturbed wheeled mobile robot are presented. We address a final objective of fixed-time pose-regulation, which means that the robot position and orientation must reach desired final values simultaneously in a user-defined time. To achieve that, we propose the robust tracking of adequate trajectories for position, which drives the robot to get a desired final orientation due to the nonholonomic motion constraint. Hence, the main contribution of the paper is a complete strategy to define adequate reference trajectories as well as robust controllers to track them in order to enforce the pose-regulation of a wheeled mobile robot in a desired time. Realistic simulations show the good performance of the proposed scheme even in the presence of strong disturbances.

In this paper, we address the problem of stabilisation of robots subject to nonholonommic constraints and external disturbances using port-Hamiltonian theory and smooth time-invariant control laws. This should be contrasted with the commonly used switched or time-varying laws. We propose a control design that provides asymptotic stability of an manifold (also called relative equilibria)-due to the Brockett condition this is the only type of stabilisation possible using smooth time-invariant control laws. The equilibrium manifold can be shaped to certain extent to satisfy specific control objectives. The proposed control law also incorporates integral action, and thus the closed-loop system is robust to unknown constant disturbances. A key step in the proposed design is a change of coordinates not only in the momentum, but also in the position vector, which differs from coordinate transformations previously proposed in the literature for the control of nonholonomic systems. The theoretical properties of the control law are verified via numerical simulation based on a robotic ground vehicle model with differential traction wheels and non co-axial centre of mass and point of contact.

Despite the recent progress in physically interactive and surgical robotics, the active deformation of compliant objects remains an open problem. The main obstacle comes from the difficulty to identify/estimate the object's deformation properties. This paper presents a new visually servoed deformation controller for unknown elastic objects. The control law is designed using the passivity-based framework. The proposed method exploits visual feedback to iteratively estimate the deformation Jacobian matrix, avoiding any identification steps. We prove that even in the presence of inexact estimations, the controller ensures input-to-state stability (i.e. dissipativity) with respect to time-varying disturbances. Finally, an experimental study with several deformation tasks is presented to validate the theory.

Despite the recent progress in physically interactive and surgical robotics, the active deformation of compliant objects remains an open problem. The main obstacle to its implementation comes from the difficulty to identify or estimate the object's deformation model. In this paper, we propose a novel vision-based deformation controller for robot manipulators interacting with unknown elastic objects. We derive a new dynamic-state feedback velocity control law using the passivity-based framework. Our method exploits visual feedback to estimate the deformation Jacobian matrix in real time, avoiding any model identification steps. We prove that even in the presence of inexact estimations, the closed-loop dynamical system ensures input-to-state stability (i.e., full dissipativity) with respect to external disturbances. An experimental study with several deformation tasks is presented to validate the theory.