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In this article, we propose a novel approach, called InPTC (Integrated Planning and Tube-Following Control), for prescribed-time collision-free navigation of wheeled mobile robots in a compact convex workspace cluttered with static, sufficiently separated, and convex obstacles. A path planner with prescribed-time convergence is presented based upon Bouligand's tangent cones and time scale transformation (TST) techniques, yielding a continuous vector field that can guide the robot from almost all initial positions in the free space to the designated goal at a prescribed time, while avoiding entering the obstacle regions augmented with safety margin. By leveraging barrier functions and TST, we further derive a tube-following controller to achieve robot trajectory tracking within a prescribed time less than the planner's settling time. This controller ensures the robot moves inside a predefined ``safe tube'' around the reference trajectory, where the tube radius is set to be less than the safety margin. Consequently, the robot will reach the goal location within a prescribed time while avoiding collision with any obstacles along the way. The proposed InPTC is implemented on a Mona robot operating in an arena cluttered with obstacles of various shapes. Experimental results demonstrate that InPTC not only generates smooth collision-free reference trajectories that converge to the goal location at the preassigned time of $250\,\rm s$ (i.e., the required task completion time), but also achieves tube-following trajectory tracking with tracking accuracy higher than $0.01\rm m$ after the preassigned time of $150\,\rm s$. This enables the robot to accomplish the navigation task within the required time of $250\,\rm s$.

In this paper, we propose a novel formation controller for nonholonomic agents to form general parametric curves. First, we derive a unified parametric representation for both open and closed curves. Then, a leader-follower formation controller is designed to form the parametric curves. We consider directed communications and constant input disturbances rejection in the controller design. Rigorous Lyapunov-based stability analysis proves the asymptotic stability of the proposed controller. Detailed numerical simulations and experimental studies are conducted to verify the performance of the proposed method., Comment: 6 pages, 6 figures

This work presents a new method to design consensus controllers for perturbed double integrator systems whose interconnection is described by a directed graph containing a rooted spanning tree. We propose new robust controllers to solve the consensus and synchronization problems when the systems are under the effects of matched and unmatched disturbances. In both problems, we present simple continuous controllers, whose integral actions allow us to handle the disturbances. A rigorous stability analysis based on Lyapunov's direct method for unperturbed networked systems is presented. To assess the performance of our result, a representative simulation study is presented.

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.

In this paper we provide the first solution to the challenging problem of designing a globally exponentially convergent estimator for the parameters of the standard model of a continuous stirred tank reactor. Because of the presence of non-separable exponential nonlinearities in the system dynamics that appear in Arrhenius law, none of the existing parameter estimators is able to deal with them in an efficient way and, in spite of many attempts, the problem was open for many years. To establish our result we propose a novel procedure to obtain a suitable nonlinearly parameterized regression equation and introduce a radically new estimation algorithm - derived applying the Immersion and Invariance methodology - that is applicable to these regression equations. A further contribution of the paper is that parameter convergence is guaranteed with weak excitation requirements.

In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it incorporates a forgetting factor allowing it to preserve alertness to time-varying parameters; (iii) thanks to the addition of a mixing step it relies on a set of scalar regression equations ensuring a superior transient performance; (iv) it is applicable to nonlinearly parameterized regressions verifying a monotonicity condition and to a class of systems with switched time-varying parameters; (v) it is shown that it is bounded-input-bounded-state stable with respect to additive disturbances; (vi) continuous and discrete-time versions of the estimator are given. The superior performance of the proposed estimator is illustrated with a series of examples reported in the literature.

In this note we study the generation of attractive oscillations of a class of mechanical systems with underactuation one. The proposed design consists of two terms, i.e., a partial linearizing state feedback, and an immersion and invariance orbital stabilization controller. The first step is adopted to simplify analysis and design, however, bringing an additional difficulty that the model loses its Euler-Lagrange structure after the collocated pre-feedback. To address this, we propose a constructive solution to the orbital stabilization problem via a smooth controller in an analytic form, and the model class identified in the paper is characterized via some easily apriori verifiable assumptions on the inertia matrix and the potential energy function.

In this paper we propose a new parameter estimator that ensures global exponential convergence of linear regression models requiring only the necessary assumption of identifiability of the regression equation,which we show is equivalent to interval excitation of the regressor vector. Continuous and discrete-time versions of the estimators are given. An extension to--separable and monotonic--non-linear parameterizations is also given. The estimators are shown to be robust to additive measurement noise and--not necessarily slow--parameter variations. Moreover, a version of the continuous-time estimator that rejects sinusoidal disturbances with unknown internal model is given. The estimator is shown to be applicable to the classical model reference adaptive control problem relaxing the conspicuous assumption of known sign of the high-frequency gain. Simulation results that illustrate the performance of the estimator are given.

In this paper, we prove that it is possible to estimate online the parameters of a classical vector linear regression equation $ Y=\Omega \theta$, where $ Y \in \mathbb{R}^n,\;\Omega \in \mathbb{R}^{n \times q}$ are bounded, measurable signals and $\theta \in \mathbb{R}^q$ is a constant vector of unknown parameters, even when the regressor $\Omega$ is not persistently exciting. Moreover, the convergence of the new parameter estimator is global and exponential and is given for both continuous-time and discrete-time implementations. As an illustration example, we consider the problem of parameter estimation of a linear time-invariant system, when the input signal is not sufficiently exciting, which is known to be a necessary and sufficient condition for the solution of the problem with the standard gradient or least-squares adaptation algorithms., Comment: submitted to System and Control Letters

It is widely recognized that the existing parameter estimators and adaptive controllers for robot manipulators are extremely complicated to be of practical use. This is mainly due to the fact that the existing parameterization includes the complicated signal and parameter relations introduced by the Coriolis and centrifugal forces matrix. In an insightful remark of their seminal paper Slotine and Li suggested to use the parameterization of the power balance equation, which avoids these terms -- yielding significantly simpler designs. To the best of our knowledge, such an approach was never actually pursued in on-line implementations, because the excitation requirements for the consistent estimation of the parameters is ``very high". In this paper we use a recent technique of generation of ``exciting" regressors developed by the authors to overcome this fundamental problem. The result is applied to general Euler-Lagrange systems and the fundamental advantages of the new parameterization are illustrated with comprehensive simulations of a 2 degrees-of-freedom robot manipulator.

Designing control systems with bounded input is a practical consideration since realizable physical systems are limited by the saturation of actuators. The actuators' saturation degrades the performance of the control system, and in extreme cases, the stability of the closed-loop system may be lost. However, actuator saturation is typically neglected in the design of control systems, with compensation being made in the form of over-designing the actuator or by post-analyzing the resulting system to ensure acceptable performance. The bounded input control of fully actuated systems has been investigated in multiple studies, but it is not generalized for under actuated mechanical systems. This article proposes a systematic framework for finding the upper bound of control effort in underactuated systems, based on interconnection and the damping assignment passivity based control (IDA-PBC) approach. The proposed method also offers design variables for the control law to be tuned, considering the actuator's limit. The major difficulty in finding the control input upper bounds is the velocity dependent kinetic energy related terms. Thus, the upper bound of velocity is computed using a suitable Lyapunov candidate as a function of closed-loop system parameters. The validity and application of the proposed method are investigated in detail through two benchmark systems.

One of the most challenging issues in adaptive control of robot manipulators with kinematic uncertainties is requirement of the inverse of Jacobian matrix in regressor form. This requirement is inevitable in the case of the control of parallel robots, whose dynamic equations are written directly in the task space. In this paper, an adaptive controller is designed for parallel robots based on representation of Jacobian matrix in regressor form, such that asymptotic trajectory tracking is ensured. The main idea is separation of determinant and adjugate of Jacobian matrix and then organize new regressor forms. Simulation and experimental results on a 2--DOF R\underline{P}R and 3--DOF redundant cable driven robot, verify promising performance of the proposed methods.

In this paper we propose a solution to the problem of parameter estimation of nonlinearly parameterized regressions--continuous or discrete time--and apply it for system identification and adaptive control. We restrict our attention to parameterizations that can be factorized as the product of two functions, a measurable one and a nonlinear function of the parameters to be estimated. Although in this case it is possible to define an extended vector of unknown parameters to get a linear regression, it is well-known that overparameterization suffers from some severe shortcomings. Another feature of the proposed estimator is that parameter convergence is ensured without a persistency of excitation assumption. It is assumed that, after a coordinate change, some of the elements of the transformed function satisfy a monotonicity condition. The proposed estimators are applied to design identifiers and adaptive controllers for nonlinearly parameterized systems. In continuous-time we consider a general class of nonlinear systems and those described by Euler-Lagrange models, while in discrete-time we apply the method to the challenging problems of direct and indirect adaptive pole-placement. The effectiveness of our approach is illustrated with several classical examples, which are traditionally tackled using overparameterization and assuming persistency of excitation.

In this note, it is shown that the results claimed in the paper [1]---as well as the examples presented there---are, unfortunately, incorrect.

Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated by some modern applications we show that the technique can also be used to solve the problem of orbital stabilization, where the final objective is to generate periodic solutions that are attractive. The feasibility of our result is illustrated with some classical mechanical engineering and electronics examples.

In this note we identify a class of underactuated mechanical systems whose desired constant equilibrium position can be globally stabilised with the ubiquitous PID controller. The class is characterised via some easily verifiable conditions on the systems inertia matrix and potential energy function, which are satisfied by many benchmark examples. The design proceeds in two main steps, first, the definition of two new passive outputs whose weighted sum defines the signal around which the PID is added. Second, the observation that it is possible to construct a Lyapunov function for the desired equilibrium via a suitable choice of the aforementioned weights and the PID gains and initial conditions. The results reported here follow the same research line as [7] and [20]---bridging the gap between the Hamiltonian and the Lagrangian formulations used, correspondingly, in these papers. Two additional improvements to our previous works are the removal of a non-robust cancellation of a potential energy term and the establishment of equilibrium attractivity under weaker assumptions.

To extend the realm of application of the well known controller design technique of interconnection and damping assignment passivity-based control (IDA-PBC) of mechanical systems two modifications to the standard method are presented in this article. First, similarly to [1], it is proposed to avoid the splitting of the control action into energy-shaping and damping injection terms, but instead to carry them out simultaneously. Second, motivated by [2], we propose to consider the inclusion of generalised forces, going beyond the gyroscopic ones used in standard IDA-PBC. It is shown that several new controllers for mechanical systems designed invoking other (less systematic procedures) that do not satisfy the conditions of standard IDA-PBC, actually belong to this new class of SIDA-PBC.

A globally exponentially stable speed observer for mechanical systems was recently reported in the literature, under the assumptions of known (or no) Coulomb friction and no disturbances. In this note we propose and adaptive version of this observer, which is robust vis--a--vis constant disturbances. Moreover, we propose a new globally convergent speed observer that, besides rejecting the disturbances, estimates some unknown friction coefficients for a class of mechanical systems that contains several practical examples.