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In this paper an artificial delay based impedance controller is proposed for robotic manipulators with uncertainty in dynamics. The control law unites the time delayed estimation (TDE) framework with a second order switching controller of super twisting algorithm (STA) type via a novel generalized filtered tracking error (GFTE). While time delayed estimation framework eliminates the need for accurate modelling of robot dynamics by estimating the uncertain robot dynamics and interaction forces from immediate past data of state and control effort, the second order switching control law in the outer loop provides robustness against the time delayed estimation (TDE) error that arises due to approximation of the manipulator dynamics. Thus, the proposed control law tries to establish a desired impedance model between the robot end effector variables i.e. force and motion in presence of uncertainties, both when it is encountering smooth contact forces and during free motion. Simulation results for a two link manipulator using the proposed controller along with convergence analysis are shown to validate the proposition.

While the Artificial Pancreas is effective in regulating the blood glucose in the safe range of 70-180 mg/dl in type 1 diabetic patients, the high intra-patient variability, as well as exogenous meal disturbances, poses a serious challenge. The existing control algorithms thus require additional safety algorithms and feed-forward actions. Moreover, the unavailability of insulin sensors in Artificial Pancreas makes this task more difficult. In the present work, a subcutaneous model of type 1 diabetes (T1D) is considered for observer-based controller design in the framework of contraction analysis. A variety of realistic multiple-meal scenarios for three virtual T1D patients have been investigated with +30 % and -30 % of parametric variability. The average time spent by the three T1D patients is found to be 77 %, 73 % and 76 %, respectively. A significant reduction in the time spent in hyperglycemia (>180 mg/dl) is achieved without any feed-forward action for meal compensation.

Physical Human-Robot Interaction (pHRI) task involves tight coupling between safety constraints and compliance with human intentions. In this paper, a novel switched model reference admittance controller is developed to maintain compliance with the external force while upholding safety constraints in the workspace for an n-link manipulator involved in pHRI. A switched reference model is designed for the admittance controller to generate the reference trajectory within the safe workspace. The stability analysis of the switched reference model is carried out by an appropriate selection of the Common Quadratic Lyapunov Function (CQLF) so that asymptotic convergence of the trajectory tracking error is ensured. The efficacy of the proposed controller is validated in simulation on a two-link robot manipulator.

A problem of computing time-fuel optimal control for state transfer of a single input linear time invariant (LTI) system to the origin is considered. The input is assumed to be bounded. Since, the optimal control is bang-off-bang in nature, it is characterized by sequences of +1 , 0 and -1 and the corresponding switching time instants. All (candidate) sequences satisfying the Pontryagin's maximum principle (PMP) necessary conditions are characterized. The number of candidate sequences is obtained as a function of the order of system and a method to list all candidate sequences is derived. Corresponding to each candidate sequence, switching time instants are computed by solving a static optimization problem. Since the candidate control input is a piece-wise constant function, the time-fuel cost functional is converted to a linear function in switching time instants. By using a simple substitution of variables, reachability constraints are converted to polynomial equations and inequalities. Such a static optimization problem can be solved separately for each candidate sequence. Finally, the optimal control input is obtained from candidate sequences which gives the least cost. For each sequence, optimization problem can be solved by converting it to a generalized moment problem (GMP) and then solving a hierachical sequence of semidefinite relaxations to approximate the minima and minimizer [1]. Lastly, a numerical example is presented for demonstration of method.

In this paper, the tracking control problem of an Euler-Lagrange system is addressed with regard to parametric uncertainties, and an adaptive-robust control strategy, christened Time-Delayed Adaptive Robust Control (TARC), is presented. TARC approximates the unknown dynamics through the time-delayed estimation, and the adaptive-robust control provides robustness against the approximation error. The novel adaptation law of TARC, in contrast to the conventional adaptive-robust control methodologies, requires neither complete model of the system nor any knowledge of predefined uncertainty bounds to compute the switching gain, and circumvents the over- and underestimation problems of the switching gain. Moreover, TARC only utilizes position feedback and approximates the velocity and acceleration terms from the past position data. The adopted state-derivatives estimation method in TARC avoids any explicit requirement of external low pass filters for the removal of measurement noise. A new stability notion in continuous-time domain is proposed considering the time delay, adaptive law, and state-derivatives estimation which in turn provides a selection criterion for gains and sampling interval of the controller.

This work proposes a new adaptive-robust control (ARC) architecture for a class of uncertain Euler-Lagrange (EL) systems where the upper bound of the uncertainty satisfies linear in parameters (LIP) structure. Conventional ARC strategies either require structural knowledge of the system or presume that the overall uncertainties or its time derivative are norm bounded by a constant. Due to unmodelled dynamics and modelling imperfection, true structural knowledge of the system is not always available. Further, for the class of systems under consideration, prior assumption regarding the uncertainties (or its time derivative) being upper bounded by a constant, puts a restriction on states beforehand. Conventional ARC laws invite overestimation-underestimation problem of switching gain. Towards this front, Adaptive Switching-gain based Robust Control (ASRC) is proposed which alleviates the overestimation-underestimation problem of switching gain. Moreover, ASRC avoids any presumption of constant upper bound on the overall uncertainties and can negotiate uncertainties regardless of being linear or nonlinear in parameters. Experimental results of ASRC using a wheeled mobile robot notes improved control performance in comparison to adaptive sliding mode control., 10 pages, 9 figures

Convergence of controller parameters in standard model reference adaptive control (MRAC) requires the system states to be persistently exciting (PE), a restrictive condition to be verified online. A recent data-driven approach, concurrent learning, uses information-rich past data concurrently with the standard parameter update laws to guarantee parameter convergence without the need of the PE condition. This method guarantees exponential convergence of both the tracking and the controller parameter estimation errors to zero, whereas, the classical MRAC merely ensures asymptotic convergence of tracking error to zero. However, the method requires knowledge of the state derivative, at least at the time instances when the state values are stored in memory. The method further assumes knowledge of the control allocation matrix. This paper addresses these limitations by using a memory-based finite-time system identifier in conjunction with a data-driven approach, leading to convergence of both the tracking and the controller parameter estimation errors without the PE condition and knowledge of the system matrices and the state derivative. A Lyapunov based stability proof is included to justify the validity of the proposed data-driven approach. Simulation results demonstrate the efficacy of the suggested method.

In this note, analysis of time delay systems using Lambert W function approach is reassessed. A common canonical form of time delay systems is defined. We extended the recent results of [6] for second order into nth order system. The eigenvalues of a time delay system are either real or complex conjugate pairs and therefore, the whole eigenspectrum can be associated with only two real branches of the Lambert W function. A new class of time delay systems is characterized to extend the applicability of the above said method. A state variable transformation is used to transform the proposed class of systems into the common canonical form. Moreover, this approach has been exploited to design a controller which places a subset of eigenvalues at desired locations. Stability is analyesed by the help of Nyquist plot. The approach is validated through an example.

In this paper, the tracking control problem of a class of Euler-Lagrange systems subjected to unknown uncertainties is addressed and an adaptive-robust control strategy, christened as Time-Delayed Adaptive Robust Control (TARC) is presented. The proposed control strategy approximates the unknown dynamics through time-delayed logic, and the switching logic provides robustness against the approximation error. The novel adaptation law for the switching gain, in contrast to the conventional adaptive-robust control methodologies, does not require either nominal modelling or predefined bounds of the uncertainties. Also, the proposed adaptive law circumvents the overestimation-underestimation problem of switching gain. The state derivatives in the proposed control law is estimated from past data of the state to alleviate the measurement error when state derivatives are not available directly. Moreover, a new stability notion for time-delayed control is proposed which in turn provides a selection criterion for controller gain and sampling interval. Experimental result of the proposed methodology using a nonholonomic wheeled mobile robot (WMR) is presented and improved tracking accuracy of the proposed control law is noted compared to time-delayed control and adaptive sliding mode control., 9 pages

In this paper, the tracking control problem of a class of uncertain Euler-Lagrange systems subjected to unknown input delay and bounded disturbances is addressed. To this front, a novel delay dependent control law, referred as Adaptive Robust Outer Loop Control (AROLC) is proposed. Compared to the conventional predictor based approaches, the proposed controller is capable of negotiating any input delay, within a stipulated range, without knowing the delay or its variation. The maximum allowable input delay is computed through Razumikhin-type stability analysis. AROLC also provides robustness against the disturbances due to input delay, parametric variations and unmodelled dynamics through switching control law. The novel adaptive law allows the switching gain to modify itself online in accordance with the tracking error without any prerequisite of the uncertainties. The uncertain system, employing AROLC, is shown to be Uniformly Ultimately Bounded (UUB). As a proof of concept, experimentation is carried out on a nonholonomic wheeled mobile robot with various time varying as well as fixed input delay, and better tracking accuracy of the proposed controller is noted compared to predictor based methodology.

Two different aspects of formation control of multiple agents subjected to linear transformation have been addressed in this paper. We consider a set of complex single integrator systems so that the dimension of the system reduces to half as opposed to the vector representation in Cartesian coordinate system. We first design a stable formation controller in an attempt to solve the formation control turned to stabilization problem and then find a collision avoidance controller in the transformed domain, respectively. Different linear transformations are used to facilitate the formation control task in a different way. For example Jacobi transformation is used to separate the shape control and trajectory control. The inverse of the transformation must have nonzero eigenvalues with both positive and negative real parts which may lead the system to instability. If the inverse of the transformation appears in closed loop then a diagonal stabilizing matrix is required to reassign the eigenvalues of the inverse of transformation in the right half of complex plane. The algorithm to find such stabilizing matrix is provided. We then define a matrix of potential in the actual domain which is the stepping stone to find a matrix of potential in the transformed domain. Thus collision avoidance controller can be designed directly in the transformed domain. The mathematical proof is given that both the actual and transformed system behaves identically. Simulation results are provided to support our claim.

Different geometric patterns and shapes are generated using groups of agents, and this needs formation control. In this paper, Centroid Based Transformation (CBT), has been applied to decompose the combined dynamics of nonholonomic Wheeled Mobile Robots (WMRs) into three subsystems: intra and inter group shape dynamics, and the dynamics of the centroid. The intra group shape dynamics can further be partitioned into the shape dynamics of each group, giving the notion of multiple group. Thus separate controllers have been designed for each subsystem. The gains of the controllers are such chosen that the overall system becomes singularly perturbed system, and different subsystems converge to their desired values at different times. Then multi-time scale convergence analysis has been carried out in this paper. Negative gradient of a potential based function has been added to the controller to ensure collision avoidance among the robots. Simulation results have been provided to demonstrate the effectiveness of the proposed controller., arXiv admin note: text overlap with arXiv:1412.6164