Luis Felipe da Cruz Figueredo

Robust kinematic control of manipulator robots using dual quaternion representation

This paper addresses the H∞ robust control problem for robot manipulators using unit dual quaternion representation, which allows an utter description of the end-effector transformation without decoupling rotational and translational dynamics. We propose three different H∞ control criteria that ensure asymptotic convergence, whereas reducing the influence of disturbances upon the system stability. Also, with a new metric of dual quaternion error in SE(3) we prove independence from robot coordinate changes. Simulation results highlight the importance and effectiveness of the proposed approach in terms of performance, robustness, and energy efficiency.

New delay-and-delay-derivative-dependent stability criteria for systems with time-varying delay

This paper provides new delay-and-delay-derivative-dependent criteria for systems with the delay and its derivative varying within intervals. With introduction of new Lyapunov-Krasovskii functionals, a less conservative upper bound for the maximum delay is achieved. Examples show that the resulting criteria outperform previously published results in the literature.

Robust stability of networked control systems

In this paper, a robust stability criterion is proposed for NCSs liable to model uncertainties and time-varying delays. The analysis concerns the establishment of a maximum allowable delay bound for continous time NCSs under parameter uncertainties. The new proposed criterion is based on the solution of a set of Linear Matrix Inequalities (LMIs). Numerical examples are given to validate the theoretical result.

A dual quaternion linear-quadratic optimal controller for trajectory tracking

This work addresses the task-space design problem of a linear-quadratic optimal tracking controller for robotic manipulators using the unit dual quaternion formalism. The efficiency, compactness, and lack of singularity of the representation render the unit dual quaternion a suitable framework for simultaneously describing the attitude and the position of the end-effector. Motivated by the advantages of this kinematic description, we propose a new task-space linear-quadratic optimal tracking controller in order to find an optimal trajectory for the end-effector, providing a tool to balance more conveniently the end-effector error and its task-space velocity. This is possible because the kinematic control problem using the dual quaternion transformation invariant error can be reduced to an affine time-varying system. The proposed optimal tracking controller allows the compensation of trajectory induced disturbances, as well as other modeled additive disturbances and known bias. Simulation results with different design parameters provide a performance overview, in comparison with standard kinematic controllers with and without a feed-forward term, for tracking a desired reference.

Switching strategy for flexible task execution using the cooperative dual task-space framework

This paper presents a new strategy for task space control in the cooperative manipulation framework. We extend the cooperative dual task-space (CDTS) - which uses dual quaternions to represent the bimanual manipulation-to explicitly regard self-motion dynamics that arise from redundant kinematics. In this sense, we propose a flexible task execution criterion that enriches the Jacobian null space with additional degrees of freedom by relaxing control requirements upon specific geometric task objectives. The criterion is satisfied with a hysteresis-based switching strategy that ensures stability and convergence upon traditional and relaxed constraints. Simulation results highlight the importance and effectiveness of the proposed technique.

Hybrid kinematic control for rigid body pose stabilization using dual quaternions

In this paper, we address the rigid body pose stabilization problem using dual quaternion formalism. We propose a hybrid control strategy to design a switching control law with hysteresis in such a way that the global asymptotic stability of the closed-loop system is guaranteed and such that the global attractivity of the stabilization pose does not exhibit chattering, a problem that is present in all discontinuous-based feedback controllers. Using numerical simulations, we illustrate the problems that arise from existing results in the literature—as unwinding and chattering—and verify the effectiveness of the proposed controller to solve the robust global pose stability problem.

Delay-Dependent Robust H∞ Output Tracking Control for Uncertain Networked Control Systems

Abstract In this paper, the H ∞ output tracking problem for networked control systems (NCSs) liable to model uncertainties and with delays varying within intervals is investigated. A new method is proposed to the robust H ∞ output tracking analysis and control design for NCSs. The results presented here are an improvement over previous ones, for the analysis incorporates state-of-the-art stability techniques for systems with time-varying delays such as convex optimization technique, piecewise analysis method, and a new delay fractioning approach with the introduction of a novel auxiliary delayed state. The analysis is enriched with a numerical example that illustrates the advantages of our criteria which outperform previous criteria in the literature. Moreover, an illustrative example shows the effectiveness of the proposed H ∞ output tracking control design.

Robust stability criteria for uncertain systems with delay and its derivative varying within intervals

In this paper, stability criteria are proposed for linear systems liable to model uncertainties and with the delay and its derivative varying within intervals. The results are an improvement over previous ones due to the development of a new Lyapunov-Krasovskii functional (LKF). The analysis incorporates recent advances such as convex optimization technique and piecewise analysis method with new delay-interval depedent LKFs terms and a novel auxiliary delayed state. Stability conditions are provided for the cases when the delay derivative is upper and lower bounded, when the lower bound is unknown, and when no restrictions are cast upon the derivative. The analysis is enriched with numerical examples that illustrate the effectiveness of our criteria which outperform previous criteria in the literature for nominal and uncertain delayed systems.

An improved stability criterion of networked control systems with dynamic controllers in the feedback loop

Despite the solid contribution of recent techniques for the analysis of networked controls systems (NCSs), the use of dynamic controllers has received little attention in the literature. Adapting these methods to consider dynamic controllers in the feedback loop is seldom trivial, however, neglecting this class of controllers restricts the universe of applications of these techniques and, consequently, the importance of previous results. In this paper, we establish a new stability criterion suitable for the analysis of NCSs with dynamic controllers. The technique stems from novel Lyapunov-Krasovskii terms and the synthesis of modern techniques for the analysis of time-delay systems adapted to this new scenario. The proposed strategy yields superior results even when particularized for the analysis of NCSs with proportional controllers. Numerical results are provided in order to illustrate the advantages of the proposed criterion and the effectiveness of the theoretical results.

Novel stabilization technique for the H ∞ control of systems with time-varying input delay

This paper addresses H∞ control strategies for time-delay systems with input delay and its derivative varying within intervals. With the development of a new Lyapunov-Krasovskii functional, we propose a new performance criterion which combines state-of-the-art stability techniques with an improved piecewise analysis method. For the H∞ control design, we state a new stabilization technique based on the use of the Simulated Annealing (SA) algorithm. We also derive traditional stabilization methods: the use of predefined scalars and a modified cone complementarity linearization algorithm, in order to compare their efficiency with the proposed control design technique. The advantages of our H∞ performance and control criteria are also highlighted with numerical examples, and an illustrative example shows the effectiveness of the new control design technique using SA algorithm.