In this brief, we propose a control method for high-order integrator systems that achieves predefined-time convergence, i.e., the system is driven to the origin in a desired settling time that can be set as an explicit parameter of the controller and it is achieved independently of the initial conditions. Our method can be applied to any single-input single-output (SISO) controllable linear system, to any SISO nonlinear system that can be transformed to the normal form with stable zero dynamics and to multiple-input multiple-output systems that can be decoupled into SISO subsystems in the previously mentioned forms. The proposed approach is based on the so-called time base generators (TBGs), which are time-dependent functions used to build time-varying control laws. The contribution of this brief is the generalization of the TBGs to develop predefined-time controllers for high-order systems, providing procedures to build the required time-dependent functions. The performance of the proposed controllers is evaluated and compared with finite-time and fixed-time controllers in simulations and experiments. We show the applicability of the proposed approach to control electromechanical systems, in particular for the dynamic control of robotic systems.

Driving mobile robots to precise locations is of recognized interest, and using vision sensors in this context supplies many advantages. We propose a novel control law based on sliding-mode theory in order to drive mobile robots to a target location, which is specified by a previously acquired reference image. The control scheme exploits the piecewise epipolar geometry of three views on the basis of image-based visual servoing, in such a way that no 3-D scene information is required. The contribution of the paper is a new control law that achieves convergence to the target with no auxiliary images and without changing to any approach other than epipolar-based control. Additionally, the use of sliding-mode control deals with singularities, thus allowing the robot to move directly toward the target as well as avoiding the need of a precise camera calibration. The effectiveness of our approach is tested with simulations and real-world experiments.

In this article, we propose a robust hierarchical inverse dynamics control scheme for redundant manipulators, which guarantees both predefined-time convergence of regulation tasks and robustness against model uncertainties/disturbances. Predefined-time convergence of a robotic task means that the task error is regulated to the origin at a desired preset time, independently of the initial state of the robot. The strict hierarchy of tasks is ensured by the so-called dynamic consistency, which avoids conflicts between decoupled task constraints. Thus, it enables the robot with more dexterity for reaching targets in its workspace while overcoming obstacles and joint limits. Predefined-time convergence facilitates the design of a time schedule to execute sequential and simultaneous tasks. All these features are supported by a stability analysis and experiments with two torque-controlled mobile manipulators in pick-and-place applications.

This paper proposes a couple of consensus algorithms for multiagent systems in which agents have first-order nonlinear dynamics, reaching the consensus state at a predefined time independently of the initial conditions. The proposed consensus protocols are based on the so-called time base generators (TBGs), which are time-dependent functions used to build time-varying control laws. Predefined-time convergence to the consensus is proved for connected undirected communication topologies and directed topologies having a spanning tree. Furthermore, one of the proposed protocols is based on the super-twisting controller, providing robustness against disturbances while maintaining the predefined-time convergence property. The performance of the proposed methods is illustrated in simulations, and it is compared with finite-time, fixed-time, and predefined-time consensus protocols. It is shown that the proposed TBG protocols represent an advantage not only in the possibility to define a settling time but also in providing smoother and smaller control actions than existing finite-time, fixed-time, and predefined-time consensus.