This paper addresses trajectory planning and control for a dual-arm free-floating space robot (FFSR) based on predefinedtime stability. Firstly, a class of general nonsingular terminal sliding mode control strategy is proposed to achieve global predefined-time stability by switching a control parameter in a form of function. Then, a high-precision trajectory planning method is proposed for a FFSR using the proposed predefined-time stability theorem, which can make the end-effector and the base reach the desired pose within a prespecified time, and reduce the adverse effect on planning accuracy resulted from the singularity avoidance algorithm and the obstacle avoidance one. Subsequently, a trajectory tracking control strategy is proposed for a FFSR employing the proposed general nonsingular predefined-time terminal sliding mode, and the tracking errors can converge within a predefined time to an arbitrarily small neighborhood of zero in the presence of persistent disturbances. The proposed trajectory planning method has the advantage of pose feedback, so can be combined with the trajectory tracking controller in the control process to further enhance the control performance for the FFSR. Simulation results validate the effectiveness of the proposed methodologies.

This paper addresses fixed-time trajectory tracking for a dual-arm free-floating space robot (FFSR) with the large initial errors and bounded uncertainty. A wrist-based trajectory planning method is improved by fixed-time stability to fast eliminate the error caused by singularity. Then, a novel low-chattering and global-nonsingular fixed-time terminal sliding mode control strategy is studied by state approaching angle and switching sliding mode; the practical fixed-reachable Lyapunov stability analysis is presented for a mechanical control system. In the end, the proposed trajectory planning method and controller are combined to improve the tracking accuracy of end-effector to the nanoscale. Simulation results validate the effectiveness of the proposed methodologies.

Adaptive Takagi-Sugeno (T-S) fuzzy control was a real-time control method without off-line input and output data, but the approximate error between this T-S fuzzy model and the actual system model was rarely considered in the existing methods. This problem can lead to the degradation of controller accuracy in practical engineering. In order to solve this problem, the mathematical expression of the upper bound for the approximate error between adaptive T-S fuzzy logic system and the actual system was derived for the first time under any number of rules. This achievement was the key to the design of robust fuzzy controller based on Lyapunov synthesis method under finite number of rules, and this controller can achieve predictability of accuracy. Compared with existing T-S fuzzy control methods, the proposed method can realize the self-adjusting accuracy control for the unknown-structure system without the off-line input and output data. The unknown non-affine control system simulation and 3-DOF robotic arm experiment were carried out to verify the effectiveness of proposed method. Note to Practitioners —Due to the wide application of T-S fuzzy model in practice control system, such as the robot control, the unmanned vehicle control and so on, the actual control accuracy of T-S fuzzy controller was concerned by many scholars. However, the actual precision degradation of the controller was a difficult problem in on-line T-S fuzzy control. In order to solve this problem, a novel adaptive T-S fuzzy control method was proposed in this paper. In practical application, T-S fuzzy model often had a large approximate error with the actual model because of structure uncertainty, and this approximate error was the key factor affecting the actual accuracy of T-S fuzzy controller. Hence, the mathematical expression of the upper bound for the approximate error between adaptive T-S fuzzy logic system and the actual system was derived for the first time under any number of rules. Based on this mathematical expression, we can design a self-adjusting accuracy robust fuzzy controller based on Lyapunov synthesis method. 3-DOF robotic arm experiment verified that the proposed method can achieve the predefined control error with or without the feedforward of robot dynamics. 3-DOF robotic arm comparison experiments verified that the advantages of proposed method.

Due to model uncertainty, system coupling and external disturbance, the mathematical structure of control system is often constructed imprecisely. This unknown structure implies the unknown system dynamic and control input direction. Hence, it is difficult for unknown-structure Multiple Input Multiple Output (MIMO) coupled control systems to prescribe the settling time and control accuracy. To solve this problem, a novel prescribed-time robust direction-adjusting control method is proposed by adaptive Takagi-Sugeno (AT-S) fuzzy approximation. More specifically, by constructing an adaptive T-S fuzzy approximator under relaxed conditions, the mismatched uncertainty of systems can be transformed into the bounded matched uncertainty. It is a pre-condition for prescribed finite-time stability. After the prescribed time terminal, an adaptive robust control designed on AT-S fuzzy model is used for prescribed-accuracy convergence. Besides, compared with existing studies, the proposed method is independent of the structure information and initial control direction. Simulations and experiments verify its effectiveness. Note to Practitioners —The robot arm system with no or lowaccuracy Lagrange dynamic identification is a typical unknownstructure MIMO coupled system. It is difficult to achieve fastconvergence and high-accuracy control for this practical system, especially with no empirical pre-adjustment of the initial input direction. To solve this practical problem, a novel prescribedtime direction-adjusting adaptive T-S fuzzy control method is proposed. Firstly, the robotic arm system is decoupled into multiple joint subsystems by virtual dimension reduction strategy to avoid rule explosion, where system coupling is also converted to bounded unmatched uncertainty. Then, the inappropriate initial direction of the actuator input signal is addressed by control direction-adjusting algorithm. Meanwhile, based on adaptive TS fuzzy approximation theorem, the mismatched uncertainty is transformed into the bounded matched uncertainty. In the end, according to the prediction of approximation accuracy, a prescribed-accuracy robust controller is designed on AT-S fuzzy model. The proposed method is effective in a practical robotic arm control experiment without identification of Lagrange dynamics. Moreover, compared with other related methods, the control precision of the proposed method is higher.

In this paper, a fuzzy neural network based predefined-time trajectory tracking control method is proposed for the tracking problem of omnidirectional mobile robots (FM-OMR) with uncertainties. Considering the requirement of tracking error convergence time, a position tracking controller based on predefined-time stability is proposed. Compared with the traditional position tracking control method, the minimum upper bound of the convergence time can be explicitly set. In order to obtain more accurate angular velocity tracking, the inner loop controller combines Type 1 fuzzy neural network (T1FNN) to estimate the uncertainty. In addition, considering the problem of feedback channel noise, a Kalman filter combining velocity and position information is proposed. Finally, the simulation results verify the effectiveness of this method.