Five-link Planar Robot Research Articles

Robust model-free control for redundant robotic manipulators based on zeroing neural networks activated by nonlinear functions

Recent studies have verified that zeroing neural network is suitable for model-free feedback control of redundant robot manipulators with excellent convergence and accuracy. Unlike previous studies using a linear activation function, this paper employs zeroing neural networks activated by nonlinear functions to control redundant robots to track desired paths without knowing kinematic models of robots, and systematically investigates the finite-time convergence and robustness of the proposed control scheme. Specifically, two nonlinear-function-activated zeroing neural networks are employed to solve the Jacobian estimation problem and trajectory tracking problem respectively. After introducing a model-free control scheme generally applicable to different types of robots, theoretical analysis proves that the proposed control scheme has finite-time convergence when employing nonlinear activation functions and the tracking error will not exceed the upper bound with the bounded noise interference. Finally, simulations based on a five-link planar robot and a PUMA 560 robot reveal the finite-time convergence of the proposed control scheme and verify that nonlinear functions can effectively increase the error convergence rate and reduce the tracking error caused by noises, compared with conventional method based on linear-function-activated zeroing neural networks.

The Application of ZFD Formula to Kinematic Control of Redundant Robot Manipulators With Guaranteed Motion Precision

Zhang et al. recently design a special difference formula called the Zhang finite-difference (ZFD) formula. This paper applies the ZFD formula for the kinematic control of redundant robot manipulators, due to its good performance in approximating first-order derivatives. Specifically, the ZFD formula is employed to discrete the pseudoinverse-based (P-based) kinematic control scheme; a new P-based kinematic control scheme with guaranteed motion precision is developed for redundant robot manipulators. Simulation results based on a five-link planar robot manipulator, which performs different end-effector paths, validate the effectiveness of the new scheme and indicate the application prospects of the ZFD formula.

G2-type SRMPC scheme for synchronous manipulation of two redundant robot arms.

In this paper, to remedy the joint-angle drift phenomenon for manipulation of two redundant robot arms, a novel scheme for simultaneous repetitive motion planning and control (SRMPC) at the joint-acceleration level is proposed, which consists of two subschemes. To do so, the performance index of each SRMPC subscheme is derived and designed by employing the gradient dynamics twice, of which a convergence theorem and its proof are presented. In addition, for improving the accuracy of the motion planning and control, position error, and velocity, error feedbacks are incorporated into the forward kinematics equation and analyzed via Zhang neural-dynamics method. Then the two subschemes are simultaneously reformulated as two quadratic programs (QPs), which are finally unified into one QP problem. Furthermore, a piecewise-linear projection equation-based neural network (PLPENN) is used to solve the unified QP problem, which can handle the strictly convex QP problem in an inverse-free manner. More importantly, via such a unified QP formulation and the corresponding PLPENN solver, the synchronism of two redundant robot arms is guaranteed. Finally, two given tasks are fulfilled by 2 three-link and 2 five-link planar robot arms, respectively. Computer-simulation results validate the efficacy and accuracy of the SRMPC scheme and the corresponding PLPENN solver for synchronous manipulation of two redundant robot arms.

Acceleration-level repetitive motion planning of redundant planar robots solved by a simplified LVI-based primal-dual neural network

In this paper, we propose a novel repetitive motion planning (RMP) scheme at the joint-acceleration level (termed, the acceleration-level RMP scheme, the ARMP scheme), which incorporates joint-angle limits, joint-velocity limits and joint-acceleration limits. To do this, Zhang et al's neural-dynamic method is employed to derive and design such an ARMP scheme. Such a scheme is then reformulated as a quadratic program (QP). To solve this QP problem online, a simplified linear-variational-inequality based primal-dual neural network (i.e., S-LVI-PDNN) is designed. With simple piecewise-linear dynamics and global exponential convergence to the optimal solution, such an S-LVI-PDNN solver can handle the strictly convex QP problem in an inverse-free manner. Finally, three given tasks, i.e., rhombic path, straight-line path and square path tracking tasks, are fulfilled by three-link, four-link and five-link planar robot arms, respectively. Computer-simulation and physical experiment results validate the physical realizability, efficacy and accuracy of the ARMP scheme and the corresponding S-LVI-PDNN solver.

Robust control of underactuated bipeds using sliding modes

SUMMARYThe purpose of this paper is to present a robust tracking control algorithm for underactuated biped robots capable of self-balancing in the presence of external disturbances. The biped is modeled as a five-link planar robot with four actuators located at hip and knee joints. A sliding mode control law has been developed for the biped to follow a human-like gait trajectory while keeping the torso nearly upright. The control forces are calculated by defining four first-order sliding surfaces as a linear combination of the torso and the four joint tracking errors. The control approach is shown to guarantee that all trajectories will reach and stay on these surfaces during each step, while the walking cycle stability is maintained through a Lyapunov function. The criteria for asymptotic stability of the surfaces are presented and a numerical search method is implemented for the selection of the corresponding surface parameters. The paper further investigates the robustness of the controller in response to disturbances. Numerical simulations demonstrate the tracking stability of the biped's multistep walk and its human-like response to an external disturbance.

Time-scaling control for an underactuated biped robot

This paper presents a control law for the tracking of a cyclic reference trajectory by an underactuated biped robot. The robot studied is a five-link planar robot. The degree of underactuation is one during the single support phase. The control law is defined in such a way that only the geometric evolution of the robot is controlled, not the temporal evolution. To achieve this objective, we consider a time-scaling control. For a given reference path, the temporal evolution during the geometric tracking is completely defined and can be analyzed through the study of the dynamic model. A simple analytical condition is deduced that guarantees convergence toward the cyclic reference trajectory. This condition implies temporal convergence after the geometric convergence. This condition is defined on the cyclic reference path. The control law is stable if the angular momentum around the contact point is greater at the end of the single support phase than at the beginning of the single support phase.