Yawu Wang

Stable Control Strategy for Planar Three-Link Underactuated Mechanical System

A stable-control strategy for a planar three-link passive-active-active underactuated mechanical system not subject to gravity constraints has been devised. The control objective is to move the end effector from any initial position to any target position. First, a dynamic model of the system is built, and its properties are analyzed. Next, based on the complete integrability of an underactuated planar acrobot (UPA), the control of a planar three-link system is divided into two stages. In each stage, keeping the angle of one active link constant reduces the planar three-link system to a UPA, thereby enabling the use of quadrature to obtain the angle constraint relationships between the passive and active links. Then, the target angles associated with the target position are calculated by particle swarm optimization based on the angle constraint relationships. Finally, a controller for each stage is designed, ensuring that the control objective will be reached. Simulation results demonstrate the validity of this control method.

A quick control strategy based on hybrid intelligent optimization algorithm for planar n-link underactuated manipulators

Abstract This paper presents a quick two-stage position control strategy based on a hybrid intelligent optimization algorithm for a planar n-link underactuated manipulator with a passive first joint. In stage 1, the system is directly reduced to a planar virtual Acrobot by controlling n-2 active links to their target angles. A hybrid intelligent optimization algorithm, which includes genetic algorithm (GA) and particle swarm optimization algorithm (PSO), is used to solve all link target angles according to the target position of the system. By coordinating GA and PSO, the hybrid intelligent optimization algorithm ensures that all link target angles, the angle of the passive link at the end of stage 1, and the initial angle of the active link of the planar virtual Acrobot meet the angle constraint of the planar virtual Acrobot. So, the position control objective of the planar n-link underactuated manipulator is realized by controlling the active link of the planar virtual Acrobot to its target angle in stage 2.

Position-Posture Control of a Planar Four-Link Underactuated Manipulator Based on Genetic Algorithm

This paper presents a position-posture control strategy based on genetic algorithm (GA) for a planar four-link passive-active-active-active (PAAA) underactuated manipulator. The control objective of the system is to move the end effector from any initial position to any target position with a specified posture. First, the integrability of the PAAA manipulator is analyzed based on its dynamic model. Then, the control process is divided into three stages based on the partial integrability of a PAAA system and the complete integrability of an Acrobot system. In each stage, the system is reduced to be an Acrobot-like system, and an angle constraint between an actuated joint and the unactuated one is derived based on the complete integrability of an Acrobot system. Next, a mathematical optimization model is constructed to solve the target angles based on multiconstraints and the control objective. And GA is applied to obtain the target angles. Finally, the controllers are designed for each stage to move one actuated joint to the target angle in turn. Simulation results demonstrate the effectiveness of the proposed control approach.

Adaptive robust control for planar n-link underactuated manipulator based on radial basis function neural network and online iterative correction method

Abstract This paper presents an adaptive robust control strategy based on a radial basis function neural network (RBFNN) and an online iterative correction method (OICM) for a planar n-link underactuated manipulator with a passive first joint to realize its position control objective. An uncertain model of the planar n-link underactuated manipulator is built, which contains the parameter perturbation and the external disturbance. The adaptive robust controllers based on the RBFNN are designed to realize the model reduction, which makes the system reduce to a planar virtual three-link underactuated manipulator (PVTUM) and simplifies the complexity of the system control. An online differential evolution (DE) algorithm is used to calculate the target angles of the PVTUM based on the nominal model parameters. The control of the PVTUM is divided into two stages, and the adaptive robust controllers are still employed to realize the control objective of each stage. Then, the OICM is used to correct the deviations of all link angles of the PVTUM caused by the parameter perturbation, which makes the end-point of the system gradually approach to its target position. Finally, simulation results of a planar four-link underactuated manipulator demonstrate the effectiveness of the proposed adaptive robust control strategy.

A quick position control strategy based on optimization algorithm for a class of first-order nonholonomic system

Abstract In this paper, we develop a quick and effective position control strategy based on the differential evolution (DE) algorithm for a planar three-link passive-active-active (PAA) underactuated system with first-order nonholonomic constraint. Due to the existence of the constraint, when the angular velocities of the two active links are proportional, the planar PAA system is transformed from a first-order nonholonomic system to a holonomic system like an Acrobot. Making full use of the angular constraint of the like-Acrobot, we employ the DE algorithm to calculate the target angles of all links and the target ratio between the angular velocities of the two active links. After that, one continuous controller for one active link is designed to ensure the target ratio in the whole control process; meantime, the other continuous controller for the other active link is designed to make its angle asymptotically converge to the corresponding target value. In this way, the angles of all links can asymptotically converge to the corresponding target values according to the angular constraint, and thus the position control of the system is realized using the continuous control method. Finally, the simulation results demonstrate the quickness and effectiveness of our proposed control method.

Effective position–posture control strategy based on switching control for planar three-link underactuated mechanical system

ABSTRACT A planar three-link passive–active–active (PAA) underactuated mechanical system is a kind of nonlinear system with a passive first joint. The position–posture control objective for the planar PAA system is to move the end effector from an initial position to a target position with a specified posture. This paper presents a switch control strategy to solve the position–posture control problem. First, a Lyapunov function is constructed based on the system control objective. Then, a set of main controllers based on this Lyapunov function are designed. However, the main controllers may make the system stabilise at one of equilibrium points, which is not the system target position. To avoid the above phenomenon, when the system is about to stabilise at one non-target position, the main controllers are switched to a set of sub-controllers, which are designed according to another Lyapunov function constructed based on the control objective of the active links. When the sub-controllers are running, their design parameters are adjusted to try to keep the derivative of the first Lyapunov function being a non-positive function. Therefore, the switch control between the main controllers and the sub-controllers realises the position–posture control objective of the system. Finally, the simulation results demonstrate the effectiveness of the switch control strategy.