Effective Control Method Based on Trajectory Optimization for Three-Link Vertical Underactuated Manipulators With Only One Active Joint.

For a three-link vertical underactuated manipulator (TVUM) with only one active joint, the control target is to swing up its endpoint from the straight-down equilibrium point (SDEP) and to stabilize the endpoint at the straight-up equilibrium point (SUEP) eventually. Up to now, there are few effective control strategies to achieve the above control target. In this article, we propose an effective control method based on the trajectory optimization to realize the system control target, and the main steps of this article are: 1) a continuous trajectory that consists of two segments with design parameters is planned for the actuated link, along which the actuated link can be swung up from the initial states to the final states; 2) the design parameters are optimized by using the intelligent optimization algorithm to guarantee that the states of the underactuated links are continuous at the junction. In this way, the underactuated links are also moved to their final states with the actuated link simultaneously; 3) a tracking controller is designed by using the sliding-mode method to track the trajectory with optimized design parameters, so the endpoint is swung up from the SDEP to the SUEP directly; and 4) a stabilizing controller is further devised through the LQR method to keep the endpoint being stable at the SUEP. Finally, simulation results show that the proposed control method achieves the swing-up and stable control target of the system, and the control performance of the proposed method is superior than that of the existing control methods through the comparisons.

Tip Position Control and Vibration Suppression of a Planar Two-Link Rigid-Flexible Underactuated Manipulator.

When a flexible link manipulator lacks a joint motor, how to use the remaining motors to achieve the control objective is a challenge, and the research in this direction is limited. This article presents a tip position control and vibration suppression approach for a planar two-link rigid-flexible (TLRF) underactuated manipulator with a passive first joint. First, we establish a dynamic model of the system by using the assumed mode method (AMM) and the Lagrangian modeling method. Then, we obtain the dynamic coupling relationship of the two links based on the dynamic model. According to this dynamic coupling relationship, we find that the passive rigid link can be controlled indirectly by controlling the active flexible link. Thus, we calculate the target angles of the two links by using the inverse kinematic method and design a controller for the active flexible link to stabilize it at its target angle and to suppress its vibration. Next, we optimize the parameters of this controller by using the genetic algorithm (GA). GA helps us simultaneously stabilize the passive rigid link at its target angle while realizing the control objective of the active flexible link. The simulation results demonstrate the effectiveness of the proposed control approach.

Motion Planning and Adaptive Neural Tracking Control of an Uncertain Two-Link Rigid-Flexible Manipulator With Vibration Amplitude Constraint.

This article deals with an uncertain two-link rigid-flexible manipulator with vibration amplitude constraint, intending to achieve its position control via motion planning and adaptive tracking approach. In motion planning, the motion trajectories for the two links of the manipulator are planned based on virtual damping and online trajectories correction techniques. The planned trajectories can not only guarantee that the two links can reach their desired angles, but also have the ability to suppress vibration, which can be adjusted to meet the vibration amplitude constraint by limiting the parameters of the planned trajectories. Then, the adaptive tracking controller is designed using the radial basis function neural network and the sliding mode control technique. The developed controller makes the two links of the manipulator track the planned trajectories under the uncertainties including unmodeled dynamics, parameter perturbations, and persistent external disturbances acting on the joint motors. The simulation results verify the effectiveness of the proposed control strategy and also demonstrate the superior performance of the motion planning and the tracking controller.

A unified and simple control strategy for a class of n-link vertical underactuated manipulator.

In this paper, we propose a unified and simple trajectory planning-based control strategy for the n-link (n≥2⋂n∈Z) vertical underactuated manipulator (VUM) with an underactuated joint. The proposed method does not need to partition the entire motion space like the traditional methods, and can quickly realize the control objective of swinging the endpoint of the system up from the vertical downward starting position and stabilizing it at the vertical upward ending position. The trajectory planned for each active link includes two stages. The first stage is to make the first active link and passive link reach the intermediate states, and other active links reach the ending states. The second stage is to move the first active link and the passive link to the ending states, while other active links keep at the ending states. Considering the above targets of two stages, the trajectory of each active link is designed and the trajectory parameters are optimized via utilizing the differential evolution algorithm. Then, the tracking controllers and stabilization controllers are designed to track the two-stage trajectories and to stay the endpoint at the ending position. Finally, the numerical simulations are carried out to show the feasibility and superiority of the proposed method.

Equivalent-input-disturbance-based robust control of drilling trajectory with weight-on-bit uncertainty in directional drilling.

Weight-on-Bit is of vital importance to the drilling trajectory orientation in directional drilling. This paper concerns robust control of drilling trajectory with weight-on-bit uncertainty for the directional drilling process. The objective is to develop an equivalent-input-disturbance-based trajectory control scheme such that the drilling trajectory is precisely controlled by suppressing the fluctuations of weight-on-bit. The motion orientation of both the drill bit and a series of stabilizers is used to describe the evolution process of the drilling trajectory. A state-space model with weight-on-bit uncertainty is derived from the evolution equation through a variable transformation. An equivalent-input-disturbance-based trajectory control system is designed, and two control loops are to track and control the trajectory inclination and azimuth, respectively. Two internal models track the trajectory inclination and azimuth respectively to elevate the control accuracy in the trajectory system. Two observer models combined with two low-pass filters estimate the trajectory inclination and azimuth by measuring the bottom hole assembly's inclination and azimuth. Some sufficient conditions are derived using linear-matrix-inequalities to obtain the control parameters by considering a reasonable fluctuation range of weight-on-bit. Finally, the control effects in the build-up and horizontal section of the drilling trajectory illustrate the proposed approach's validity.

Position control for planar four-link underactuated manipulator with a passive third joint.

This paper presents a position control strategy based on the differential evolution (DE) algorithm for a planar four-link underactuated manipulator (PFUM) with a passive third joint, which is to move its end-point from any initial position to any target position. Based on the structural characteristic of the PFUM, a model reduction method is conceived to reduce the PFUM to a planar virtual three-link manipulator and a planar Acrobot in turn. Considering the existence of the angle constraint in the planar Acrobot, the DE algorithm is used to optimize and coordinate the control objective of each reduced system, and also to ensure the target angles of the planar Acrobot corresponding to the target position of the PFUM can be found. Simulations demonstrate the validity of the proposed control strategy.

Comprehensive unified control strategy for underactuated two-link manipulators.

This paper presents a unified treatment of the motion control of underactuated two-link manipulators, including acrobots and pendubots. The motion space is divided into two areas: swing-up and attractive; and control laws are designed for each. First, a control law based on a weak-control Lyapunov function (WCLF) is employed to increase the energy of and control the posture of the actuated link in the swing-up area. Next, one parameter of the WCLF is chosen to be a nonlinear function of the state to avoid singularities. Then, another parameter of the control law is adjusted based on the state to improve the control performance. Finally, an optimal control law is designed for the attractive area. Stability is guaranteed in the swing-up area by the use of a WCLF based on LaSalle's invariance principle. Moreover, the global stability of the control system is guaranteed by integrating the WCLF and a nonsmooth Lyapunov function.