Dynamic Decoupling of Robot Manipulators

In this chapter, a review of the main methods permitting to achieve the dynamic decoupling of robot manipulators is presented. The design approaches based on the variation of mechanical parameters are disclosed via three sub-groups: decoupling of dynamic equations via mass redistribution; decoupling of dynamic equations via actuator relocation and decoupling of dynamic equations via addition of auxiliary links. The last approach is illustrated via two examples. In the first solution, the optimal design is achieved via gears used as counterweights. It is allows a considerable reduction of the total masses of links of the decoupled manipulator. In the second solution, the dynamic decoupling of robot manipulators is achieved by using an epicyclic gear train. Special attention is paid to the dynamic decoupling of robot manipulators through the use of the double integrator. The second-order linear and time-invariant dynamical system, called double integrator, is one of the most fundamental systems in control applications. It can be considered as single-degree-of-freedom translational and rotational motion. The present review considers in detail the aim of this solution, as well as the advantages of the joint application development inclosing mechanical and control solutions.

In this chapter, a new approach for dynamic decoupling of serial planar manipulators, which is a symbiosis of mechanical and control solutions is proposed. It is based on the opposite motion of manipulator links and the optimal command design. The opposite motion of links with optimal redistribution of masses allows the cancellation of the coefficients of nonlinear terms in the manipulator’s kinetic and potential energy equations. Then, based on this completely linearized and decoupled manipulator, the simple linear control method is used. Furthermore, the changing payload is taken into account as a forward compensation in the controller. Finally, in order to stabilize the manipulator linearized and decoupled, a full state feedback is set up. The suggested design methodology is illustrated by simulations carried out using ADAMS and MATLAB software, which have confirmed the efficiency of the developed approach.

This chapter deals with a new dynamic decoupling principle, which involves connecting to a serial manipulator with revolute joints a two-link group forming a Scott-Russell mechanism with the initial links of the manipulator. The opposite motion of links in the Scott-Russell mechanism combined with optimal redistribution of masses allows the cancellation of the coefficients of nonlinear terms in the manipulator’s kinetic and potential energy equations. Then, by using the optimal control design, the dynamic decoupling due to the changing payload is achieved. The suggested design methodology is illustrated by simulations carried out using ADAMS and MATLAB software, which have confirmed the efficiency of the developed approach.

This chapter deals with the robustness properties of serial manipulators with decoupled and coupled dynamics derived by tolerance analysis. After having introduced some performance indices of the manipulators, the tolerance capabilities of four manipulators are analyzed. In order to quantify the influencing degree, two kinds of the indices are defined. They are angular error and position error. Two kinds of simulation are designed here. The first kind of simulation is implemented by fixed parametric error. Then, the influencing degrees of all variables on the positioning accuracy of the manipulators are analyzed respectively. In order to obtain the models closer to the practical situation, the random parametric errors are introduced in the second kind of simulation. Furthermore, the parametric errors of all the variables are added at the same time during one simulation. The simulation results prove that the manipulators that decoupled by the mechatronic methods are more robust.

Due to the eccentric load of parallel manipulator, dynamic coupling occurs between the various degrees of freedom. As a typical parallel mechanism, the dynamic model of redundant shaking table is built. Coupling force observaction based on coupling model is introduced to the DoFs control structure. The coupling forces are controlled as disturbance forces on hydraulic system by distributing it to each actuator through Jacobi matrix transformation. Decoupling control is given based on the dynamic model as well as a feed forward disturbance force compensation control strategy. However, due to the fact that differentiating acceleration which contains large noise is needed in decoupling control based on dynamic model, modal decoupling control is given. Modal equation of redundant shaking table is given by considering hydraulic cylinder as a hydraulic spring. Through standard modal matrix and its inverse matrix, the redundant shaking table is controlled in non-coupling modal space instead of DoFs space. By analyzing the relationship between the modal matrix and the coupling characteristics of different modal DoFs, an experimental method is given for determining the modal matrix. Simulation analysis shows that compared with decoupling control based on dynamic model, the modal space decoupling control can more effectively reduce the dynamic coupling among DoFs of the redundant shaking table. A control system of the redundant shaking table is developed using rapid control prototyping technology based on xPC Target. Detailed experimental analysis and research are carried out on the proposed coupling characteristic analysis and decoupling control strategies. Experimental results demonstrate that the proposed decoupling control strategies are effective and advanced.

Parallel mechanisms (PMs) with six degree of freedoms (DOF) are widely used in such different segments of industry as a measuring, tooling, and positioning device. The spatial 6-DOF mechanism is examined in this chapter. The mechanism studied has both kinematic and dynamic decoupling. The kinematic problem solution is presented. The control algorithm of handling PMs was tested on the basis of nonlinear systems control theory. The velocity and control problems were solved with the use of dynamic and kinematic decoupling.

Parallel robots often show superior accuracy, performance and load capacity alongside with a fairly simple control. Robot designs featuring kinematic and dynamic decoupling of motion, additionally improve the dynamic characteristics and further simplify the control algorithms. Parallel robots with 3D translatory motion of the end-effector (including micro-manipulator design variants) can be considered as mechatronic systems combining these advantages.