A comparison study of some control methods for delta spatial parallel robot

A comparison between three methods applied to parallel robot control namely: Computed torque controller, sliding mode control and sliding mode control using neural networks is presented in this paper. The simulation results show that PD control method is only accurate when model parameters are precisely identified.
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A comparison study of some control methods for delta spatial parallel robotJournal of Computer Science and Cybernetics, V.31, N.1 (2015), 71–81DOI: 10.15625/1813-9663/31/1/5088A COMPARISON STUDY OF SOME CONTROL METHODS FORDELTA SPATIAL PARALLEL ROBOTNGUYEN VAN KHANG1,a , NGUYEN QUANG HOANG1,b , NGUYEN DUC SANG1 , andNGUYEN DINH DUNG21 Departmentof Applied Mechanics, School of Mechanical Engineering,Hanoi University of Science and Technologya khang.nguyenvan2@hust.edu.vn; b hoang.nguyenquang@hust.edu.vn2 Phuong Dong UniversityAbstract.A comparison between three methods applied to parallel robot control namely: computed torque controller, sliding mode control and sliding mode control using neural networks ispresented in this paper. The simulation results show that PD control method is only accurate whenmodel parameters are precisely identified. In case of uncertain parameters, sliding mode and neuralnetwork sliding mode control methods are applied instead. Three controllers are implemented inMatlab for simulation. The results show that the control quality is improved by using the neuralnetwork sliding mode control method in comparison with two others.Keywords. Delta parallel robot, computed-torque control, sliding mode control, neural networkcontrol.1.INTRODUCTIONToday, parallel robotic manipulators are used widely in industrial applications owing to light compactstructure, high stiffness and accuracy. Delta robot is one of the most successful parallel robots, withthousands of versions created around the world for several applications such as in food factories andmedical field. Invented by Reymond Clavel in the early ’80s, this parallel robot uses the parallelogramstructure to create three translational degrees of freedom by three revolute actuators.In most applications, the robot must move rapidly from one position to another position orfollow a desired trajectory in three dimensional spaces with high precision. In order to performthis task, recently, several control methods have been investigated such as computed torque withPD controller [17], sliding mode controller [14,15,16]. The computed torque controller is easy toimplement, but it cannot meet the control quality due to uncertainties in the system model anddisturbances. The sliding mode controller is robust and can improve control quality. However, due toa discontinuous part, this control method can lead to chattering phenomenon, which makes difficultyto control and reduces quality control [14,15]. Another drawback of the sliding mode controller is thatit requires the bounds of uncertainties and disturbances being available. The sliding mode controlwith online learning neural networks has been applied to serial robotic manipulators, in which thesystem uncertainties and disturbances are estimated by a function approximation technique [8,19-25].In this paper, three control algorithms including inverse dynamic based, sliding mode and neuralnetwork based controllers are implemented for the delta spatial parallel robot. The simulation resultsshow the outstanding features of the neural network based controller to the two others.c 2015 Vietnam Academy of Science & Technology72NGUYEN VAN KHANG, NGUYEN QUANG HOANG, NGUYEN DUC SANG, NGUYEN DINH DUNG2.DYNAMIC MODELThe equations of motion of a parallel robot can be obtained by either sub-structural method, NewtonEuler equations [1- 4] or Lagrangian multiplier equation [5,6,7]. These equations are written in matrixform as follows:λM(q)¨ + C(q, q)q + Dq + g(q) =Bu + ΦT (q)λq˙ ˙˙φ (q) =0(1)where M(q), C(q, q)q, Dq, g(q), and u are mass matrix, Coriolis and centrifugal forces, damping˙ ˙˙φforces, gravitational forces, and control inputs, respectively; φ (q), Φ(q) = ∂φ (q)/∂q, and λare constrained equations, Jacobian matrix and vector of Lagrangian multipliers, respectively; q =θ[θ T , ΨT , xT ]T is generalized coordinate vector which includes actuated and auxiliary angles, andposition of the mobile platform.Using the method of coordinate separation and Lagrangian multipliers elimination [10-13] yields themotion equations in the form of minimum generalized coordinates as followsθ ¨θ ˙ ˙θ ˙ ˙θMθ (θ )θ + Cθ (θ , θ )θ + Dθ (θ , θ )θ + gθ (θ ) = u.(2)θIn dynamics (2) the following properties hold: Mθ (θ ) - positive definite and symmetric matrix,˙˙ θ (θ ) − 2Cθ (θ , θ )] - skew-symmetric matrix, and Dθ (θ , θ ) - semi-positive definite matrix.θθ ˙N = [M θIn the next section, Eq. (2) will be used for designing controller.3.REVIEW OF THREE CONTROL METHODS FOR PARALLEL ROBOTSThe objective of the control problem is to find control forces u acting on the robot to drive the mobileplatform to track the desired motion xd (t). This means to control the actuated coordinates θ (t) tofollow its desired motion θ d (t) corresponding to the desired motion of mobile platform xd (t). Threecontrol algorithms are shown in this section.3.1.Computed-torque controllerThe computed-torque controller has been applied to serial robotic manipulators [16, 17]. This approach can also be applied to parallel manipulators. By applying this approach, the control input iscomputed as followingθθ ˙ ˙θ ˙ ˙θu = Mθ (θ )a + Cθ (θ , θ )θ + Dθ (θ , θ )θ + gθ (θ )(3)¨˙ ˙θa = θ d − Kd (θ − θ d ) − Kp (θ − θ d ),(4)withwhere Kd , Kp are positive definite matrices:Kp = diag (kp1 , kp2 , ..., kpna ), kpi > 0, Kd = diag (kd1 , kd2 , ..., kdna ), kdi > 0.Substituting (3) and (4) into Eqs. (2) results in¨˙˜˜˜θ ˜Mθ (θ )(θ + Kdθ + Kpθ ) = 0, θ = θ − θ d .(5)A COMPARISON STUDY OF SOME CONTROL METHODS FOR DELTA SPATIAL PARALLEL ROBOT73θNote that Mθ (θ ) is a positive definite matrix, it can be eliminated from Eq. (5):¨˙˜˜˜θ + Kdθ + Kpθ = 0.(6)Based on the dynamics of error shown in Eq. (6), the controller parameters are chosen as2kpi = ωi , kdi = 2δi ωi , wit ...