2015 International Conference on Mechatronics, Electronics and Automotive Engineering
Kinematics Modeling and Experimental Validation of a CyberForce Haptic Device Based on Passive Control System Juan D. Ram´ırez-Zamora1 , Gerardo Mart´ınez-Ter´an2 , Omar A. Dom´ınguez-Ram´ırez1 , Luis E. Ramos-Velasco1 , Vicente Parra-Vega3 , Ismaylia Saucedo-Ugalde 4 1 Universidad Aut´onoma del Estado de Hidalgo, 2 Universidad Polit´ecnica de Pachuca, 3 Centro de Investigaci´on y de Estudios Avanzados, Unidad Saltillo. 4 Universidad Polit´ecnica de Sinaloa. juanda
[email protected],
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Abstract
sent the stabilization law point to point in trajectory tracking, as shown in the Figure 1 [8].
This paper shows the experimental validation of the forward and inverse kinematic model (position and velocity), of the CyberForce haptic device (CHD). For trajectory tracking is used a passive control technique in operational coordinates (cartesian workspace) and its experimental results in the joint-space. The contribution in passive haptic guidance, is on virtual maze navigation with purposes of diagnosis and rehabilitation of upper limb, and training only as a proof platform without any patients; to this end, for the motion planning is used a time base generator for tracking in finite time.
Figure 1: Block diagram of the feedback control. This paper proposes the development and implementation of a proportional-derivative robust classic passive-type controller on a CyberForce haptic device and a comparative study on the effect / shift with the use of kinematic model of the robotic platform trajectories convergence of positions under the same operating conditions.
Keywords: CyberForce, Haptic Interface, Force Feedback, Motion Planning, PD Control , Robot Kinematics.
2
CyberForce Haptic Device
1. Introduction The system - exoskeleton (CyberTeam) is constituted of a electromechanical structure with 6 degrees of freedom (CyberForce) ensuring the positioning and orientation of an exoskeleton of 5 degrees of freedom (CyberGrasp) used in handling tasks in virtual environments dynamic deformable (force feedback), the feedback on flexion-extension and adduction-abduction phalanges are used 22 carbon fiber sensors in the glove (CyberGlove).
In engineering practice commonly it exists the need for a physical system to a certain point with some degree of accuracy. A control system is the set of techniques and tools that guide a physical system to the desired conditions. The foundation of the automatic control is to compute corrective action, u depending of the error, e that is defined as the difference between the actual output of the plant:y, and the desired output: yref . This is known as feedback control and consists of three basic parts: a process that define the plant, a sensor as a feedback loop and a controller that repre∗
2.1
The main system components are shown in Figure 2. A 22-sensor CyberGlove system is the core of the
Corresponding author
978-1-4673-8329-5/15 $31.00 © 2015 IEEE DOI 10.1109/ICMEAE.2015.40
System components
105
the extended error in operational coordinates; θ˜ = θ − ˜= θd ∈ R3x1 is the vector of the joint position error, x x−xd ∈ R3x1 is the vector of the operational error; θd y xd represents all the desired joint position and desired cartesian position that define the trajectories; Kθ ∈ R3x3 , Kx ∈ R3x3 , αθ ∈ R3x3 y αx ∈ R3x3 stands for the control gain matrices positive definite and symmetric.
interface, and it is used to measure the joint angles of the fingers. This information is used by the host to display a graphical hand on the screen or control a telerobotic manipulator. The CyberGrasp system is responsible for providing force feedback to the fingers. The CyberGrasp exoskeleton attaches to the back of the hand and guides force-applying tendons to the fingertips. The CyberForce system measures the position and orientation (6 degrees of freedom) of the hand and generates translational (3 degrees of freedom) force feedback. The Force Control Unit (FCU) is the interface between the devices worn by the user and the host computers, which communicate via Ethernet. The host computers need only communicate with the FCU, which in turn communicates with all other peripherals (CyberGlove, CyberGrasp, and CyberForce) [6].
3.1
Motion planning
The task TDH (t), as a set-point of motion applied to the haptic device, it is constituted by three paths; TDH−1 (t) corresponds to the operational regulation based on trajectory tracking in finite time, with purpose to resolve the inertial dynamics due to movement or static condition, and to establish a convergence time tb1 . The trajectory TDH−2 (t), represent to the circumference as a reference (Equation 3) in time TC2 = 2π/ω seconds; with ω as the angular velocity, r is the radio, [Xc , Yc , Zc ] given as the center of the circumference and TCn = tbn − tbn−1 is the convergence time of the trajectory number n TDH (t). TDH−3 (t) is the operational regulation based on trajectory tracking to the initial condition of the task. ⎧ ⎨ TDH−1 (t) TDH−2 (t) TDH (t) = ⎩ TDH−3 (t)
; ; ;
tb0 ≤ t ≤ tb1 tb1 < t ≤ tb2 tb2 < t ≤ tb3
⎤ ⎡ ⎤ Xc + rcos(ωt) Xd (t) ⎦ ⎣ Yd (t) ⎦ = ⎣ Yc Zc + rsin(ωt) Zd (t) ⎡
The trajectories TDH−1 (t) and TDH−3 (t), are defined by the polynomial equation 4, with a time base TCn ; and represent the trajectory used in joint-space and workspace to tracking according to the control law applied, with a smooth performance with the limit of the electromechanical efforts, and ensures perfect tracking in finite time; its derivative ξ˙n (t) allows to compute the velocity in each space (joint and operational) with the maximum value is in the middle of that regulation time ([1],[2],[5]).
Figure 2: CyberForce Haptic Device.
3
Passive Control for Experimental Validation of the Kinematics Model
In order to validate the kinematic position and velocity of the Cyberforce haptic device in motion planning, implementing a classical strategy of passiverobust control ( proportional-derivative) in joint-space (Equation 1) and operational coordinates or workspace (Equation 2) [3]. τ = −Kθ Sθ
(3)
(t − tbn−1 )3 (t − tbn−1 )4 (t − tbn−1 )5 −15 +6 TCn 3 TCn 4 TCn 5 (4) Given the motion planning in the operational space, the trajectories that involve the regulation based on tracking are described as: ξn (t) = 10
(1)
(2) f = −Kx Sx ˜ + αθ θ represents the extended error where, Sθ = x in the joint space; and Sx = d˜ ˜ corresponds to dt + αx x dθ˜ dt
• TDH−1 (t) : {(Xc + r)ξ(t), Yc ξ(t), Zc ξ(t)} t ≤ tb1 106
in tb0 ≤
• TDH−3 (t) : {X0 ξ(t), Y0 ξ(t), Z0 ξ(t)} t ≤ tb3
in
tb2
