Passive Tool Dynamics Rendering for Nonlinear Bilateral Teleoperated Manipulators

-In the companion paper [1], a control law renders a 2n-degree of freedom (DOF) nonlinear teleoperator (consisting of n-DOF master and slave robots) as a n-DOF common passive mechanical tool which has the usual robotic dynamics. In this paper~ we develop a control methodology to endow the resulting n-DOF common passive mechanical tool with useful passive tool dynamics which incorporates inertia scaling, guidance / avoidance system while preserving energetic passivity of the closed-loop system. A fictitious energy storage is used to scale the apparent inertia of the teleoperator. The passive velocity field control [2] for a velocity field tracking and artificial potential function are utilized for guidance / avoidance system. Thus, with the control law proposed in [1]~ the control law renders the 2nDOF teleoperator as a n-DOF common passive mechanical tool which has programmable apparent inertia and moves under the effects of velocity / potential field tailored to task objectives and obstacles in the workspace. I. I N T R O D U C T I O N Consider a 2n-degree of freedom (DOF) n o n l i n e a r teleoperator consisting of n-DOF master and slave robots: fl{Ml(ql)Cll -JrC l ( q l , Cll)Cll : T1 -JrF1} (1) M2(q2)~12 + C2(q2,/t2)/t2 = T2 + F2 (2) where p > 0 is a user-specified power scaling factor, M . , C . , q . F . T . are the inertia matrices, Coriolis matrices, configurations, human/environmental forcings, and control commands to the master and slave robots, respectively. By achieving perfect coordination between the master and the slave configurations (i.e. a n-DOF holonomic constraint (ql = q2) is imposed) and energetic passivity of the closed loop system, the control law proposed in [1] reduces the 2n-DOF teleoperator (1)-(2) to a n-DOF common passive mechanical tool with the usual robotic dynamics: M r ( q ) ~ l r + C r ( q , / t ) / t r = TL + FL, (3) where qT _ [qT, qT] a n d / l T -[/l T,/IT]. Here, ML(q) -p g l ( q l ) -~M2 (q2) and CL (q,/t) = pC l (q l , Ctl) + C2(q2,/t2) are the naturally obtained inert ia/ /Coriol is matrices of the coordinated teleoperator (by summing (1) and , • Corresponding author. Research supported by National Science Foundation under grant CMS-9870013 (2) with ql = q2), FL = pF1 -~F2 is transformed human / /environmental forcings and TL is control to be designed. We call (3) the locked system, since it represents the teleoperator after being perfectly coordinated (locked). In this paper, we propose a control methodology to endow the locked system (3) with useful task-specific passive tool dynamics, so that it becomes a n-DOF passive tool that assists the operator to perform the task efficiently. In order to do that , the control law will be designed to achieve the followings: 1. I n e r t i a Sca l ing to scale d o w n / / u p the apparent inertia of the teleoperator according to tasks. For example, scaling down the inertia is useful for good kinesthetic coupling or haptic feedback. Recall that ideal transparency of linear teleoperators is implied by zero apparent inertia with perfect coordination [3]. 2. V e l o c i t y F i e ld T r a c k i n g to guide the teleoperator so that it moves along a preferred direction specified by a desired velocity field. See figure 1 for an example of velocity field, which guides the robot on x-y plane toward a preferred path. The Passive Velocity Field Control (PVFC) approach ([2], [4], [5]) is utilized in this paper to achieve velocity field tracking. 3. Ar t i f i c i a l P o t e n t i a l F i e l d ([6], [7], [8]) to impose prohibited regions for obstacle avoidance system or to render virtual contours for guiding the teleoperator as the virtual wall of the "Cobots" [9]. See figure 1 for an example of artificial potential field ("U" shape contour). 4. E n e r g e t i c P a s s i v i t y of the closed loop system to enhance safety of the operator and physical environments. Thus, the c o n t r o l o b j e c t i v e is to design T L in (3) to achieve: 1. Useful target tool dynamics: [Mr(q)~lr + Cr (q , / t ) / l r ] ¢ (q , / t ) = FL (4) which incorporates (a) Inertia scaling with the factor U > 0 (b) Guidance / avoidance system ¢(q , / t ) through velocity field tracking and artificial potential field. The design of ¢ (q , / t ) will be discussed in II-A and II-B. 3284 30 Plot of PotentiatFunction andVelocity Fields