Control for Teleoperation and Haptic Interfaces

Septimiu E. Salcudean

Department of Electrical and Computer Engineering, University of British Columbia Canada

The concept of teleoperation has evolved to accommodate not only manip- ulation at a distance but manipulation across barriers of scale and in vir- tual environments, with applications in many areas. Furthermore, the design of high-performance force-feedback teleoperation masters has been a signifi- cant driving force in the development of novel electromechanical or "haptic"

computer-user interfaces that provide kinesthetic and tactile feedback to the computer user. Since haptic interfaces/teleoperator masters must interact with an operator and a real or virtual dynamic slave that exhibits signifi- cant dynamic uncertainty, including sometimes large and unknown delays, the control of such devices poses significant challenges. This chapter presents a survey of teleoperation control work and discusses issues of simulation and control that arise in the manipulation of virtual environments.

1.

Teleoperation and Haptic

Since its introduction in the 1940s, the field of teleoperation has expanded its scope to include manipulation at different scales and in virtual worlds.

Teleoperation has been used in the handling of radioactive materials, in sub- sea exploration and servicing. Its use has been demonstrated in space [20], in the control of construction/forestry machines of the excavator type [36], in microsurgery and micro-manipulation experiments [33, 39] and other areas.

T h e goal of teleoperation is to achieve "transparency" by mimicking hu- man motor and sensory functions. Within the relatively narrow scope of ma- nipulating a tool, transparency is achieved if the operator cannot distinguish between maneuvering the master controller and maneuvering the actual tool.

The ability of a teleoperation system to provide transparency depends largely upon the performance of the master and the performance of its bilateral controller. Ideally, the master should be able to emulate any environment encountered by the tool, from free-space to infinitely stiff obstacles.

The need for force-feedback in general purpose computer-user interfaces has been pointed out in the 1970s [5]. The demand is even higher today, as performance improvements in computer systems have enabled complex applications requiring significant interaction between the user and the com- puter. Examples include continuous and discrete simulation and optimization,

52 S.E. Salcudean

searching through large databases, mechanical and electrical design, educa- tion and training.

Thus actuated devices with several degrees of freedom can serve as so- phisticated input devices that also provide kinesthetic and tactile feedback to the user. Such devices, called "haptic interfaces", have been demonstrated in a number of applications such as molecular docking [35], surgical training [42], and graphical and force-feedback user interfaces [25].

The design of haptic interfaces is quite challenging, as the outstanding motion and sensing capabilities of the human arm are difficult to match. The performance specifications that haptic interfaces must meet are still being developed, based on a number of psychophysical studies and constraints such as manageable size and cost [19]. Peak acceleration, isotropy and dynamic range of achievable impedances are considered to be very important. A design approach that considers the haptic interface controller has been presented in [29].

This chapter is concerned with the design of controllers for teleoperation and haptic interfaces. A survey of control approaches is presented in Sect. 2.

Interesting teleoperation control research topics, at least from this author's perspective, are being discussed in Sect. 3. Issues of haptic interface control for manipulation in virtual environments are discussed in a limited manner in Sect.4. mainly stressing aspects common to teleoperation.

2.

T e l e o p e r a t o r Controller

The teleoperation controller should be designed with the goal of ensuring stability for an appropriate class of operator and environment models and satisfying an appropriately defined measure of performance, usually termed as transparency.

2.1 Modeling Teleoperation Systems

A commonly used teleoperation system model, e.g. [3, 17], is one with five interacting subsystems as shown in Fig. 2.1. The master manipulator, con- troller, and slave manipulator can be grouped into a single block representing the teleoperator as shown by the dashed line. For n-degree-of-freedom manip- ulation, the teleoperator can be viewed as a 2n-port master-controller-slave (MCS) network terminated at one side by an n-port operator block and at the other by an n-port environment network, as shown in Fig. 2.2. The force-voltage analogy is more often used than its dual to describe such sys- tems [3, 17]. It assigns equivalent voltages to forces and currents to velocities.

With this analogy, masses, dampers and stiffness correspond to inductances, resistances and capacitances, respectively.

H u m a n

F

I

Control for Teleoperation and Haptic Interfaces 53

M a s t e r

l

I

L . . . . . . Teleoperato

Fig. 2.1. Teleoperation system model

V rn> Vs

>

Zh t~- Teleoperator _-~fe ~

MCS Ze

Fig. 2.2. 2n-port network model of teleoperation system

A realistic assumption a b o u t the environment is t h a t it is passive or strictly passive as defined in [12]. Following research showing t h a t the op- erator hand behaves very much like a passive system [21], the o p e r a t o r block is usually also assumed to be passive.

For simplicity, the above network equivalents are almost always modeled as linear, time-invariant systems in which the dynamics of the force trans- mission and position responses can be m a t h e m a t i c a l l y characterized by a set of network flmctions. Even though this limits the t y p e of environment and o p e r a t o r interaction t h a t can be characterized, it allows the control system designer to draw upon well-developed network theory for synthesis and anal- ysis of the controller.

T h e MCS block can be described in terms of hybrid network p a r a m e t e r s as follows:

vs = a ~ 1 Ys0 fc '

where Z,~0 is the m a s t e r impedance and Gp is the position gain with the slave in free motion, and Y,0 is the slave a d m i t t a n c e and G : is the force gain with the m a s t e r constrained.

Alternative MCS block descriptions t h a t are useful can be written in terms of the a d m i t t a n c e o p e r a t o r Y m a p p i n g f = [fT f•]T to V = [V T V~] T and the scattering o p e r a t o r S = (I - Y ) ( I + y ) - i m a p p i n g the input wave into the o u t p u t wave f - v -- S ( f + v). The a d m i t t a n c e o p e r a t o r is proper so it fits in the linear controller design formalism better than the hybrid operator

54 S.E. Salcudean

[4, 22], while the norm or structured singular value of the scattering operator provides important passivity/absolute stability conditions [3, 11].

2.2 R o b u s t Stability C o n d i t i o n s

The goal of the teleoperation controller is to maintain stability against var- ious environment and operator impedances, while achieving performance or transparency as will be defined below.

For passive operator and environment blocks, a sufficient condition for stability is passivity of the teleoperator (e.g. [3]).

It was shown in [11] that the bilateral teleoperator shown in Fig. 2.2 is stable for all passive operator and environment blocks if and only if the scattering operator S of the 2n-port MCS is bounded-input-bounded-output stable and satisfies sup~ pa(jco) _< 1. The structured singular value # ~ is taken with respect to the 2-block structure diag{Sh, S~}, where Sh and Sc are the scattering matrices of strictly passive Zh and Z~, respectively. This result is an extension of Llewellyn's criterion for absolute stability of 2-ports terminated by passive impedances [32]. Various extensions of the result to nonlinear systems are discussed in [11].

Following common practice, robust stability conditions can be obtained from bounds on nominal operator and environment dynamic models using structured singular values [10].

2.3 P e r f o r m a n c e Specifications

For the operator to be able to control the slave, a kinematic correspondence law must be defined. In position control mode, this means that the uncon- strained motion of the slave must follow that of the master modulo some pre-defined or programmable scaling. Position tracking does not need to per- form well at frequencies above 5-10 Hz (the human hand cannot generate trajectories with significant frequency content above this range). In terms of the hybrid parameters defined in Eq. 2.1), Gp should approximate a position gain % I at low frequencies.

Forces encountered by the constrained slave should be transmitted to the hand by the master in a frequency range of up to a few hundred Hz. In terms of the hybrid parameters defined in Eq. 2.1,

Gf

Teleoperation system transparency can be quantified in terms of the match between the mechanical impedance of the environment encountered by the slave and the mechanical impedance transmitted to or felt by the operator at the master [17, 28], or by the requirement that the position/force responses of the teleoperator master and slave be identical [48]. If fe = Zevs, the impedance transmitted to the operator's hand fh = Z t h V m is given by

Z t h = Z m o + GfZ¢(I - YsoZc)-IG~ 1. (2.2)