Haptic Interaction within a Planar Environment

A haptic simulation environment to simulate planar threedegree-of-freedom motion has been developed by the authors. The system consists of a novel parallel manipulandum and associated control, collision detection and dynamic simulation software running on a QNX PC. This paper describes haptic interface control and outlines the control systems that have been designed for the haptic rendering of virtual environments. Virtual environment design and implementation are also discussed. Using the haptic simulation environment that has been developed, a four-channel teleoperation architecture is shown to be an e ective means to display a variety of simulated environments and is compared with a popular impedance-based approach. INTRODUCTION Several haptic interaction systems have been developed in the past. Most of these have addressed point interaction (see for example Zilles and Salisbury, 1995), while only a few have addressed rigid-body interaction (see Chang and Colgate, 1997). Some of the most complete rigid-body simulations, to date, have been reported in (Cohen and Chen, 1999) and in (Berkelman et al, 1999), which describes the 6-DOF haptic interaction of a magnetically levitated haptic device with the dynamic simulator developed by (Bara , 1995). Such systems present several challenges for the design of haptic interface mechanisms, the simulation of virtual environments as well as for haptic control. The haptic simulation environment described in this paper comprises a planar 3-DOF haptic device with parallel and redundant actuation; an observer that estimates hand forces and velocities applied to the haptic interface, without direct measurement; virtual slave and environment models; a controller that coordinates both force and position information between the haptic device and the virtual environment; and a graphical display, all depicted in Figure 1. With respect to other haptic interaction systems, Figure 1. The virtual environment system architecture. this approach allows a reasonable motion range (the motion range available in (Berkelman et al, 1999) is small), signi cant forces and torques (the torque level available in (Cohen and Chen, 1999) is small), and decouples interactive virtual environment design from haptic controller design. The paper begins with a description of the haptic simulation system architecture and is followed by an outline of the haptic device design, its dynamics, actuation and sensing. Interface control, virtual environment simulation and their implementation within a teleoperation framework are detailed and evaluated experimentally. Finally, concluding remarks and scope for future work are presented. HAPTIC SIMULATION ARCHITECTURE A typical haptic display system comprises three majour components, namely: (i) the haptic interface that measures positions and forces applied by the user's hand, and that applies feedback forces on the hand; (ii) a virtual environment that includes both tool and environment dynamic models; and (iii) a control system that coordinates the haptic interface and virtual environment simulation. The issue of haptically rendering interactive virtual environments is essentially a teleoperation problem in which the haptic interface and the virtual tool are almost always both kinematically and dynamically dissimilar, resulting in some di culty in realizing transparent interaction between the user and the synthetic environment (Salcudean, 1997). For haptic displays, direct coupled impedance and admittance simulations have been proposed (Adams et al, 1998; Yoshikawa and Ueda, 1996; Nahvi et al, 1998). Virtual couplings have also been used (see Colgate et al, 1995). Impedance display, the more widespread of these, passes sensed hand positions to the dynamic simulator, while forces are returned from the environment. This is essentially a two-channel approach. The transmission of positions and forces in both directions between master and slave has been found to be important for achieving high performance in teleoperation systems (Lawrence, 1993; Salcudean, 1997). We employ a novel multi-channel architecture for haptic simulation, as well as the use of an explicitly modelled virtual slave that is designed independently of the haptic control system. A four-channel coupling between the haptic interface and dynamic simulation allows the interface to behave either as a force sensor, or as a position sensor depending upon the impedance of the virtual environment, and is therefore a hybrid of the two traditionally adopted approaches (Salcudean, 1997; Sirouspour, 2000). This strategy is evaluated within a haptic simulation system described in subsequent sections. THE PLANAR PANTOGRAPH HAPTIC INTERFACE The haptic interface has three degrees of freedom allowing for translation in a plane and unlimited rotation about an axis orthogonal to . This is achieved by using a dual pantograph arrangement, as shown in Figure 2. Each pantograph is driven by two DC motors located at the base joints, while their endpoints are coupled by means of a linkage, to which the interface handle is connected. This linkage forms a crank that allows for unlimited rotation of the handle. Mechanism Dynamics An accurate model of haptic interface dynamics is desirable for control purposes and begins with the derivation of Figure 2. The three-degree-of-freedom planar pantograph interface. the equations of motion using the Euler-Lagrange approach (Spong and Vidyasagar, 1989). The equations of motion for a single pantograph in actuated joint variables, = [ 1 2] T , are expressed in terms of the parameters shown in Figure 3: Dp( ) + Cp( ; _ ) _ = p J T e Fe = + env ; (1) where p is a vector of the applied actuator torques, Je is the manipulator Jacobian and Fe is the hand force applied to the end-e ector. Mass and Christo el matrices Dp and Cp are also present. The equations of motion describing the Figure 3. Pantograph con guration and parameters. workspace dynamics of two coupled pantographs take the following standard form (see Sirouspour, 2000 for details): Mc  Xc + Cc _ Xc = Fh + J T c = Fh + u ; (2) where Xc is a vector of interface handle coordinates [xc yc ], Fh is the hand force acting on the interface handle and is a vector of actuator torques. The internal force acting longitudinally along the linkage bar does not a ect the system dynamics since the actuator torques which constitute this force lie in the null space of J c . Note that as the pantographs are oriented horizontally, there are no gravity terms. Friction is insigni cant and can be neglected. Actuation and Sensing Four 90W DC motors provide actuation at the active pantograph joints and are considered, for the purposes of control, to be torque sources. Each of the four joint angles is measured by a digital optical encoder with a resolution of 0:09 degrees. Velocities, accelerations and forces are not directly measurable and are computed purely from joint angle measurements and applied motor torques by using a system state observer (Hacksel and Salcudean, 1994). Given an accurate dynamic model, as well as measured joint angles and applied actuator forces, the system states (angular joint velocity) and unknown external disturbances (hand force applied to the interface end-e ector) can be observed and computed, as indicated in Figure 4. This approach has