Cambridge , Massachusetts 02139 Proceedings of the Fourth PHANTOM Users

It is well known that realistic haptic rendering depends on high update rates. Nevertheless, there are many applications for which haptic interfaces could be useful where haptic data cannot be delivered at these rates. In VR and real-time dynamic simulation of deformable objects, for instance, update rates are limited by the computation time. In distributed systems, as telerobotics or network-based simulators, communication rates are unstable and limited by the network features. In this paper we show how this problem can be minimised using a "buffer model" between the haptic interface and the data source (the system being interfaced). This buffer is intended to be able to deliver data to the haptic device at the required rate and its role is to maximise the information contained in the data flow. The buffer is implemented as a local numerical model of the data source. The buffer model must be simple, generic and easily adaptable. The data flow will be used to continuously update a number of parameters of this model in order to render it locally as close as possible of the data source. We will show also how a buffer model can be useful to easily implement a proxy-based calculation of the haptic forces. We will finish showing how we used this approach to interface a PHANToM with a deformable objects simulator. 1. Introduction We are interested in simplifying the conception of a haptic interface in an existing Virtual Reality (VR) system. In a haptic interface the force feedback represents the contact forces between the haptic probe and the objects of a virtual scene. This physically based scene will typically be simulated in real-time by a VR software component. The instantaneous contact forces depend directly on the instantaneous scene state, and the scene state can be affected by the user actions. Consequently, the haptic systems are usually organised in a way that for each haptic refresh cycle we have also a virtual scene update. In this configuration, the haptic rate depends entirely on the scene simulator computational delay. The estimation of haptic forces can also present some difficulties. In physical simulators, surface contacts are usually modelled using penalty or impulse-based methods. Impulse based methods compute state changes, not forces. Penalty based methods compute repulsive forces and can work well to model simple obstacles, such planes or spheres, but we can find a number of difficulties when trying to extend these models to display more complex environments. A better suited framework to estimate contact forces for generic haptic display are the constraint based methods [zilles-94] [ruspini-97], but most of the existing physical simulators do not use it. In this paper we propose an approach to conceive haptic interfaces where the haptic rendering does not depend directly on the physical simulation rates nor on the methods used by the simulator. The haptic interface is conceived as an external module of a VR system, connected to this system by a buffer model. This buffer model is a generic numerical model, that will locally emulate the haptic interaction between the user and the virtual environment simulated by the VR system. We do not care about the methods used to simulate this environment. The buffer model will act as a very simple local physical model, and the haptic loop will interact with this local model instead of interacting with the virtual environment. The simplicity of the buffer model makes easy and fast the collisions detection and the estimation of contact forces. A buffer manager process will communicate with the VR system to inform the user motions and to obtain relevant data to update the buffer model. The buffer model will be updated at a rate proportional to the VR computational delay, but this will not compromise the haptic loop rate. 2. Conceiving an haptic interface based on a buffer model The central idea in our approach is that the haptic interface locally emulates the virtual environment, continuously adapting its own simple physical model. Inside the virtual environment, the user is represented by a virtual object, the probe. The user is controlling the probe and the probe is interacting with the other virtual objects. Inside the haptic interface we use a constraint-based framework. The user is represented by a virtual proxy, as proposed in [ruspini-97]. In our approach, the proxy is a point moving in the configuration space of the haptic device. The proxy interacts with one constraint non deformable surface, corresponding to one configuration space obstacle (c-obstacle). This surface represents the nearest portion of the nearest object in the virtual environment with respect to the probe. The position and the shape of this surface will be defined by a set of parameters, continuously adapted to fit the closest c-obstacle form. The haptic interface is defined by two processes: the model manager and the haptic loop. The model manager interacts with the simulator, informing the user motions and obtaining the minimum distance between the probe and its closest neighbour in the virtual environment. Using this distance and its derivatives, the manager will adapt the constraint surface to locally fit these values. The simulator must to inform also the local stiffness of the neighbour. The haptic loop follows the constraint based rendering framework. 2.1. The model manager The model manager role is to inform to the VR simulator the user motions and to continuously update the constraint surface. We assume that the VR simulator is prepared to accept this interaction. It means that the simulator can handle our demand within its real-time loop. The mapping between the probe in the virtual environment and the proxy will be determined by the haptic device features. In an ideal framework, the haptic device would offer force and torque feedback, and the proxy would move in a 6-D configuration space. In this case, the proxy motions could be expressed in full probe motions (6 dof : translation and rotation). In the case of a haptic device with no torque feedback, the proxy would be a point in a 3-D configuration space, and its motions would be expressed only by translations of the probe in the virtual environment (3 dof). The probe would not rotate. After the probe position update, the VR simulator will find its nearest neighbour, estimate the minimum distance between these two objects and estimate the partial derivatives of this distance with respect to the probe degrees of freedom. The VR simulator will return the estimated values to the model manager and will update its dynamic state (motions and deformations). The model manager uses the obtained distance d and its partial derivatives d' to update the buffer model. Let us consider the distance d as being defined by an unknown mapping f : Rn → R: The buffer model can be defined as a function f : Rn+r → R, which can be written as : ) (x f d =       ∂ ∂ ∂ ∂ = n x f x f d Κ 1 ' for certain u=[u1… ur]T ∈ Rr .We will refer to u1… ur as the parameters and to x1… xn as the variables . The variables correspond to the configuration space dimensions. We define also the partial derivatives for f: The fitting algorithm to adapt the buffer model with respect to f is based on the following first order approximations : We define du=[Du1… Dur] as the vector of corrections to be applied to the model parameters, dx=[dx1… dxn]T as the vector of the partial derivatives of f, ddx=[ddx1… ddxn] as the vector of differences over the partial derivatives that we obtain applying du to u, df as the difference on f we obtain applying du to u and dxu as the matrix of partial derivatives of dx with respect to u: Writing in a matrix form : We consider the problem of fitting f to locally emulate f as the problem of finding the du corrections to be applied to the model parameters u so that the model estimation errors (df,ddx) are minimised. The model estimation errors are assumed to be : We use the pseudo-inverse of J (J† = (JT J)-1 JT) to estimate the parameters corrections (du): Using iteratively this approach the model manager will continuously keep f(u,x)» f(x) nearby the probe position. 2.2. The haptic loop The haptic loop estimates the contact forces using the constraint surface defined by the buffer model. This estimation is based on a very simple physical simulation, with a point interacting with a non deformable surface determined by the points x respecting f(x)=0. The proxy location is defined by two values: the haptic device effective position and a virtual location, subject to the constraint surface. The effective position must to be informed to characterise the collisions in the virtual environment, but the distance we need to update the buffer model must be estimated ) , ( ) ( x u x f f ≡ ) , 1 ( ) , ( n i x x u dx i i Κ = ∂ ∂ = f