ABSTRACT
Real-time simulation of haptic interaction with deformable objects is computationally demanding. In particular in finite-element (FE) based analysis of such interactions, a large system of equations must be solved at an update rate of 100-1,000 Hz for simulation fidelity and stability. A new hardware-based parallel implementation of a Preconditioned Conjugate Gradient (PCG) algorithm is proposed for solving the linear systems of equations arising from FE-based deformation models. Concurrent utilization of a large number of fixed-point computing units on a Field-Programmable Gate Array (FPGA) device yields a very fast solution to these equations. Quantization and overflow errors in the fixed-point implementation of the iterative solver are minimized through dynamic scaling and preconditioning. Numerical accuracy of the solution, the architecture design, and issues pertaining to the degree of parallelism and scalability of the architecture are discussed in detail. The implementation of the solver on an Altera EP3SE110 FPGA device has enabled real-time simulation of three-dimensional linear elastic deformation models with 1,500 nodes at an update rate of up to 2,500 Hz.
ABSTRACT
Two adaptive nonlinear controllers are proposed for the coupling of haptic devices with impedance-type and admittance-type virtual environments, respectively. Rigid contacts in admittance-type environments are modeled either as a stiff spring or a constraint on the haptic device motion. Both controllers employ user position and force measurements to replace the natural dynamics of the haptic interface with that of an adjustable mass-damper tool. The transparency and stability of the resulting systems are investigated using a Lyapunov analysis and by taking into account uncertain nonlinear dynamics for the haptic device, and uncertain mass-spring-damper type dynamics for the user and virtual environment. It is shown analytically that low-pass filtering of selected terms in the control signal can significantly reduce a stability related lower bound on the achievable synthesized mass of the haptic interface in a discrete-time implementation of the controllers. An optimization problem is formulated and solved to balance impedance reduction against noise amplification in choosing the filter gain and bandwidth. The proposed controllers as well as a conventional penalty-based method are compared in a set of experiments. The results indicate that the controller with an admittance-type constraint-based rigid environment has far superior performance in terms of the range of impedances that it can stably display to the user.
