Problem Statement

Realtime simulators in virtual reality are a leading-edge technology to provide standardized training and evaluation that contribute to operator safety. They aim to reduce accidents due to operator inexperience by training an operator in scenarios before they are expected to perform these same tasks in reality. To satisfy the high frame-rate requirements of real-time simulation, algorithms to solve these models must be extremely efficient and yield predictable and reproducible results.

The simulation of heavy equipment involves simulating both physical bodies in motion and hydraulic pressures. For example, one might wish to simulate a system involving a combustion engine coupled to several hydraulic pumps,motors, and cylinders that drive mechanical components. Over the past decades, numerous models and algorithms have been developed for these applications. Recently, position-based dynamics (PBD) has emerged as a strong contender for realtime simulation. Focusing on updating positional constraints, rather than the more traditional force or impulse based methods, allows it to be simple, stable, performant, while still converging to the same solution as the traditional methods ¹. This approach has been shown to be easily applicable to the simulation of rigid bodies ². Similarly in the hydraulic domain, many methods are too computationally expensive to be viable for a real time simulation. For example, ³ provides a thorough review of lumped-parameter hydraulic simulation; however, due to the relative incompressibility of fluids, the equations in their provided form are computationally expensive to solve.

The goal of this project is to develop an approach to the simulation of fluid pressure volumes that can be interfaced with a PBD simulation. This approach can then be applied to the simulation of many types of heavy equipment. At a high-level, PBD involves 3 steps: position prediction, application of constraints, and velocity calculation. For hydraulics, it should be possible to develop a collection of constraints that affect the pressures and flows of hydraulic volumes. Specifically, models for the following components should be defined:

• Hydraulic cylinder, which couples two fluid volumes (input/output) and two rigid bodies (both ends of the cylinder)
• Hydraulic pump/motor, which couples two fluid volumes (input/output) and a single rigid body
• Orifice, which connects two fluid volume

Skills

• Programming in a language geared toward scientific-computing, e.g. Python, MATLAB, Fortran.
• Strong background in applied mathematics.

References