Techniques for Modular Simulation of Hybrid Systems

Joel Esposito, Yerang Hur, and George Pappas

In traditional simulation techniques all components of the system must be simulated with the same global time step.  This can decrease the efficiency of the simulation by forcing all the components to be integrated at the smallest acceptable time step, which is dictated by the fastest changing  component of the system.  We are developing numerical techniques to enhance and compliment existing Multi-Rate techniques, which allow different components of coupled systems to be integrated at different rates.  The challenge here will come from that fact that the system components are not only coupled through their continuos dynamics but also through the discrete dynamics of hybrid systems and inter-agent messaging and communication.   However we are hoping to exploit the underlying heiarchy present robotic systems to simplify the problem.
 
 

The underlying idea behind traditional linear multistep integration methods, is to use local polynomial interpolations and extrapolations to approximate the right hand side of the differential equation.  We are reconstructing the interpolants at minimal extra cost and are using them to approximate off-mesh point values.   This approach allows asynchronous integration and can also be used to facilitate event detection.  We are also experimenting with using the Lie Derivative information as a heuristic for event detection.  To tackle the inter-agent communication problem a Time-Warp approach is being investigated

For more information about embedded software for multi-agent communicating hybrid systems and the use of the CHARON language, visit the MoBIES Project homepage.