Simulation of Hybrid Systems in Virtual Environments

Hybrid systems are dynamical systems with both continuous and discrete-time dynamics. The continuous-time dynamics are usually inherited by the environment, analog devices, and continuous-time processes; while the discrete-time dynamics are usually introduced by digital devices, computers, impact phenomenon, etc. In this project, we simulate a particular hybrid system in a virtual environment: a bouncing ball impacting on a controlled platform. Our main goal is to design a virtual environment that, in the future, can be personalized to different tasks for the haptic device, including bouncing, touching, and juggling. We implement the hybrid system in a virtual environment coded in the programming language OpenGL, an standard in 3D computer rendering. We employ the haptic device Phantom Omni to control the platform where the ball bounces. We use both the HLAPI (higher level of programming) and HDAPI (higher description level of programming) Phantom Omni's libraries to program the haptic device. Our final results consist of the simulation of a ball bouncing vertically on a platform that is controlled by the stylus provided in the haptic device. We present experimental data of the simulation and a high-level description of our simulation program coded in C/C++. Some world applications of this research include path-planning of mobile robots in virtual terrains, and simulation of remotely-assisted surgery.