Motion Planning for Chemical Systems: Consecutive Reactions

Abstract

Motion planning is widely used for analyzing and controlling nonlinear systems, such as mobile robot navigation and robotic automation. When a mathematical model of the system is available, motion planning allows for system analysis and control without the need for sampling or physical intervention, thereby avoiding any disturbance to the behavior of the system. This study explores the application of motion planning methods to chemical reac- tion systems. Specifically, it demonstrates how to define desired trajectories for consecutive reactions using the parametrized function class method. The planning assumes isothermal conditions, which are modeled by setting the temperature as a constant time function. Under this assumption, the system describing consecutive reactions becomes linear. Starting from the kinetic model, we derive the time-dependent behavior of the state variables. Based on these results, a controller is designed for a two-step consecutive reaction. The state of the system can be determined at any time from the computed time functions, and the future be- havior of the system can be accurately predicted. This approach helps prevent accidents and undesired outcomes by ensuring the reaction proceeds along the planned trajectory.