A Real-time Local Planner Design for Smart Wheelchairs Based on Koopman Bilinear Model Predictive Control

The paper introduces a Koopman bilinear model predictive control (KBMPC) as a local planner for smart wheelchair systems. This approach leverages the Koopman Operator to streamline the nonlinear terms in MPC, aiming to achieve superior real-time performance. In particular, we employ the Extended Dynamic Mode Decomposition (EDMD) method to approximate the infinite dimensional Koopman operator. To tackle the challenge of designing lifting functions, we systematically utilize the derivatives of known nonlinear structures to methodically derive lifting functions. This systematic approach facilitates the identification of a precise bilinear model. Next, we formulate the corresponding Koopman bilinear MPC problem. Finally, an iterative algorithm is employed to efficiently solve the KBMPC problem. This method linearizes the bilinear model around estimations and iteratively solves the resulting quadratic programming problem to refine estimations. This allows KBMPC to function as a real-time local planner for smart wheelchairs. The prediction of nonlinear terms shows that the identified Koopman bilinear model increases the prediction accuracy. Furthermore, experiments demonstrate the advantages of the designed KBMPC local planner, highlighting its superior real-time performance and predictive capabilities.