Physics-Constrained Data-Driven Dynamic Modeling of Underactuated Robotic Systems

Underactuated robots are intriguing systems that have found numerous applications across various fields. These systems are characterized by having fewer actuators than degrees of freedom, resulting in complex behaviors that challenge traditional modeling and control techniques. Despite the prevalent use of data-driven modeling, extracting the dynamic model of underactuated systems is particularly challenging. This paper focuses on deriving from data the dynamic model of the Double Inverted Pendulum on a Cart (DIPC). The Euler-Lagrange equations are employed to derive the model's terms from the symbolic form of the DH parameters of the system. The coefficients of the model terms are obtained by formulating a constrained least-squares (LS) problem. The constraints leverage the properties of the robot's dynamic equations to limit the solution space to the physically possible ones. The conventional LS method failed to calculate the coefficients of the underactuated DIPC and got only the trivial solution. The proposed method accurately identifies the dynamic model of the underactuated DIPC, overcoming issues related to finding a solution by searching the null space of the regressor matrix and dealing with ill-conditioned regressor matrices. The proposed method provides a systematic approach for determining the dynamic model of actuated or underactuated robotic systems. Additionally, it can extend the capabilities of dynamic simulation software by extracting the nonlinear dynamic model of the robot from simulation data.