Data-driven physical law learning model for chaotic robot dynamics prediction

A robot control system is a multivariable, nonlinear automatic control system, as well as a dynamic coupling system. To address the difficult problem of data prediction under a chaotic system, a data-driven physical law learning model (DPM) is proposed, which can learn the underlying physical rules that the data follow. First, two independent autoencoder neural networks are stacked and merged to explore potential physical rules. Then, a virtual Hamiltonian represented as the sum of kinetic energy and potential energy of chaotic data is introduced. Combined with the Hamiltonian equation, the learned Hamiltonian is transformed into a symplectic transformation, whose first-order differential w.r.t. the generalized coordinates and momentum can be regarded as a time-dependent prediction instead of a direct numerical approximation. Finally, the DPM continuously learns implicit Hamiltonian equations from chaotic data until it can fit the law of phase space motion in a chaotic environment. The experimental results show that the model has a better robot dynamics prediction ability in long-term chaotic systems than the existing SOTA methods.