A Unified and Differentiable Handling of Multilevel Constraint Method for Time-Varying Quadratic Optimal Problem and Its Application to Robot Control

Practical robotic control tasks are frequently formulated as time-varying quadratic programming (TVQP) problems. Recurrent Neural Network (RNN) exhibit superior efficacy in addressing TVQP, attributed to their inherent parallel processing and dynamic tracking capabilities. However, conventional techniques encounter significant challenges when handling multilevel inequality constraints, such as concurrent joint position and velocity limits, as their reliance on non-smooth piecewise functions inevitably induces control chattering. This study proposes a unified and differentiable multilevel constraint handling framework. By ensuring global differentiability, the proposed method satisfies the rigorous demand for continuous derivative information in gradient-based neurodynamics, while maintaining compatibility with traditional numerical solvers. Simulation experiments on a Franka robot arm executing complex trajectories demonstrate that the proposed approach achieves high-precision tracking while ensuring strict adherence to multilevel constraints.