AdapJ: An Adaptive Extended Jacobian Controller for Soft Manipulators

The nonlinearity and hysteresis of soft robot motions present challenges for control. To solve these issues, the Jacobian controller has been applied to approximate the nonlinear behaviors in a linear format. Accurate controllers like neural networks (NNs) can handle delayed and nonlinear motions, but they require large datasets and exhibit low adaptability. Based on a novel analysis on these controllers, we propose an adaptive extended Jacobian controller, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">AdapJ</i>, for soft manipulators. This controller retains the concise format of the Jacobian controller but introduces independent parameters. Similar to NNs, its initialization and updating mechanism leverages the inverse model without building the corresponding forward model. In the experiments, we first compare the performance of the Jacobian controller, model predictive controller (MPC), NN controller, iterative feedback controller (IFC), and AdapJ in simulation. We further analyze how AdapJ parameters adapt in response to the physical property change. Then, real-world experiments have validated that AdapJ outperforms the NN controller, MPC, and IFC with fewer training samples and adapts robustly to varying conditions, including different control frequencies, material softness, and external disturbances. Future work may include online adjustment of the controller format and adaptability validation in more scenarios.