Dynamic control of soft continuum robots (SCRs) holds great potential for expanding their applications, but remains a challenging problem due to the high computational demands of accurate dynamic models. While data-driven approaches like Koopman-operator-based methods have been proposed, they typically lack adaptability and cannot reconstruct the full robot shape, limiting their applicability. This work introduces a real-time-capable nonlinear model-predictive control (MPC) framework for SCRs based on a domain-decoupled physics-informed neural network (DD-PINN) with adaptable bending stiffness. The DD-PINN serves as a surrogate for the dynamic Cosserat rod model with a speed-up factor of 44000. It is also used within an unscented Kalman filter for estimating the model states and bending compliance from end-effector position measurements. We implement a nonlinear evolutionary MPC running at 70 Hz on the GPU. In simulation, it demonstrates accurate tracking of dynamic trajectories and setpoint control with end-effector position errors below 3 mm (2.3% of the actuator's length). In real-world experiments, the controller achieves similar accuracy and accelerations up to 3.55 m/s2.

翻译：软体连续体机器人（SCRs）的动态控制具有拓展其应用场景的巨大潜力，但由于精确动力学模型的高计算需求，这仍是一个具有挑战性的问题。尽管已提出基于Koopman算子的数据驱动方法，但它们通常缺乏适应性且无法重建完整的机器人形状，限制了其适用性。本研究提出了一种基于具有可适应弯曲刚度的域解耦物理信息神经网络（DD-PINN）的、具备实时能力的软体连续体机器人非线性模型预测控制（MPC）框架。该DD-PINN作为动态Cosserat杆模型的替代模型，实现了44000倍的加速。它还被用于无迹卡尔曼滤波器中，以根据末端执行器位置测量值估计模型状态和弯曲柔度。我们在GPU上实现了一个以70 Hz频率运行的非线性进化MPC。在仿真中，它展示了对动态轨迹的精确跟踪和设定点控制，末端执行器位置误差低于3毫米（占驱动器长度的2.3%）。在真实世界实验中，该控制器实现了相似的精度和高达3.55 m/s²的加速度。