Adaptive Model-Predictive Control of a Soft Continuum Robot Using a Physics-Informed Neural Network Based on Cosserat Rod Theory

TL;DR

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 is introduced based on a domain-decoupled physics-informed neural network (DD-PINN) with adaptable bending stiffness.

Abstract

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.

Figures (14)

• Figure 1: Overview of the proposed control and estimation framework utilizing a domain-decoupled physics-informed neural network, which is trained on Cosserat rod dynamics.
• Figure 2: Discretization of the rod model. The illustration shows an example to elaborate on considerations in spatial discretization. Here, two nodes ($N=2$) as well as three subintervals $n_\mathrm{sub} = 3$ are depicted. i) As an example, the steps in scalar internal force ${}^{\mathrm{b}}{n}_k$ are shown at $s=0$ and $s=\ell_0$ as an orange line. The index $k$ refers to the $k$-th component of the respective vector quantity. The steps introduce the two new state variables and their respective derivative as expressed in \ref{['eq.numerics.transission_condition_discrete']}. ii) The integration of $\mathrm{SE}(3)$ is conducted for each subinterval with length $\delta$, assuming the strains to be constant in these intervals but linear between two nodes $i$ and $i+1$. This is illustrated with the blue line. The respective algorithm is given in Algorithm \ref{['algorithm.gravity']}.
• Figure 3: Drawing of the soft pneumatic actuator used and a table of the dimensions. The parameter $\ell_0$ written in blue was identified from static data.
• Figure 4: Experiment 1: End-effector positions calculated by the linear (LIN) and nonlinear (NL) model. A trajectory with sequential steps (80kPa) smoothed by a low-pass filter (4Hz) is conducted to excite the dynamics. (a) mae between linear and nonlinear model for the position model outputs over the amplitude of the sequential steps trajectory. (b) The trajectory corresponding to 80kPa is displayed.
• Figure 5: Overview of the control architecture including the model predictive control and unscented Kalman filter based on a domain-decoupled physics-informed neural network.