Soft robots can revolutionize several applications with high demands on dexterity and safety. When operating these systems, real-time estimation and control require fast and accurate models. However, prediction with first-principles (FP) models is slow, and learned black-box models have poor generalizability. Physics-informed machine learning offers excellent advantages here, but it is currently limited to simple, often simulated systems without considering changes after training. We propose physics-informed neural networks (PINNs) for articulated soft robots (ASRs) with a focus on data efficiency. The amount of expensive real-world training data is reduced to a minimum — one dataset in one system domain. Two hours of data in different domains are used for a comparison against two gold-standard approaches: In contrast to a recurrent neural network, the PINN provides a high generalizability. The prediction speed of an accurate FP model is exceeded with the PINN by up to a factor of 467 at slightly reduced accuracy. This enables nonlinear model predictive control (MPC) of a pneumatic ASR. Accurate position tracking with the MPC running at 47 Hz is achieved in six dynamic experiments.

Sophisticated models can accurately describe deformations of continuum robots while being computationally demanding, which limits their application. Especially when considering sampling-based path planning, the model has to be evaluated frequently, which can lead to substantially increased computation times. We present a new approach to compute the entire shape of a tendon-driven continuum robot by a physics-informed neural network (PINN). The underlying physics is modelled with the Cosserat rod theory and incorporated into the PINN’s loss function. The boundary values for the training are obtained from a reference model, solved by the shooting method. Our approach allows for a computation of the learned Cosserat rod model multiple orders of magnitude faster than a publicly available reference model. The median position deviation from the reference model lies below 1mm (0.5% of the simulated robot length) for each of the robot’s 20 disks.

This paper presents a new approach to determine single and multiple simultaneous contact forces on a tendon-driven continuum robot (CR). The estimation is based solely on the proprioceptive tendon force and length sensors that are already present. Unlike for rigid-body robots, only indirect measurements of the external forces' deflection is available. The required full kinetostatic model, which is prone to local minima due to the unknown contacts, is solved with a particle filter. The method is validated by simulative studies and experimental investigations on a new robot setup for visual inspection of aircraft engines. The algorithm allows the estimation of single contacts with an error up to 4.43 mm or 2.9 % of the robot's length. Multiple contacts can only be correctly determined at the two distal of the three segments.