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

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 capture 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.

Fast Contact Detection via Fusion of Joint and Inertial Sensors for Parallel Robots in Human-Robot Collaboration

Fast contact detection is crucial for safe human-robot collaboration. Observers based on proprioceptive information can be used for contact detection but have first-order error dynamics, which results in delays. Sensor fusion based on inertial measurement units (IMUs) consisting of accelerometers and gyroscopes is advantageous for reducing delays. The acceleration estimation enables the direct calculation of external forces. For serial robots, the installation of multiple accelerometers and gyroscopes is required for dynamics modeling since the joint coordinates are the minimal coordinates. Alternatively, parallel robots (PRs) offer the potential to use only one IMU on the end-effector platform, which already presents the minimal coordinates of the PR. This work introduces a sensor-fusion method for contact detection using encoders and only one low-cost, consumer-grade IMU for a PR. The end-effector accelerations are estimated by an extended Kalman filter and incorporated into the dynamics to calculate external forces. In real-world experiments with a planar PR, we demonstrate that this approach reduces the detection duration by up to 50% compared to a momentum observer and enables the collision and clamping detection within 3-39ms.

Generalizable and Fast Surrogates: Model Predictive Control of Articulated Soft Robots using Physics-Informed Neural Networks

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 improved with the PINN by up to a factor of 466 at slightly reduced accuracy. This enables nonlinear model predictive control (MPC) of the pneumatic ASR. In nine dynamic MPC experiments, an average joint-tracking error of 1.3{\deg} is achieved.

SafePR: Unified Approach for Safe Parallel Robots by Contact Detection and Reaction with Redundancy Resolution

Fast and safe motion is crucial for the successful deployment of physically interactive robots. Parallel robots (PRs) offer the potential for higher speeds while maintaining the same energy limits due to their low moving masses. However, they require methods for contact detection and reaction while avoiding singularities and self-collisions. We address this issue and present SafePR - a unified approach for the detection and localization, including the distinction between collision and clamping to perform a reaction that is safe for humans and feasible for PRs. Our approach uses information from the encoders and motor currents to estimate forces via a generalized-momentum observer. Neural networks and particle filters classify and localize the contacts. We introduce reactions with redundancy resolution to avoid type-II singularities and self-collisions. Our approach detected and terminated 72 real-world collision and clamping contacts with end-effector speeds of up to 1.5 m/s, each within 25-275 ms. The forces were below the thresholds from ISO/TS 15066. By using built-in sensors, SafePR enables safe interaction with already assembled PRs without the need for new hardware components.

Learning-based Nonlinear Model Predictive Control of Articulated Soft Robots using Recurrent Neural Networks

Soft robots pose difficulties in terms of control, requiring novel strategies to effectively manipulate their compliant structures. Model-based approaches face challenges due to the high dimensionality and nonlinearities such as hysteresis effects. In contrast, learning-based approaches provide nonlinear models of different soft robots based only on measured data. In this paper, recurrent neural networks (RNNs) predict the behavior of an articulated soft robot (ASR) with five degrees of freedom (DoF). RNNs based on gated recurrent units (GRUs) are compared to the more commonly used long short-term memory (LSTM) networks and show better accuracy. The recurrence enables the capture of hysteresis effects that are inherent in soft robots due to viscoelasticity or friction but cannot be captured by simple feedforward networks. The data-driven model is used within a nonlinear model predictive control (NMPC), whereby the correct handling of the RNN's hidden states is focused. A training approach is presented that allows measured values to be utilized in each control cycle. This enables accurate predictions of short horizons based on sensor data, which is crucial for closed-loop NMPC. The proposed learning-based NMPC enables trajectory tracking with an average error of 1.2deg in experiments with the pneumatic five-DoF ASR.

Autonomous Iterative Motion Learning (AI-MOLE) of a SCARA Robot for Automated Myocardial Injection

Stem cell therapy is a promising approach to treat heart insufficiency and benefits from automated myocardial injection which requires highly precise motion of a robotic manipulator that is equipped with a syringe. This work investigates whether sufficiently precise motion can be achieved by combining a SCARA robot and learning control methods. For this purpose, the method Autonomous Iterative Motion Learning (AI-MOLE) is extended to be applicable to multi-input/multi-output systems. The proposed learning method solves reference tracking tasks in systems with unknown, nonlinear, multi-input/multi-output dynamics by iteratively updating an input trajectory in a plug-and-play fashion and without requiring manual parameter tuning. The proposed learning method is validated in a preliminary simulation study of a simplified SCARA robot that has to perform three desired motions. The results demonstrate that the proposed learning method achieves highly precise reference tracking without requiring any a priori model information or manual parameter tuning in as little as 15 trials per motion. The results further indicate that the combination of a SCARA robot and learning method achieves sufficiently precise motion to potentially enable automatic myocardial injection if similar results can be obtained in a real-world setting.

Dispelling Four Challenges in Inertial Motion Tracking with One Recurrent Inertial Graph-based Estimator (RING)

In this paper, we extend the Recurrent Inertial Graph-based Estimator (RING), a novel neural-network-based solution for Inertial Motion Tracking (IMT), to generalize across a large range of sampling rates, and we demonstrate that it can overcome four real-world challenges: inhomogeneous magnetic fields, sensor-to-segment misalignment, sparse sensor setups, and nonrigid sensor attachment. RING can estimate the rotational state of a three-segment kinematic chain with double hinge joints from inertial data, and achieves an experimental mean-absolute-(tracking)-error of 8.10 +/- 1.19 degrees if all four challenges are present simultaneously. The network is trained on simulated data yet evaluated on experimental data, highlighting its remarkable ability to zero-shot generalize from simulation to experiment. We conduct an ablation study to analyze the impact of each of the four challenges on RING's performance, we showcase its robustness to varying sampling rates, and we demonstrate that RING is capable of real-time operation. This research not only advances IMT technology by making it more accessible and versatile but also enhances its potential for new application domains including non-expert use of sparse IMT with nonrigid sensor attachments in unconstrained environments.

Towards Optimized Parallel Robots for Human-Robot Collaboration by Combined Structural and Dimensional Synthesis

Parallel robots (PR) offer potential for human-robot collaboration (HRC) due to their lower moving masses and higher speeds. However, the parallel leg chains increase the risks of collision and clamping. In this work, these hazards are described by kinematics and kinetostatics models to minimize them as objective functions by a combined structural and dimensional synthesis in a particle-swarm optimization. In addition to the risk of clamping within and between kinematic chains, the back-drivability is quantified to theoretically guarantee detectability via motor current. Another HRC-relevant objective function is the largest eigenvalue of the mass matrix formulated in the operational-space coordinates to consider collision effects. Multi-objective optimization leads to different Pareto-optimal PR structures. The results show that the optimization leads to significant improvement of the HRC criteria and that a Hexa structure (6-RUS) is to be favored concerning the objective functions and due to its simpler joint structure.

Domain-decoupled Physics-informed Neural Networks with Closed-form Gradients for Fast Model Learning of Dynamical Systems

Physics-informed neural networks (PINNs) are trained using physical equations and can also incorporate unmodeled effects by learning from data. PINNs for control (PINCs) of dynamical systems are gaining interest due to their prediction speed compared to classical numerical integration methods for nonlinear state-space models, making them suitable for real-time control applications. We introduce the domain-decoupled physics-informed neural network (DD-PINN) to address current limitations of PINC in handling large and complex nonlinear dynamic systems. The time domain is decoupled from the feed-forward neural network to construct an Ansatz function, allowing for calculation of gradients in closed form. This approach significantly reduces training times, especially for large dynamical systems, compared to PINC, which relies on graph-based automatic differentiation. Additionally, the DD-PINN inherently fulfills the initial condition and supports higher-order excitation inputs, simplifying the training process and enabling improved prediction accuracy. Validation on three systems - a nonlinear mass-spring-damper, a five-mass-chain, and a two-link robot - demonstrates that the DD-PINN achieves significantly shorter training times. In cases where the PINC's prediction diverges, the DD-PINN's prediction remains stable and accurate due to higher physics loss reduction or use of a higher-order excitation input. The DD-PINN allows for fast and accurate learning of large dynamical systems previously out of reach for the PINC.

A Soft Robotic System Automatically Learns Precise Agile Motions Without Model Information

Many application domains, e.g., in medicine and manufacturing, can greatly benefit from pneumatic Soft Robots (SRs). However, the accurate control of SRs has remained a significant challenge to date, mainly due to their nonlinear dynamics and viscoelastic material properties. Conventional control design methods often rely on either complex system modeling or time-intensive manual tuning, both of which require significant amounts of human expertise and thus limit their practicality. In recent works, the data-driven method, Automatic Neural ODE Control (ANODEC) has been successfully used to -- fully automatically and utilizing only input-output data -- design controllers for various nonlinear systems in silico, and without requiring prior model knowledge or extensive manual tuning. In this work, we successfully apply ANODEC to automatically learn to perform agile, non-repetitive reference tracking motion tasks in a real-world SR and within a finite time horizon. To the best of the authors' knowledge, ANODEC achieves, for the first time, performant control of a SR with hysteresis effects from only 30 seconds of input-output data and without any prior model knowledge. We show that for multiple, qualitatively different and even out-of-training-distribution reference signals, a single feedback controller designed by ANODEC outperforms a manually tuned PID baseline consistently. Overall, this contribution not only further strengthens the validity of ANODEC, but it marks an important step towards more practical, easy-to-use SRs that can automatically learn to perform agile motions from minimal experimental interaction time.