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.

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.

SPONGE: Open-Source Designs of Modular Articulated Soft Robots

Soft-robot designs are manifold, but only a few are publicly available. Often, these are only briefly described in their publications. This complicates reproduction, and hinders the reproducibility and comparability of research results. If the designs were uniform and open source, validating researched methods on real benchmark systems would be possible. To address this, we present two variants of a soft pneumatic robot with antagonistic bellows as open source. Starting from a semi-modular design with multiple cables and tubes routed through the robot body, the transition to a fully modular robot with integrated microvalves and serial communication is highlighted. Modularity in terms of stackability, actuation, and communication is achieved, which is the crucial requirement for building soft robots with many degrees of freedom and high dexterity for real-world tasks. Both systems are compared regarding their respective advantages and disadvantages. The robots' functionality is demonstrated in experiments on airtightness, gravitational influence, position control with mean tracking errors of <3 deg, and long-term operation of cast and printed bellows. All soft- and hardware files required for reproduction are provided.

Collision Isolation and Identification Using Proprioceptive Sensing for Parallel Robots to Enable Human-Robot Collaboration

Parallel robots (PRs) allow for higher speeds in human-robot collaboration due to their lower moving masses but are more prone to unintended contact. For a safe reaction, knowledge of the location and force of a collision is useful. A novel algorithm for collision isolation and identification with proprioceptive information for a real PR is the scope of this work. To classify the collided body, the effects of contact forces at the links and platform of the PR are analyzed using a kinetostatic projection. This insight enables the derivation of features from the line of action of the estimated external force. The significance of these features is confirmed in experiments for various load cases. A feedforward neural network (FNN) classifies the collided body based on these physically modeled features. Generalization with the FNN to 300k load cases on the whole robot structure in other joint angle configurations is successfully performed with a collision-body classification accuracy of 84% in the experiments. Platform collisions are isolated and identified with an explicit solution, while a particle filter estimates the location and force of a contact on a kinematic chain. Updating the particle filter with estimated external joint torques leads to an isolation error of less than 3cm and an identification error of 4N in a real-world experiment.

Quantifying Uncertainties of Contact Classifications in a Human-Robot Collaboration with Parallel Robots

In human-robot collaboration, unintentional physical contacts occur in the form of collisions and clamping, which must be detected and classified separately for a reaction. If certain collision or clamping situations are misclassified, reactions might occur that make the true contact case more dangerous. This work analyzes data-driven modeling based on physically modeled features like estimated external forces for clamping and collision classification with a real parallel robot. The prediction reliability of a feedforward neural network is investigated. Quantification of the classification uncertainty enables the distinction between safe versus unreliable classifications and optimal reactions like a retraction movement for collisions, structure opening for the clamping joint, and a fallback reaction in the form of a zero-g mode. This hypothesis is tested with experimental data of clamping and collision cases by analyzing dangerous misclassifications and then reducing them by the proposed uncertainty quantification. Finally, it is investigated how the approach of this work influences correctly classified clamping and collision scenarios.

Towards Human-Robot Collaboration with Parallel Robots by Kinetostatic Analysis, Impedance Control and Contact Detection

Parallel robots provide the potential to be leveraged for human-robot collaboration (HRC) due to low collision energies even at high speeds resulting from their reduced moving masses. However, the risk of unintended contact with the leg chains increases compared to the structure of serial robots. As a first step towards HRC, contact cases on the whole parallel robot structure are investigated and a disturbance observer based on generalized momenta and measurements of motor current is applied. In addition, a Kalman filter and a second-order sliding-mode observer based on generalized momenta are compared in terms of error and detection time. Gearless direct drives with low friction improve external force estimation and enable low impedance. The experimental validation is performed with two force-torque sensors and a kinetostatic model. This allows a new identification method of the motor torque constant of an assembled parallel robot to estimate external forces from the motor current and via a dynamics model. A Cartesian impedance control scheme for compliant robot-environmental dynamics with stiffness from 0.1-2N/mm and the force observation for low forces over the entire structure are validated. The observers are used for collisions and clamping at velocities of 0.4-0.9m/s for detection within 9-58ms and a reaction in the form of a zero-g mode.

Safe Collision and Clamping Reaction for Parallel Robots During Human-Robot Collaboration

Parallel robots (PRs) offer the potential for safe human-robot collaboration because of their low moving masses. Due to the in-parallel kinematic chains, the risk of contact in the form of collisions and clamping at a chain increases. Ensuring safety is investigated in this work through various contact reactions on a real planar PR. External forces are estimated based on proprioceptive information and a dynamics model, which allows contact detection. Retraction along the direction of the estimated line of action provides an instantaneous response to limit the occurring contact forces within the experiment to 70N at a maximum velocity 0.4m/s. A reduction in the stiffness of a Cartesian impedance control is investigated as a further strategy. For clamping, a feedforward neural network (FNN) is trained and tested in different joint angle configurations to classify whether a collision or clamping occurs with an accuracy of 80%. A second FNN classifies the clamping kinematic chain to enable a subsequent kinematic projection of the clamping joint angle onto the rotational platform coordinates. In this way, a structure opening is performed in addition to the softer retraction movement. The reaction strategies are compared in real-world experiments at different velocities and controller stiffnesses to demonstrate their effectiveness. The results show that in all collision and clamping experiments the PR terminates the contact in less than 130ms.

Learning-based Position and Stiffness Feedforward Control of Antagonistic Soft Pneumatic Actuators using Gaussian Processes

Variable stiffness actuator (VSA) designs are manifold. Conventional model-based control of these nonlinear systems is associated with high effort and design-dependent assumptions. In contrast, machine learning offers a promising alternative as models are trained on real measured data and nonlinearities are inherently taken into account. Our work presents a universal, learning-based approach for position and stiffness control of soft actuators. After introducing a soft pneumatic VSA, the model is learned with input-output data. For this purpose, a test bench was set up which enables automated measurement of the variable joint stiffness. During control, Gaussian processes are used to predict pressures for achieving desired position and stiffness. The feedforward error is on average 11.5% of the total pressure range and is compensated by feedback control. Experiments with the soft actuator show that the learning-based approach allows continuous adjustment of position and stiffness without model knowledge.

Intuitive Telemanipulation of Hyper-Redundant Snake Robots within Locomotion and Reorientation using Task-Priority Inverse Kinematics

Snake robots offer considerable potential for endoscopic interventions due to their ability to follow curvilinear paths. Telemanipulation is an open problem due to hyper-redundancy, as input devices only allow a specification of six degrees of freedom. Our work addresses this by presenting a unified telemanipulation strategy which enables follow-the-leader locomotion and reorientation keeping the shape change as small as possible. The basis for this is a novel shape-fitting approach for solving the inverse kinematics in only a few milliseconds. Shape fitting is performed by maximizing the similarity of two curves using Fr\'echet distance while simultaneously specifying the position and orientation of the end effector. Telemanipulation performance is investigated in a study in which 14 participants controlled a simulated snake robot to locomote into the target area. In a final validation, pivot reorientation within the target area is addressed.