Real-Time Trajectory Generation for Soft Robot Manipulators Using Differential Flatness

Soft robots have the potential to interact with sensitive environments and perform complex tasks effectively. However, motion plans and trajectories for soft manipulators are challenging to calculate due to their deformable nature and nonlinear dynamics. This article introduces a fast real-time trajectory generation approach for soft robot manipulators, which creates dynamically-feasible motions for arbitrary kinematically-feasible paths of the robot's end effector. Our insight is that piecewise constant curvature (PCC) dynamics models of soft robots can be differentially flat, therefore control inputs can be calculated algebraically rather than through a nonlinear differential equation. We prove this flatness under certain conditions, with the curvatures of the robot as the flat outputs. Our two-step trajectory generation approach uses an inverse kinematics procedure to calculate a motion plan of robot curvatures per end-effector position, then, our flatness diffeomorphism generates corresponding control inputs that respect velocity. We validate our approach through simulations of our representative soft robot manipulator along three different trajectories, demonstrating a margin of 23x faster than real-time at a frequency of 100 Hz. This approach could allow fast verifiable replanning of soft robots' motions in safety-critical physical environments, crucial for deployment in the real world.

Self-Sensing for Proprioception and Contact Detection in Soft Robots Using Shape Memory Alloy Artificial Muscles

Estimating a soft robot's pose and applied forces, also called proprioception, is crucial for safe interaction of the robot with its environment. However, most solutions for soft robot proprioception use dedicated sensors, particularly for external forces, which introduce design trade-offs, rigidity, and risk of failure. This work presents an approach for pose estimation and contact detection for soft robots actuated by shape memory alloy (SMA) artificial muscles, using no dedicated force sensors. Our framework uses the unique material properties of SMAs to self-sense their internal stress, via offboard measurements of their electrical resistance and in-situ temperature readings, in an existing fully-soft limb design. We demonstrate that a simple polynomial regression model on these measurements is sufficient to predict the robot's pose, under no-contact conditions. Then, we show that if an additional measurement of the true pose is available (e.g. from an already-in-place bending sensor), it is possible to predict a binary contact/no-contact using multiple combinations of self-sensing signals. Our hardware tests verify our hypothesis via a contact detection test with a human operator. This proof-of-concept validates that self-sensing signals in soft SMA-actuated soft robots can be used for proprioception and contact detection, and suggests a direction for integrating proprioception into soft robots without design compromises. Future work could employ machine learning for enhanced accuracy.

Maximizing Consistent Force Output for Shape Memory Alloy Artificial Muscles in Soft Robots

Soft robots have immense potential given their inherent safety and adaptability, but challenges in soft actuator forces and design constraints have limited scaling up soft robots to larger sizes. Electrothermal shape memory alloy (SMA) artificial muscles have the potential to create these large forces and high displacements, but consistently using these muscles under a well-defined model, in-situ in a soft robot, remains an open challenge. This article provides a system for maintaining the highest-possible consistent SMA forces, over long lifetimes, by combining a fatigue testing protocol with a supervisory control system for the muscles' internal temperature state. We propose a design of a soft limb with swap-able SMA muscles, and deploy the limb in a blocked-force test to quantify the relationship between the measured maximum force at different temperatures over different lifetimes. Then, by applying an invariance-based control system to maintain temperatures under our long-life limit, we demonstrate consistent high forces in a practical task over hundreds of cycles. The method we developed allows for practical implementation of SMAs in soft robots through characterizing and controlling their behavior in-situ, and provides a method to impose limits that maximize their consistent, repeatable behavior.

Safe Balancing Control of a Soft Legged Robot

Legged robots constructed from soft materials are commonly claimed to demonstrate safer, more robust environmental interactions than their rigid counterparts. However, this motivating feature of soft robots requires more rigorous development for comparison to rigid locomotion. This article presents a soft legged robot platform, Horton, and a feedback control system with safety guarantees on some aspects of its operation. The robot is constructed using a series of soft limbs, actuated by thermal shape memory alloy (SMA) wire muscles, with sensors for its position and its actuator temperatures. A supervisory control scheme maintains safe actuator states during the operation of a separate controller for the robot's pose. Experiments demonstrate that Horton can lift its leg and maintain a balancing stance, a precursor to locomotion. The supervisor is verified in hardware via a human interaction test during balancing, keeping all SMA muscles below a temperature threshold. This work represents the first demonstration of a safety-verified feedback system on any soft legged robot.

Safe Supervisory Control of Soft Robot Actuators

Although soft robots show safer interactions with their environment than traditional robots, soft mechanisms and actuators still have significant potential for damage or degradation particularly during unmodeled contact. This article introduces a feedback strategy for safe soft actuator operation during control of a soft robot. To do so, a supervisory controller monitors actuator state and dynamically saturates control inputs to avoid conditions that could lead to physical damage. We prove that, under certain conditions, the supervisory controller is stable and verifiably safe. We then demonstrate completely onboard operation of the supervisory controller using a soft thermally-actuated robot limb with embedded shape memory alloy (SMA) actuators and sensing. Tests performed with the supervisor verify its theoretical properties and show stabilization of the robot limb's pose in free space. Finally, experiments show that our approach prevents overheating during contact (including environmental constraints and human contact) or when infeasible motions are commanded. This supervisory controller, and its ability to be executed with completely onboard sensing, has the potential to make soft robot actuators reliable enough for practical use.

Learned Dynamics of Electrothermally-Actuated Soft Robot Limbs Using LSTM Neural Networks

Modeling the dynamics of soft robot limbs with electrothermal actuators is generally challenging due to thermal and mechanical hysteresis and the complex physical interactions that can arise during robot operation. This article proposes a neural network based on long short-term memory (LSTM) to address these challenges in actuator modeling. A planar soft limb, actuated by a pair of shape memory alloy (SMA) coils and containing embedded sensors for temperature and angular deflection, is used as a test platform. Data from this robot are used to train LSTM neural networks, using different combinations of sensor data, to model both unidirectional (one SMA) and bidirectional (both SMAs) motion. Open-loop rollout results show that the learned model is able to predict motions over extraordinarily long open-loop timescales (10 minutes) with little drift. Prediction errors are on the order of the soft deflection sensor's accuracy, even when using only the actuator's pulse width modulation inputs for learning. These LSTM models can be used in-situ, without extensive sensing, helping to bring soft electrothermally-actuated robots into practical application.

Robust Control of a Multi-Axis Shape Memory Alloy-Driven Soft Manipulator

Control of soft robotic manipulators remains a challenge for designs with advanced capabilities and novel actuation. Two significant limitations are multi-axis, three-dimensional motion of soft bodies alongside actuator dynamics and constraints, both of which are present in shape-memory-alloy (SMA)-powered soft robots. This article addresses both concerns with a robust feedback control scheme, demonstrating state tracking control for a soft robot manipulator of this type. Our controller uses a static beam bending model to approximate the soft limb as an LTI system, alongside a singular-value-decomposition compensator approach to decouple the multi-axial motion and an anti-windup element for the actuator saturation. We prove stability and verify robustness of our controller, with robustness intended to account for the unmodeled dynamics. Our implementation is verified in hardware tests of a soft SMA-powered limb, showing low tracking error, with promising results for future multi-limbed robots.

Trajectory Optimization for Thermally-Actuated Soft Planar Robot Limbs

Practical use of robotic manipulators made from soft materials will require planning for complex motions. We present the first approach for generating trajectories of a thermally-actuated soft robotic manipulator. Based on simplified approximations of the soft arm and its shape-memory-alloy (SMA) wires, we justify a dynamics model of a discretized rigid manipulator with joint torques proportional to wire temperature. Then, we propose a method to calibrate this model from hardware data, and demonstrate that the simulation aligns well with a test trajectory. Finally, we use direct collocation trajectory optimization with the non-linear dynamics to derive open-loop controls for feasible trajectories that closely align with desired reference inputs. Two example trajectories are verified in hardware. The results show promise for both open-loop planning as well as for future applications with feedback.

An Untethered Brittle Star Robot for Closed-Loop Underwater Locomotion

Soft robots are capable of inherently safer and more stable interactions with their environment since they can mechanically deform in response to unanticipated interactions. However, their complex mechanics can make operation difficult, particularly with tasks such as locomotion, and robust systems are needed for evaluating and testing new planning and control algorithms. In this work, we present the first mobile and untethered underwater crawling soft robot. PATRICK is a robotic testbed inspired by brittle stars that demonstrates closed-loop locomotion planning. PATRICK contains five soft legs actuated by a total of 20 shape-memory-alloy (SMA) wires, providing a rich variety of possible motions. This testbed is the first instance of real-time position tracking for an untethered soft crawling robot. Experiments demonstrate that a motion planner can command the robot to locomote to a goal state, given a simple set of motion primitives. This work demonstrates progress toward full autonomy of soft, mobile robotic systems

Design, Simulation, and Testing of a Flexible Actuated Spine for Quadruped Robots

Walking quadruped robots face challenges in positioning their feet and lifting their legs during gait cycles over uneven terrain. The robot Laika is under development as a quadruped with a flexible, actuated spine designed to assist with foot movement and balance during these gaits. This paper presents the first set of hardware designs for the spine of Laika, a physical prototype of those designs, and tests in both hardware and simulations that show the prototype's capabilities. Laika's spine is a tensegrity structure, used for its advantages with weight and force distribution, and represents the first working prototype of a tensegrity spine for a quadruped robot. The spine bends by adjusting the lengths of the cables that separate its vertebrae, and twists using an actuated rotating vertebra at its center. The current prototype of Laika has stiff legs attached to the spine, and is used as a test setup for evaluation of the spine itself. This work shows the advantages of Laika's spine by demonstrating the spine lifting each of the robot's four feet, both as a form of balancing and as a precursor for a walking gait. These foot motions, using specific combinations of bending and rotation movements of the spine, are measured in both simulation and hardware experiments. Hardware data are used to calibrate the simulations, such that the simulations can be used for control of balancing or gait cycles in the future. Future work will attach actuated legs to Laika's spine, and examine balancing and gait cycles when combined with leg movements.