An Inductance-Based Sensing System for Bellows-Driven Continuum Joints in Soft Robots.

In this work we present a novel, inductance-based system to measure and control the motion of bellows-driven continuum joints in soft robots. The sensing system relies on coils of wire wrapped around the minor diameters of each bellows on the joint. As the bellows extend, these coils of wire become more distant, decreasing their mutual inductance. Measuring this change in mutual inductance allows us to measure the motion of the joint. By dividing the sensing of the joint into two sections and measuring the motion of each section independently, we are able to measure the overall deformation of the joint with a piece-wise constant-curvature approximation. This technique allows us to measure lateral displacements that would be otherwise unobservable. When measuring bending, the inductance sensors measured the joint orientation with an RMS error of 1.1 °. The inductance sensors were also successfully used as feedback to control the orientation of the joint. The sensors proposed and tested in this work provided accurate motion feedback that would be difficult to achieve robustly with other sensors. This sensing system enables the creation of robust, self-sensing soft robots based on bellows-driven continuum joints.

Folded-Tube Soft Pneumatic Actuators for Bending.

This article presents a model and experimental results for a new class of bending soft pneumatic actuators (SPAs) made from a single section of thin-walled flexible tubing. The actuator is formed by creasing the tubing into fin-like rectangular folds and inserting the folds through regularly spaced slits in a high-strength fabric. When pressurized, the folds inflate and press against one another to create a bending moment. The actuator bends with a constant-length arc formed by the fabric. The walls of the tubing behave like an inextensible membrane. This membrane reinforcement allows the actuator to create large motions with limited material strain. Accordingly, the actuator can actuate over large bending angles without generating large elastic restoration forces in its structure. Spacing the slits for the folds closer together increases the bending moment for the same angle and pressure. Three folded-tube SPAs with different fold-spacings were experimentally characterized for this work. The strongest of the three was able to produce >190 N of tension and an estimated 10 Nm of bending moment with only 60 kPa. Even after bending 160°, the bending moment was still ∼5.7 Nm at the same pressure. The model presented in this work describes the moment per unit pressure of the actuators over the measured range of motion. For the 40 and 60 kPa tests, the model differed from the data with an average absolute error of <13% for all three actuators.

Smart Braid Feedback for the Closed-Loop Control of Soft Robotic Systems.

This article experimentally investigates the potential of using flexible, inductance-based contraction sensors in the closed-loop motion control of soft robots. Accurate motion control remains a highly challenging task for soft robotic systems. Precise models of the actuation dynamics and environmental interactions are often unavailable. This renders open-loop control impossible, while closed-loop control suffers from a lack of suitable feedback. Conventional motion sensors, such as linear or rotary encoders, are difficult to adapt to robots that lack discrete mechanical joints. The rigid nature of these sensors runs contrary to the aspirational benefits of soft systems. As truly soft sensor solutions are still in their infancy, motion control of soft robots has so far relied on laboratory-based sensing systems such as motion capture, electromagnetic (EM) tracking, or Fiber Bragg Gratings. In this article, we used embedded flexible sensors known as Smart Braids to sense the contraction of McKibben muscles through changes in inductance. We evaluated closed-loop control on two systems: a revolute joint and a planar, one degree of freedom continuum manipulator. In the revolute joint, our proposed controller compensated for elasticity in the actuator connections. The Smart Braid feedback allowed motion control with a steady-state root-mean-square (RMS) error of [1.5]°. In the continuum manipulator, Smart Braid feedback enabled tracking of the desired tip angle with a steady-state RMS error of [1.25]°. This work demonstrates that Smart Braid sensors can provide accurate position feedback in closed-loop motion control suitable for field applications of soft robotic systems.

Contraction Sensing with Smart Braid McKibben Muscles.

The inherent compliance of soft fluidic actuators makes them attractive for use in wearable devices and soft robotics. Their flexible nature permits them to be used without traditional rotational or prismatic joints. Without these joints, however, measuring the motion of the actuators is challenging. Actuator-level sensors could improve the performance of continuum robots and robots with compliant or multi-degree-of-freedom joints. We make the reinforcing braid of a pneumatic artificial muscle (PAM or McKibben muscle) "smart" by weaving it from conductive, insulated wires. These wires form a solenoid-like circuit with an inductance that more than doubles over the PAM contraction. The reinforcing and sensing fibers can be used to measure the contraction of a PAM actuator with a simple, linear function of the measured inductance. Whereas other proposed self-sensing techniques rely on the addition of special elastomers or transducers, the technique presented in this work can be implemented without modifications of this kind. We present and experimentally validate two models for Smart Braid sensors based on the long solenoid approximation and the Neumann formula, respectively. We test a McKibben muscle made from a Smart Braid in quasistatic conditions with various end-loads and in dynamic conditions. We also test the performance of the Smart Braid sensor alongside steel.

"Body-In-The-Loop": Optimizing Device Parameters Using Measures of Instantaneous Energetic Cost.

This paper demonstrates methods for the online optimization of assistive robotic devices such as powered prostheses, orthoses and exoskeletons. Our algorithms estimate the value of a physiological objective in real-time (with a body "in-the-loop") and use this information to identify optimal device parameters. To handle sensor data that are noisy and dynamically delayed, we rely on a combination of dynamic estimation and response surface identification. We evaluated three algorithms (Steady-State Cost Mapping, Instantaneous Cost Mapping, and Instantaneous Cost Gradient Search) with eight healthy human subjects. Steady-State Cost Mapping is an established technique that fits a cubic polynomial to averages of steady-state measures at different parameter settings. The optimal parameter value is determined from the polynomial fit. Using a continuous sweep over a range of parameters and taking into account measurement dynamics, Instantaneous Cost Mapping identifies a cubic polynomial more quickly. Instantaneous Cost Gradient Search uses a similar technique to iteratively approach the optimal parameter value using estimates of the local gradient. To evaluate these methods in a simple and repeatable way, we prescribed step frequency via a metronome and optimized this frequency to minimize metabolic energetic cost. This use of step frequency allows a comparison of our results to established techniques and enables others to replicate our methods. Our results show that all three methods achieve similar accuracy in estimating optimal step frequency. For all methods, the average error between the predicted minima and the subjects' preferred step frequencies was less than 1% with a standard deviation between 4% and 5%. Using Instantaneous Cost Mapping, we were able to reduce subject walking-time from over an hour to less than 10 minutes. While, for a single parameter, the Instantaneous Cost Gradient Search is not much faster than Steady-State Cost Mapping, the Instantaneous Cost Gradient Search extends favorably to multi-dimensional parameter spaces.