Soft Bending Actuation Module with Proprioceptive Curvature Sensing

This article introduces the proprioceptive magnetic curvature sensor design and fabrication and the method how to embed the senor inside soft bending actuation module. Figure 1 shows the soft bidirectional bending actuator with curvature sensor.

 

Actuator
Figure.1 CAD model (left) and experimental prototype (right) of the proposed soft bidirectional bending actuator module with integrated curvature sensing.

This documentation set contains files and instructions to support the Design and Fabrication of curvature sensor and soft bending actuator with curvature sensor, The FEA analysis for the optimal sensor design and Testing. The curvature sensor is able to be embeded in the soft actuator.

Design

Soft Bidirectional Bending Actuator

Our soft bidirectional bending actuator consists of two chambers each wrapped in a double-helix of thread mounted on either side of an inextensible constraint layer (Figure.2). Each chamber is connected to an external air supply, and when pressurized causes the segment to curve in the opposite direction. The central constraint layer contains a flexible curvature sensor which measures the kinematic state of the actuator. Figure.3 shows the static behavior of our bending module.

Actuator-exp
Figure.2 Soft Bidirectional Bending Actuator

snapshot
Figure.3 Static response of the bending soft robotic module in a range of 150 degree at ±11 psi.
 

Curvature Sensor

Our curvature sensor contains a miniature magnet and a Hall effect measurement integrated circuit (IC). The magnet is positioned in a specific way with respect to the Hall element on a flexible cirucit to measure the curvature of bidirectional out-of-plane deformations in a standalone package, without the need for external electronics (Figure.4).

Circuit
Figure.4 Circuit design of the curvature sensor

Fabrication

The fabrication of the soft bending actuator with magnetic curvature sensor

The steps of fabrication can be summarized as follows:

Step 1: Two inner bodies (i.e., linear muscles) of the module are fabricated first using a three-dimensional (3D) printed mold and silicone rubber (Smooth-On Ecoflex 0030) (Figure.5).

Step1-soft actuator
Figure.5 Step1

 

 

 

 

 

 

 

 

 

Step 2: Inextensible sewing thread is wrapped and bonded around each linear muscle (Figure.6).

Step2-Soft actuator
Figure.6 Step2

Step 3: With the flexible curvature sensor in the middle, two pieces of self-adhesive laminate sheet are laser cut and attached together to form the constraint layer (Figure.7).

Step3-soft actuator
Figure.7 Step3
     
Laminating sheet
Figure.8 Laminating sheet

Step 4: The constraint layer and two inner bodies are placed in a second 3D printed mold and filled with silicone rubber (Figure.9).

Step4-soft actuator
Figure.9 Step4

Step 5: Acrylic end-connector caps and vent screws are attached to both ends of the body (Figure.10).

Step5-Soft actuator
Figure.10 Step5

 

The fabrication of the magnetic curvature sensor:

The entire fabrication process consists of three steps as below.

Step 1 : Circuit traces are designed and printed on a copper-clad flexible substrate (Pyralux, 3M, Figure.11(a)) using a solid ink printer (Xerox Color 8570, Figure.11(b)).

Printerand sheet
Figure.11 (a) Flex PCB Material - Pyralux (b) ColorQube 8570, Color Printers: Xerox.

Step 2: The patterned copper-clad substrate is placed in a ferric chloride (Figure.12(a)) etching tank (Figure.12(b)) that remove all exposed copper, leaving the electrical traces intact. Usually take around 15 min.

Ferric and etching
Figure.12 (a) Ferric chloride copper etchant solution. (b) Etching tank
   

Step 3: Discrete circuit components (AH49E) are soldered and the miniature magnet  is mounted on its precise position using a microscope.

 

 

Finite Element Analysis Modeling

This section shows how to choose the optimal design for curvature sensor. We considered two main parameters: the orientation of the magnet and the distance between the magnet and the Hall element. First, we generated magnetic field data using COMSOL, an example of which can be seen in Figure 13a. We used this to calculate the strength of the magnetic field at the Hall element with respect to the circuit design. Figure 13b shows the geometric relationship between the magnet and the Hall element on a bending segment. The origin is located at the base of the magnet, L is the arc-length along the flexible circuit between the origin and the center of the Hall element, hm is the height of the center of the magnet (point M), and hs is the height of the Hall effect sensor element (point S). We assume that the flexible sensor is under constant curvature, allowing us to calculate the positions of these two points.

We can calculate the vector between M and S, and then use the COMSOL magnetic field data Bx and By at S to determine the expected field registered by the Hall element (in its normal direction) via the following rotation equation:

Bn=BycosΘ-BxsinΘ

where Bn is the magnetic field density, which the onedimensional Hall effect sensor could sense when the bending angle is h. When analyzing the sensor simulation, we considered the working range of the bending actuator to be 90, representing the bounds of h. Figure 13c shows the model prediction of the magnetic field with respect to curvature at a distance of L ¼ 3.1 mm, the results of which can be approximated using a linear fit. To determine the optimal distance and magnet orientation, we calculated the range of measured magnetic fields for L ranging between 3.1 and 4.6 mm with the magnetic north pointing upward (along y-axis) and sideways (along x-axis), the results of which can be seen in Figure 4d.This range was chosen to keep the sensor from coming into contact with the magnet at larger curvature values, as well as keep the magnetic field from becoming too weak to be measured effectively. These sensor readings can each be approximated by a linear fit, as in Figure 13c. We compared the residuals (R2 values) for these fits for top- and side-facing magnets for the same range of L, representing the linearity of the resulting data. The results of this analysis can be seen in Figure 13e. We conclude that the top-facing magnet orientation is superior, because the working range is 30% larger and the data are more linear. In addition, it is found to be advantageous to minimize L to maximize the range of magnetic field readings.

FEA-Sensor
Figure.13 Finite element analysis of the flexible curvature senor. (a) A two dimensional view of magnetic field vectors from our COMSOL simulation. (b) The geometric relationship between the magnet and the Hall effect sensor. (c) The simulated magnetic field data at the sensor (solid line) and a corresponding first-order fit (dashed line) as a function of curvature. The magnet is facing out of the sensor (the N direction is upward) and the distance L is 3.1 mm. (d) The effect of changing L and magnet orientation on measured magnetic field at a 90 bending angle. The solid line shows the data where the magnet is facing upward (y-axis) and the dashed line shows the magnet facing sideways (x-axis, i.e., toward the Hall effect sensor). (e) The residuals of linear fits on data from (d) representing the linearity of the data.

Testing

This section shows how to choose the optimal design for curvature sensor. We considered two main parameters: the orientation of the magnet and the distance between the magnet and the Hall element. First, we generated magnetic field data using COMSOL, an example of which can be seen in Figure 13a. We used this to calculate the strength of the magnetic field at the Hall element with respect to the circuit design. Figure 13b shows the geometric relationship between the magnet and the Hall element on a bending segment. The origin is located at the base of the magnet, L is the arc-length along the flexible circuit between the origin and the center of the Hall element, hm is the height of the center of the magnet (point M), and hs is the height of the Hall effect sensor element (point S). We assume that the flexible sensor is under constant curvature, allowing us to calculate the positions of these two points.

We can calculate the vector between M and S, and then use the COMSOL magnetic field data Bx and By at S to determine the expected field registered by the Hall element (in its normal direction) via the following rotation equation:

Bn=BycosΘ-BxsinΘ

where Bn is the magnetic field density, which the onedimensional Hall effect sensor could sense when the bending angle is h. When analyzing the sensor simulation, we considered the working range of the bending actuator to be 90, representing the bounds of h. Figure 13c shows the model prediction of the magnetic field with respect to curvature at a distance of L ¼ 3.1 mm, the results of which can be approximated using a linear fit. To determine the optimal distance and magnet orientation, we calculated the range of measured magnetic fields for L ranging between 3.1 and 4.6 mm with the magnetic north pointing upward (along y-axis) and sideways (along x-axis), the results of which can be seen in Figure 4d.This range was chosen to keep the sensor from coming into contact with the magnet at larger curvature values, as well as keep the magnetic field from becoming too weak to be measured effectively. These sensor readings can each be approximated by a linear fit, as in Figure 13c. We compared the residuals (R2 values) for these fits for top- and side-facing magnets for the same range of L, representing the linearity of the resulting data. The results of this analysis can be seen in Figure 13e. We conclude that the top-facing magnet orientation is superior, because the working range is 30% larger and the data are more linear. In addition, it is found to be advantageous to minimize L to maximize the range of magnetic field readings.

FEA-Sensor
Figure.13 Finite element analysis of the flexible curvature senor. (a) A two dimensional view of magnetic field vectors from our COMSOL simulation. (b) The geometric relationship between the magnet and the Hall effect sensor. (c) The simulated magnetic field data at the sensor (solid line) and a corresponding first-order fit (dashed line) as a function of curvature. The magnet is facing out of the sensor (the N direction is upward) and the distance L is 3.1 mm. (d) The effect of changing L and magnet orientation on measured magnetic field at a 90 bending angle. The solid line shows the data where the magnet is facing upward (y-axis) and the dashed line shows the magnet facing sideways (x-axis, i.e., toward the Hall effect sensor). (e) The residuals of linear fits on data from (d) representing the linearity of the data.

Case Studies

Third Generation WPI Soft Robotic Snake

WPI third generation soft robotics snake is incorporates on-board electrical and fluidic power, embedded control, and distributed solenoid valves for tetherless operation (Figure.16). Custom magnetic curvature sensors are incorporated within each soft bending actuation segment for real-time proprioceptive measurements.

3rdWPI SRS
Figure.16 .CAD model (left) and experimental prototype (right) of the self-contained soft robotic snake.

 

Adapting to Flexibility: Model Reference Adaptive Control of Soft Bending Actuators

Soft pneumatic actuators enable robots to interact safely with complex environments, but often suffer from imprecise control and unpredictable dynamics. This section addresses these challenges through the use of model reference adaptive control, which modulates the input to the plant to ensure that it behaves similarly to a reference dynamic model. We use adaptive control to standardize the performance of soft actuators and eliminate their non-linear behavior. We implement an adaptive controller chosen for its simplicity and efficiency, and study the ability of this controller to force different soft pneumatic actuators to behave uniformly under a variety of conditions. Next, we formulate an inverse dynamic feedforward controller, allowing soft actuators to quickly follow reference trajectories. We test the performance of the proposed feedforward controller with and without the adaptive controller, to study its open-loop effectiveness and highlight the improvements the adaptive controller offers. Our experimental results indicate that soft actuators can follow unstructured continuous signals through the use of the proposed adaptive control approach.

WPI Soft Robotics Snake

The video shows the WPI SRS performace:

We recoder the four modules sensor data and plot with the vision tracking data (Figure.17):

Sensor
Figure.17 Performance verification of the four embedded curvature sensors using external motion-capture data as ground truth, for ω = 2 Hz and ϕ = 0. (a)–(d) represent each segment from head to tail.

Adapting to Flexibility: Model Reference Adaptive Control of Soft Bending Actuators

The video shows the model refernece adaptive control for soft bending actuator

Downloads

The flexible circuit trace: circuit_trace_0.pdf

The soft bending actuator mold (STL for 3D print mold and SLDPRT for cap (Laser cutter)): softactuatorstl.zip

 

softactuatorstl.zip709 KB
circuit_trace_0.pdf388 KB

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