The first step in this project was to design the pneumatic actuators. The idea was to design actuators that extend when compressed air is injected inside them, contrary to the operation of the McKibben actuators that contract when pressurized. Actuators made of silicone that do not require a braided sleeve in order to constrain the deformation were desired. This choice led to a design of our actuators with a “folded” shape, similar to an accordion.

When pressure is applied inside the cavity of the actuator, the walls of the actuator unfold and produce an elongation of the actuator.

Since the time required to build the actuators is considerable, we first simulated it to confirm the expected behavior. This simulation is based on the Finite Element model of the actuator and was performed using the SOFA Framework (https://www.sofa-framework.org). Once the simulation provides satisfying results, we proceed with the fabrication of the actuators.

Having the simulation of the deformable parts of the prototype is of great help because it gives a good idea how  these parts will behave before their fabrication. By analyzing the simulation, we know if the design needs modifications without having to test the real part in the lab. Also, a suitable way to pilot this model is by using using this model in open loop with the real prototype.

To achieve bending in our robot, three actuators are arranged in parallel configuration as one section of the manipulator. A rigid platform at the end of the array holds the actuators in place. By applying different pressure values to each actuator, we can displace or orientate this platform.

When differential pressures are applied to the actuators of one section, the top platform is oriented in different ways. If equal pressure is applied to all the actuators, the manipulator elongates longitudinally.

The design of the platform is very simple. It is composed of 3 sockets that receive the actuators and hold them in place. A hole at the bottom of each socket provides the necessary space to connect a plastic tube, from the air supply to the actuator, and a central hole in the platform allows us to pass the tube that will supply the air to the actuators of the second section. Smaller holes located between the sockets serve as cable guides for the tendons.

The manipulator is composed by serially connecting two sections. The pose of the manipulator is controlled by six pneumatic inputs, while the stiffness is controlled by six antagonist cable actuators. These cables run along the same direction of the pneumatic actuators and pass through holes in the rigid platform. The cables are positioned carefully to avoid contact with the pneumatic actuators and minimize the friction during bending.

Once the behavior of one section of the manipulator was proven, another simulation was made to include both sections to better picture the behavior of the whole manipulator.

Each tendon is attached to a servomotor. More specifically, to a pulley that is connected to the shaft of each servomotor. This is why six supports of servomotors and six pulleys were designed and built. The servomotors used are rated to a 0° to 180° span, although in practice, each one turns in the range of  35° and 158°. That means we need to use a pulley that could give us enough force to pull the different parts of the manipulator, while keeping an appropriate stroke according to the simulation's results. Each section of the manipulator was measured to an elongation of 1.5cm, twice this distance must be considered for the second section. Therefore, a pulley of 3.6cm of diameter was designed , giving a safe 3.8 cm of stroke. To keep the servomotors in place, a support visible on the picture below had to be designed. This design allows the six actuators to work in a reduced volume, while keeping the cables free from tangling up and leaving at the same time enough room for the pneumatics tubing.

This section presents all the steps needed to build the prototype. Some comments regarding possible problems or improvements in the process were added. These steps are:

1. Fabrication of pneumatic actuators
2. Printing the rigid platforms
3. Building one section of the robot
4. Building the base frame
5. Final assembly

Fabrication of the pneumatic actuators

The soft backbone of the manipulator is composed of pneumatic actuators. These actuators are made of silicone rubber, and when inflated, they elongate longitudinally.

The first step to casting the actuators is printing the mold. The molds were designed to hold half of the actuator. In this case, the molds were made out of plaster using the ProJet 460 Plus printer, but molds made of a conventional plastic for 3D printing should do just fine as long as its surface is conveniently lubricated. This choice was motivated by the smoother surfaces produced by the plaster post-treatment with cyanoacrylate, making the unmolding much easier. 

Once the molds are printed, it is time to cast the actuators. For this, Dragon Skin 10A silicone rubber is used. This silicone comes in a two-compound presentation which is really easy to prepare: just mix part A and part B in a 1:1 ratio, according to the amount of silicone you will need. If you have access to a vacuum chamber, you can put the silicone mixture in it to take out all the bubbles that can appear when the two parts are mixed. This allows to have a really homogeneous silicone piece.

 

Once the silicone mixture is ready, simply pour some mixture into the molds until the mold cavity is completely full. Then, put the cap on the mold while being careful with the alignment between the mold and the cap. For this initial test, we casted just two halves to have one actuator.

The two halves of the actuator should cure after about 3 to 4 hours. To join them, put some silicone on the edge of the wall of the piece and use the molds to align each half. Once the silicone is cured, you can take out the actuator from the molds. Use a hobby knife to remove any excess of silicone from the actuator.

The rigid platforms

There are three different types of rigid platforms involved in the assembly of the manipulator. These platforms have sockets that allow us to keep the actuators in place. The sockets have an entry hole for the polyethylene tubes. All of these platforms use a second piece on top that functions as a cap, this cap makes it easier to put the actuators on the sockets. 

The first platform is the base, which is attached to the wooden plank and receive the first three pneumatic actuators. To attach this platform to the plank, Ø4mm bolts were used, long enough so that nuts can be fastened to the other side of the plank. Another three Ø2.5mm 10mm long bolts are used in the center part of the platform to fix the cap in place. Six more holes between the sockets are used to guide the cables along the manipulator.

 

The cap is placed on top of the platform and is fixed to it using bolts.

The middle platform is based on the same design. This platform connects the first section to the second and is composed of four pieces because it has six sockets in total and 2 caps. There are no 4mm holes and the bolts used to assembly these part are longer (30mm). A slight modification is done to the upper socket part in order to allow the connection of the tubes that supply pressure to the second section. Both cap pieces used in this platform are exactly the same.

The top platform receives the second set of pneumatic actuators and completes the second section. The design is the same as for the middle platforms.

 

Building one section of the robot

Once three actuators are made and a couple of platforms are printed, the assembly of one section of the manipulator is an easy task. Just put the actuators in the sockets of a sandwich of platforms, connect the tubes for the pressure supply, and close the caps.

Building the base frame

In order to have a suitable fixation base for the manipulator, a frame made of beams was built. This frame is composed by 12 beams of 30cm of length with some A-brackets to keep it together. OpenBeams were chosen because of the readiness of the materials and because more brackets can be 3D printed needed.

Cover the frame with the wooden plank. With the use of the electric drill, cut suitable holes in the shape of the base rigid platform of the manipulator, so that there is easy access to the connection holes of the sockets and also the cable guides.

Finally, attach the plank to the frame using bolts from the bottom up. The servos will be placed on top of the cover, while the manipulator will be attached to the plank at the bottom side. The manipulator will be operating hanging from the cover of the base.

Final assembly

Once all the parts of the manipulator are fabricated, we can start the final assembly of the robot. The first step is to attach the base platform to the bottom of the plank in the base frame. As explained before, long bolts of Ø4mm and nuts are used to fix the platform.

The next step is to connect the second section to the first one.  30mm long Ø2.5mm bolts are used to attach the two parts of the middle rigid platform; this was done with the objective of having a small gap between the two parts of the middle platform, so that the tubes that supply the air to the second set of pneumatic actuators could have some room to bend.

With both sections in place, we can start putting the cables through their dedicated holes. There are six cables in total, three of them go from the base to the middle platform, while the other three go from the base to the top platform. The cables are actuated by servos placed on top of the base cover. Special care is needed while putting the servos in place, to make sure that the pulleys attached to the servos are aligned with the cable holes at the base platform. Nuts were tied up at the end of each cable so that the cables can apply forces to the platforms.

          

After every part is in its place, the robot looks like this:

The robot is composed of 6 pneumatic actuators and 6 cables. The robot is thus highly redundant and composed of hybrid actuation. 

To drive the 12 actuators in a coherent manner, a new approach is needed for control. Bosman et al. recently proposed a method dedicated to continuum robots with rigid vertebrae. One important contribution of this work is to demonstrate that the method of control can be extended to hybrid and redundant actuation.

The first step of the method is to build a detailed FEM model of one intervertebra attached to a vertebra. For that, we use SOFA and the plugin dedicated to soft robots. The simulation is able to mix deformable and rigid parts, thanks to a generic definition of the degrees of freedom available on SOFA platform. 

The second step is the heart of the method: to avoid computation burden and allow for real-time computation of the robot model, we use a model reduction method based on a domain decomposition approach. The algorithm computes the equivalent non-linear stiffness of the intervertebra. 

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The third step consists in building a simplified model of the whole robot and placing the cables. To compute a motion of the cavities with no precise simulation of the intervertebra (because we are using a simplified model), we use a technique often used in computer graphics that is called skinning. From the 6D frame of each intervertebra, the skinning provides a deformable motion of the inner cavity. In SOFA, we can reverse this skinning as done in [Duriez et al 2008] to compute the equivalent force on the frame, due to the pressure applied on cavity walls.

The last step is to launch the inverse control method, presented in [Duriez 2013] and extended in [Bosman et al. 2015]. It consists on inverting the deformable model, thanks to an optimization method and finding the actuator value given the desired position of the effector (here we control all the degrees of freedom (DOF) of the effector, except the twist, so 5DOF). As the robot is highly redundant, we add more criteria in the optimization to get a single solution to the problem: the method minimizes the pressure value (to put as little pressure as possible in the cavities) and it also minimizes the energy of deformation. 

Along with the fabrication phase, the performance of the pneumatic actuators was tested, as well as the real behavior of the "Stewart platform"-like section of the manipulator.

The initial test conducted on a 5cm long actuator showed that a maximum extension of 47% (2.35cm) could be obtained when a pressure of 0.3 bars is applied. If the cavity pressure increases further, the actuator deforms radially. It is then important to operate the actuator inside the pressure range of 0 – 0.3 bars.

A preliminary test of the real behavior of the pneumatic based Stewart platform was conducted. This test was done without the cable actuators.

The modeling method and simulation described previously to pilot the robot was used. The inverse model is computed in real-time to obtain the actuation required to orientate and position the manipulator as desired. This position is controlled by moving manually a control point attached to the top platform in the simulation.

The first test was conducted using only cable actuation.

In the second test, antagonistic (both cable and pneumatics) actuation was implemented in the simulation.