CAPITULO DE SUSPENSION

Since the robot should reflect the morphology of Carausius morosus not only the legs were scaled from the biological model but also their relative positions were adopted. Table 2.2 lists the positions of the leg onsets along the body axis of insect and robot, both relative to the respective onsets of the hind legs. Diverging from the planned scaling factor of 20 between insect and robot, the positions of the front legs were shifted by 10 mm to the front to increase the space for the PC/104 in the middle segment. According to Cruse (1976b), the variance for the distance between the front and the middle legs of the insect is in the range of ±1.3 mm. Therefore, the shifted position of the front legs can still be considered biologically plausible.

For the lateral positioning of the legs the scaling had to be modified as well. The dis- tances between contralateral leg pairs of Carausius morosus were measured to be in the range of ∼1.5-5 mm with the smallest distance between the front legs. Due to the size of the actuators, an accurate scaling (∼30-100 mm) would require a considerable reduction of the angular workspace of the legs since the housings of β-drives of contralateral legs might otherwise collide with each other. Therefore, in a first step, the desired move- ment angles of the leg joints were approximated based on the leg workspaces of stick insects (Cruse 1976b). Whereas the insect’s middle leg workspaces are nearly centered, the front and hind leg workspaces are shifted relative to the leg onsets to the front and back, respectively. The desired angular limits for the leg joints of the robot are listed in table 2.3. To realize these angular movement ranges and still prevent collisions of the

β-drive housings of contralateral legs, the distance between contralateral leg onsets had

to be increased to 140 mm.

Before the design of the body segments could be started, the maximum available space had to be defined which is not intersected by any part of the legs for all combinations of joint angles within the desired joint angle workspaces. For this purpose, the movements

front middle hind

left leg right leg left leg right leg left leg right leg

α-range [rad] [-0.6, 1.4] [-1.4, 0.6] [-1.0, 1.0] [-1.0, 1.0] [-1.6, 0.5] [-0.5, 1.6]

β-range [rad] [-1.6, 0.8] [-0.8, 1.6] [-1.6, 0.8] [-0.8, 1.6] [-0.8, 1.6] [-1.6, 0.8]

γ-range [rad] [-1.2,1.2] [-1.2,1.2] [-1.2,1.2] [-1.2,1.2] [-1.2,1.2] [-1.2,1.2] Table 2.3.: Desired joint angle ranges for the six legs ofHECTOR. The values were approximated based on the leg workspaces of Carausius morosus. For the neutral positions (joint angles at 0◦_{), see fig.A.2.}

of the leg segments were simulated for the desired movement ranges of the joints.5 _Based on this simulation, the maximum available space was computed that is not intruded by any part of the legs. In the actual design process of the body segments, all parts of the body housing must lie entirely within this maximum body space.

Due to the asymmetry in the leg setup (as mentioned, the femora are off-centered), the workspace that needs to be clear for the movement of the leg segments changes depending on the mounting direction of the β- and γ-drives. To find a suitable configuration, the

maximum body space was computed for different leg setups. Exemplarily, the results for

three of these configurations are depicted in fig. 2.9. For each combination of x- and z- positions along the symmetry plane of the robot, the closest y-coordinate is plotted that can be reached by any leg segment (for joint output angles within the desired working ranges). In fig. 2.9(a), the maximum body space is depicted for a leg setup, in which all β-joint output flanges are directed backwards (the γ-drives are always oriented in the same way as the β-drives). Therefore, also the femora are positioned rearwards relative to the leg plane (indicated in the pictogram on the right side of the figure). The graphic shows that due to the off-centered femur, the workspace of the hind legs extends inwards up to the symmetry plane of the robot (indicated by dashed lines in the robot pictograms). To prevent collisions between the hind leg segments and the body, this area would need to be spared in the body design. For the middle and front legs, directly behind the leg onsets, nearly vertical indentations must be left open for the femur to slew into. In fig. 2.9(b), the maximum body space is depicted for a leg setup with all β-joint outputs and femora directed to the front. In comparison to the setup shown in (a), the vertical indention must now be left in front of each leg onset since the asymmetric orientation of the femur is reversed. As previously for the hind legs, in this configuration, the workspace of the front legs extends to the symmetry plane. Therefore, mounting of sensors at the front of the robot would not be possible as these might collide with the segments of the front legs.

Based on these results, a mixture of the two previous designs was chosen for the robot setup. In this configuration, the β-joint outputs of the front and middle legs are directed backwards, whereas the β-joint outputs of the hind legs are directed forwards.

5_{To reduce the complexity of the simulation, femur and tibia were modeled as cylinders with a diameter}

of 40 mm. The diameter of the cylinders was chosen such that they envelop the complex outline of the actual leg segment housings.

-0.1 0.2 x-position [m] z-position [m] -0.0 0.1 x y z -0.1 x-position [m] z-position [m] -0.0 0.1 x y z (b) (c) (a) 0.2 -0.2 0 0.2 0.4 0.8 -0.1 0.2 x-position [m] z-position [m] -0.0 0.1 -0.1 0.1 0.3 0.5 x y z -0.3 -0.25 -0.2 -0.15 -0.1 0 y-position [m] -0.05 0.6 0.7 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 z z z b-joint outputs directed backwards b-joint outputs directed to the front

mixed configuration of

b-joint output directions

Figure 2.9.: Depictions of the maximum body spaces for three different mounting con- figurations of the legs (schematically illustrated in the respective pictogram on the right). The subfigures on the left indicate the maximum body spaces, therefore the maximum outlines for the design of the body segments such that collisions between the body and the leg segments can be precluded. The data is shown for the right side of the robot. However, since the leg workspaces are symmetric for both sides of the robot, also the outlines of the maximum body space will be symmetrical. Since the femora are off-centered relative to the leg planes (see robot pictograms on the right) the maximum body space depends on the mounting directions of the β- and

γ-drives, and the corresponding position of the femora. (a) shows the configuration

for all femora oriented towards the back of the robot. (b) shows the configuration with all femora oriented towards the front of the robot. (c) depicts a mixed con- figuration, in which the femora of the front and middle legs are oriented backwards whereas the femora of the hind legs are oriented to the front. The points around which the β-joints rotate (corresponding to the leg onsets in the insect) are marked by black dots. In y-direction, these are located at -0.07 m. Figure2.11 shows the final body design in combination with the last configuration.

(a) (b)

(d) (c)

Figure 2.10.: Different steps in the design of the robot. (a) shows an early drawing that illustrates the segmentation of the main body and the concept of exchangeable elements: all white parts can be replaced, e.g., by 3D-printed plastic parts (cour- tesy of Achim Seemayer). (b) shows the first draft for the leg orientation shown in fig.2.9(c) (courtesy of Achim Seemayer). (c) Rendering of the final housing de- sign. All segments are constructed of an upper and a lower housing (and a lid, if applicable) due to requirements of the manufacturing process (courtesy of Martin Schulz). (d) Image of the three body segments without legs and intersegmental drives (courtesy of Martin Schulz).

The resulting outline of the maximum body space is shown in fig. 2.9(c). The thorax of stick insects is divided into three segments with the leg onsets close to the back of each segment. For the robot, a similar setup was planned. Since the body segments are intended to be slewable relative to each other, the outline of the body must be constricted at the transitions to prevent collisions between the body segments. This enables the front and middle legs to slew into the space between the body segments. For the hind legs, dedicated indentations had to be provided in the hind segment in front of the leg onsets.

With these restrictions for the maximum outline of the body segments, the design process was initiated. Figure 2.10 shows four relevant stages of this process. In (a), the conceptual drawing is depicted that shows the envisioned segmentation of the main

body. As the computer and the batteries are to be mounted within the body housing, lids must be provided for easy access. Figure2.10(b) shows a preliminary design sketch by Achim Seemayer is shown for a left-side turn of the robot. This sketch visualizes the body segment actuators and the off-centered assembly of the femur joints.

Since one of the goals in the fabrication of the body housings from CFRP was the reduction of mass as compared to a metal body, the body segments are supposed to be self-supporting without the need of additional, internal support structures (e.g., an endoskeleton). A rendering of the body housing design that complies with this concept is shown in fig. 2.10(c). The body segments are connected to each other by the body segment actuators. Since the front segment is supposed to be completely exchangeable, this segment was fabricated without the requirement to be self-supporting. Thus, the legs are connected directly to the frame of the body segment actuator. To fix the legs to the middle and hind body segments, small metal inlays were embedded into theCFRP hull to allow reversible connections between the legs and the housings using screws. These metal inlays were also used to define connection points for the segment actuators. By limiting the size of the middle and hind segment lids, and the housing of the front segment to a volume that is printable by an available 3D-printer (203 mm x 203 mm x 305 mm build size; Dimension SST 768, Stratasys, Eden Prairie, USA), an easy adaptability to various optional sensor systems was ensured. Thus, if a 360◦_camera is supposed to be mounted on the middle segment, the design of the corresponding lid can be adapted and printed. In the front segment, different sensors are imaginable— ranging from cameras for visual feedback to tactile antennae. Due to the modular setup, appropriate front segment housings can be designed for the different sensor systems.

The final housings are shown in fig.2.10(d). The bright metallic spots on the housing are the mentioned metal inlays, to which the legs and the body segment actuators are to be fixed.

In fig. 2.11, the final design of the body segments is shown again together with the limiting surface of the legs’ workspaces that was already depicted in fig. 2.9(c). Due to the asymmetry of the leg setup, the spaces between the body segments can be utilized to realize the angular working ranges of the leg joints.

The wiring within the segments is considerably reduced due to distributed control electronics of the actuators, as depicted in fig.2.12. Therefore, it is sufficient to connect the joint drives with the power supply and the BioFlex bus to exchange data with the central controller. To connect the embedded PC/104-system to the RS-485–based

BioFlex bus, custom transmitter boards were developed by Schäffersmann (2011) that allow to link viaUSB (Universal Serial Bus). These boards are also distributed onto the three body segments.

All electronic components in the robot are powered with the same voltage that was defined to be in the range of 15 to 40 V. It is either supplied by a LiPo (Lithium-ion Polymer)battery embedded in the hind segment or an external power supply. Therefore, it is unnecessary to route different voltages throughout the robot. However, this neces- sarily requires each component to convert the common supply voltage to the required voltages locally.

-0.2 0 0.2 0.4 0.8 -0.3 0.0 x-position [m] y-position [m] -0.2 -0.1 -0.1 0.1 0.3 0.6 -0.1 0.2 x-position [m] z-position [m] -0.0 0.1 -0.2 0.1 0.4 0.2 0.3 -0.4 0.7 0.5 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 (a) (b)

Figure 2.11.: Depiction of the final body design in (a) top and (b) side view in combination with the restricting surface already shown in fig.2.9(c). The colors of the restricting surface are not to scale with the colormap shown in fig. 2.9 due to the transparency and light effects.

A scaled image of Carausius morosus in direct comparison with a rendering of the robot is shown in fig. 2.13(a). As can be seen, the dimensions of the thorax segments have been transferred together with the leg morphology to the technical system. The COMsof the biological and the technical system have been indicated in the illustration. Whereas the COM of the insect is located roughly between the hind leg onsets, the COMof the robot is shifted forwards, slightly in front of the middle leg onsets since the abdomen of the insect was not replicated in the robot setup. In fig. 2.13(a), an image of the assembled robot is shown. The robot has a mass of 13 kg, which is mostly due to the combined mass of the leg joint actuators (18 × 0.39 kg ≈ 7 kg). The length of the body is 95 cm and the width during walking is roughly 60 cm due to the sprawled leg posture.

3x 3x 3x 3x 3x 3x front leg middle leg hind leg PC/104 LiPo-battery USB power supply BioFlex bus bus master b.m. b.m.

Figure 2.12.: Schematic of the wiring between the components of the robot. Since each of the actuators is capable of receiving/transmitting controller commands via the BioFlex protocol, they need to be connected only to the power supply (red lines) and the BioFlex bus (green lines). The bus masters (b.m.), responsible for transmitting messages to/from the clients, are connected to the main controller, a PC/104 computer, viaUSB(blue lines).