The Design of Stretch: A Compact, Lightweight Mobile Manipulator for Indoor Human Environments

A. The Structure of Indoor Human Environments

Indoor human environments have Cartesian structure with horizontal planes and vertical surfaces, including floors, countertops, walls, doors, and cabinet faces. Humans have engineered these environments to facilitate perception, navigation, and manipulation by people. Flat surfaces help objects remain in place. People often rest their bodies on approximately flat surfaces, such as the tops of beds and chair seats. Important locations tend to be accessible via clutter-free paths wide enough to walk through, and important objects tend to be visible from human head heights and reachable by human arms.

Pets and people, including children, older adults, and people with disabilities, are common occupants of indoor human environments, which creates challenges for safe operation. Falls, pinch points, high velocities, and high accelerations all present hazards. Motions that are difficult to predict can create challenges too, making it harder for pets and people to avoid risky situations. For example, doors and drawers represent common hazards, yet their motions are predictable and people learn to manage the risks.

Given these considerations, we created a statically-stable wheeled robot to avoid hazards associated with dynamic stability. Stretch weighs 23 kg, which is above safety guidelines for a single person to lift [49], but light enough for two people to lift or a single person to roll around. Our design emphasizes predictable Cartesian motions matched to the Cartesian structure of human environments. Stretch can reach the floor at 0 cm up to 110 cm, enabling manipulation on standard 36-inch high countertops (≤ 92 cm) (see Fig. 2).

B. Matching Human Dimensions

Using anthropometry, we show that Stretch matches key human dimensions (see Fig. 2). Rather than being a humanoid root, we think of Stretch as an example of “robotic cubism”, where the human form has been deconstructed and reassembled in a manner reminiscent of Cubism [52].

When navigating with its arm stowed, Stretch is 34 cm wide, which is less than 50^th percentile hip widths for adult females, 37.1 cm, and males, 36.1 cm [53]. Paths wider than the width of human hips facilitate comfortable walking, and are thus likely to be common in human environments. 34 cm is also the diameter of the first Roomba [54].

Frequently manipulated objects tend to be reachable by human arms. The outer edge of Stretch’s closed fingertips reaches 71 cm out from the edge of the mobile base, which is similar to 50^th percentile arm lengths for adult females, 67.3 cm, and males, 72.6 cm [53].

Frequently observed parts of the environment tend to be visible from human head height. Stretch’s color camera is 131 cm above the ground, which is between 50^th percentile sitting eye heights for adult females, 112.3 cm, and males, 121.9 cm, and 50^th percentile standing eye heights for adult females, 151.4 cm, and males, 164.3 cm [53].

To facilitate assisting people with disabilities, the center of Stretch’s closed fingertips reaches 112 cm high, which is close to 95^th percentile right shoulder heights of female, 109.7 cm, and male, 113.4 cm, wheelchair users [55].

C. The Four Main Joints

Stretch’s core design consists of four actuators that produce Cartesian motion at the end of the arm and mobility across a flat floor (see Fig. 3). We prioritized reducing actuator requirements, since actuators influence the weight, complexity, and cost of robots. Each actuator requires power, signals, and control. Conventional electric motors with transmissions add weight, and actuators for proximal joints tend to be heavier.

One of Stretch’s four main actuators extends and retracts a horizontal telescoping arm orthogonal to the mobile base’s forward direction of motion. The arm has a small cross section, reducing the mass and swept volume. Its linear motion is readily interpretable, such as when handing an object to a person. Another actuator moves the telescoping arm up and down a vertical mast, which we refer to as the lift. The mast also has a small cross section, which reduces mass and line-of-sight occlusion, and increases reach when the mobile base moves underneath a surface. The remaining two actuators drive the wheels of the differential-drive mobile base to which the mast is mounted.

Stretch’s four main joints represent a minimalist design to achieve Cartesian end-of-arm motion and mobility. Many alternatives have practical limitations. For example, the telescoping arm could have a fixed length and its actuator could be moved to the mobile base to achieve omnidirectional motion using three omniwheels [56]. However, a long arm would increase the robot’s width, creating a hazard and limiting movement, while a short arm would lose the benefits of a human-length arm. Adding one or more actuators for omnidirectional base motion would increase the actuator count and could complicate traversal of thresholds and other deviations from flat ground, such as throw rugs, rug fringe, cables, and tile.

To achieve Cartesian motion, the base drives forward and backward $\left(\pm q_m\right)$ moving the end of the arm left and right $\left(\pm y_e\right)$. The lift $\left(\pm q_l\right)$ moves the end of the arm up and down $\left(\pm z_e\right)$, and the telescoping arm $\left(\pm q_a\right)$ moves it out and in $\left(\pm x_e\right)$. Across the full workspace, $\left[x_e,y_e,z_e\right]=\left[q_a,q_m,q_l\right]$, the Jacobian is the identity matrix, $I$, and the manipulability ellipsoid is an axis-aligned sphere [57].

Notably, the mobile base plays a critical role in manipulation, since the lift and telescoping arm only position the end of the arm within a vertical plane. This contrasts with approaches to mobile manipulation that keep a mobile base stationary while manipulating with an arm. Our approach also differs from mounting a conventional serial manipulator to a mobile base. Arms with prismatic joints that extend beyond twice their retracted length are uncommon [58]–[61].

When operating on flat floors, only the lift actuator works directly against gravity. The telescoping arm uses lightweight materials (e.g., carbon fiber) to achieve a long reach with low weight, reducing the lift actuator’s requirements. The arm’s lightweight structure also reduces its influence on the robot’s center of mass (COM) when it is extended or raised.

D. Two Modes of Operation

While they do not represent all achievable motions, it is conceptually helpful to consider two modes of operation: navigation mode and manipulation mode (see Fig. 3).

E. The Wrist and the Stretch Dex Wrist Accessory

Stretch comes with a wrist yaw joint with a 330° range of motion that can stow a tool in the footprint of the mobile base without changing the tool’s orientation with respect to gravity. In the navigation mode, the arm retracts and the wrist stows the tool. In the manipulation mode, the wrist swings the tool out, deploying it for use. Stowing tools in this manner makes the effective size of the robot smaller when navigating, avoiding collisions between the tool and the environment.

In addition to stowing the tool inside the footprint of the base, the wrist yaw joint provides task-relevant dexterity. It is a fifth DOF that adds dexterous redundancy to pure rotations of the mobile base. This is advantageous for manipulation on flat, horizontal surfaces. For example, it can rotate a camera to see behind objects on a shelf and orient the gripper to grasp elongated objects.

While the yaw joint is sufficient for a variety of tasks, some tasks benefit from additional degrees of freedom. The Stretch Dex Wrist is a recent accessory that adds a pitch joint followed by a roll joint in a serial chain. Together with the yaw joint, this results in a 3-DOF wrist and a 7-DOF robot.

The Dex Wrist enables tasks such as pouring and operating door knobs (see Fig. 9). It also increases the height the center of the closed fingertips can reach to approximately 130 cm above the ground, which is close to 95^th percentile right eye heights of female, 125.5 cm, and male, 127.0 cm, wheelchair users [55]. The pitch joint works against gravity, but is a distal joint with a relatively small moment arm. In general, the four main joints provide gross movements over large distances, while the 3-DOF wrist and tools perform fine movements.

F. The Stretch Compliant Gripper

In May of 2017 at Georgia Tech, we developed a low-cost compliant gripper (see Fig. 4). Human-operated grabbers have long been used as affordable assistive devices to help people with disabilities reach and grasp objects in human environments. The grabbers are operated by pulling a cable that can be actuated [63].

To identify promising candidates, we used Amazon to find and purchase the highest-rated grabbers. Candidates had thousands of ratings and detailed reviews. We purchased ten grabbers ranging from $13.00 to $33.95 in price with an average price of $19.28.

We then conducted an informal evaluation to select the top candidates. We asked six lab members with expertise in assistive robotics to try the grabbers with objects relevant to assistive robotics, including objects from [62] (see Fig. 4). Based on their feedback, we selected the “Reacher Grabber by VIVE” and the “Japanese Reacher Grabber Pickup Tool”.

We found the rubber fingertips and spring steel flexures of the “Reacher Grabber by VIVE” to be highly capable and created a robotic prototype. The commercial version (Stretch Compliant Gripper) that comes with Stretch provides kinematic and torque feedback from the actuator and can exert significantly more grip force than the original human-operated grabber, which is important for tasks such as operating door knobs. It also includes a mount point at a 90° angle with a hook useful for operating doors and drawers. The standard gripper tilts downwards, which permits grasping objects from above and from the side without use of a pitch joint. The Dex Wrist comes with a different version of this gripper that points straight out, since the Dex Wrist can both pitch and roll the gripper.

G. Stretch’s Sensors

Stretch can sense applied loads with its actuators using current sensing. The four main joints have low gear ratios that facilitate this form of haptic sensing. The prismatic joints for the lift and arm enable straightforward contact detection, since their non-contact loads remain similar across configurations of the robot. Due to their sensitivity, the robot can autonomously open a a variety of drawers by extending its arm until contacting the drawer’s surface, lowering its arm until contacting the handle, and then retracting (see Fig. 9).

The robot’s RGB-D camera (Intel RealSense D435i) is on a pan-tilt head with a 346° pan range of motion (ROM) and a 115° tilt ROM. The head can pan to look in the direction of forward travel while navigating and at the end-of-arm tool while manipulating. It can also look straight down at its mobile base.

We rotated the camera 90° from its typical orientation to increase its vertical field of view (i.e., 87° for depth and 69° for color). This enables it to simultaneously obtain depth imagery from straight ahead and from the floor near the mobile base while navigating. It also gives it a fuller view of the arm’s workspace while manipulating. Panning the camera at a fixed downward tilt can capture a useful 3D representation of the surrounding environment, except for the region occluded by the mast. Viewing body-mounted ArUco markers on the mobile base, the wrist, and the proximal part of the arm supports kinematic calibration [64].

The robot has a laser range finder on its mobile base suitable for standard navigation methods. Only the mast occludes the laser range finder when the arm is raised. The robot has a microphone array on the top of the lift for speech recognition and sound source localization. The mobile base also has an inertial measurement unit (IMU) with rate gyros, accelerometers, and a magnetometer that can be used for navigation and tilt detection to avoid tipping and toppling. The wrist has accelerometers that can be used for bump sensing, and the D345i has rate gyros and accelerometers useful for visual perception.

A. Planar Models of Static Stability

Planar models that represent the robot just before it tips highlight the design tradeoffs. These models assume the robot is in static equilibrium and all but one wheel is losing contact with the ground (see Fig. 5).

B. Static Stability with a Triangular Support Polygon

Stretch uses a single passive omni wheel to help the drive wheels stay in contact when traversing thresholds and other uneven areas. This is similar to the first Roomba. In practice, Stretch tips over the sides of the support triangle formed by its three wheels.

During development, we updated our planar models to account for this difference (see Fig. 6). To simplify analysis, we assume that the robot’s COM is equidistant from the two drive wheels. The moment arm of the robot’s COM becomes $d_{rs}$, which is the perpendicular distance to the left and right sides of the support triangle. $d_{rs}=c\sin \alpha$, where $c$ is the distance from the robot’s COM to the back wheel’s point of contact and $\alpha =\arctan \left(\frac{w}{2l}\right)$, where $w$ is the full width of the robot’s support triangle and $l$ is its length.

The moment arm of the payload changes to $d_{ps}.d_{ps}=v\text{cos}\alpha$, where $v=d_p+\frac{t}{\tan \beta },\beta =\frac{\pi }{2}-\alpha$, and $t$ is the distance from the front side of the support triangle to the middle of the telescoping arm. As with our planar models, $d_p$ represents the reach of the telescoping arm beyond the contact point for the right front wheel (see Fig. 5). Brought together, $d_{ps}=\left(d_p+\frac{t}{\tan \left(\frac{\pi }{2}-\alpha \right)}\right)\cos \alpha$.

For pulling, only the component of the pulling force orthogonal to the side of the support triangle, $F_s$, plays a role, where $F_s=F_{pull}\text{cos}\alpha$. Due to our simplifying assumption for the position of the robot’s COM, this model results in the magnitude of the maximum pushing force being the same as the magnitude of the maximum pulling force. As with our planar models, $d_F$ represents the height of the telescoping arm above the floor (see Fig. 5). The resulting equations for the maximum payload, $m_{payload}$, and the maximum magnitude of the pulling/pushing force, $F_{pull/push}$, as functions of the reaching distance, $d_p:0\le d_p\le D$, and height of the telescoping arm, $d_F:0\le d_F\le H$ follow:

$H,D$, and $W$ define the height, depth, and width of the robot’s Cartesian workspace, $H\times D\times W$, given idealized forward and backward motion of the mobile base. $W$ can be arbitrarily large, since it depends on environmental constraints. We also model the maximum force the robot can apply driving backwards, $F_{backpush}=m_{r}g\frac{(l-c)}{d_F}$, based on the height of the arm, $d_F$, and the moment arm for the robot’s COM with respect to the front of the support triangle, $l-c$.

C. Other Design Considerations

A higher COM creates a greater risk of toppling due to acceleration, bumps, thresholds, and ramps. The lightweight aluminum mast, carbon fiber telescoping arm, and small head reduce elevated mass. The batteries and three of the four main actuators are located in the mobile base. When paused, Stretch can be tilted over its drive wheels and rolled around in a manner similar to an upright vacuum cleaner, which can improve ease of use, but also increase the risk of toppling. Ignoring other factors, widening the mobile base by $i$ cm allows the full extension of the arm to be increased by up to $ni$ cm, where $n$ is the number of telescoping elements.

D. Measurements & Model Predictions

We applied our models to a low serial number Stretch RE1 with the default Stretch Compliant Gripper rotated to achieve maximum reach. We used the centers of the wheels for the support triangle and balanced the robot on a metal cylinder to estimate the COM’s location giving $w=0.315\text{m}$, $l=0.24\text{m}$, $m_r=23\text{kg}$, $g=9.807\frac{m}{s^2}$, and $c=0.16\text{m}$. Our derivations assumed the load was applied to the middle of the end of the arm. For our evaluation, we applied forces near the fingertips with a Nextech digital force gauge. For this location, $H=1.125\text{m}$, $D=0.693\text{m}$, and $t=0.005\text{m}$. Our models predict that $m_{payload}=\frac{1\text{kg}}{0.0014+0.4141{\text{m}}^{-1}{d}_p}$, $F_{pull/push}=\frac{23.68\text{N m}}{d_F}$, and $F_{backpush}=\frac{18.04\text{N m}}{d_F}$.

We teleoperated the robot to a pose, measured the height of contact, $d_F$, and took five pulling force measurements. We used the gauge’s hook to pull until the robot began to tip over. For the results in Figure 8, each circle shows the average of five measurements. Each group of five measurements has a standard deviation less than 1N. Since our model assumes the COM is equidistant from the left and right sides of the support triangle, we made measurements with the arm fully retracted and fully extended.

We measured the worst case payload by teleoperating the robot to its maximum reaching distance, $d_p=0.693\text{m}$, and pulling down with the gauge’s hook until the robot began to tip over (see Fig. 7). The average of five measurements was 3.46 kg (SD of 0.065 kg), which closely matches our model’s 3.47 kg prediction for $m_{payload}$.

We confirmed that static stability limits the robot’s capabilities by fixing the force gauge to the ground near the robot. We disabled the robot’s force limits and teleoperated it to pull with > 70 N and lift with > 60 N (> 6.12 kg). To avoid damage, we did not attempt to apply the maximum achievable forces.

The stably achievable forces and payloads are sufficient for assistive tasks reported in the literature, including opening many drawers and cabinet doors (< 20N of pulling force) [65], [66], face wiping and shaving (< 10N of pushing force) [67], and lifting objects prioritized for retrieval by people with disabilities (< 1.2 kg) [62].