This page is about the geometry and joint properties of Upkies. Mechanics and electronics are discussed in the Hardware wiki.

Frames

Anchor frames

Locations of anchor frame

Anchor frames are attached to the stator of the ankle on each leg. Their orientation compared to the stator frame is such that they are aligned with the torso in the neutral configuration.

Right-click on the image to the right and open it in a new tab/window to see the frame orientation better. This image was generated by running python examples/display_frames.py --filter contact from the upkie_description repository.

IMU frame

Location of the IMU frame

The IMU frame has the orientation of the pi3hat IMU:

x-axis: from the IMU towards the back of the robot (CAN/HDMI connectors on the Raspberry Pi).
y-axis: from the IMU towards the left of the robot (USB ports of the Raspberry Pi).
z-axis: from the IMU towards the wheels of the robot (from the Raspberry Pi towards the pi3hat).

Right-click on the image to the right and open it in a new tab/window to see the frame orientation better. This image was generated by running python examples/display_frames.py --only imu from the upkie_description repository.

Joint limits

Joint	Limit	Value (±)	Why?
Hip	Position	1.26 rad	Geometry: cables fully stretched
Hip	Velocity	28.8 rad/s	See qdd100 details below
Hip	Torque	16.0 Nm	Peak torque (< 1 s) from the qdd100 spec
Knee	Position	2.51 rad	Geometry: wheels touching hip actuators.
Knee	Velocity	28.8 rad/s	See qdd100 details below
Knee	Torque	16 Nm	Peak torque (< 1 s) from the qdd100 spec
Wheel	Position	-	No limit
Wheel	Velocity	111 rad/s	See mj5208 details below
Wheel	Torque	1.7 Nm	See mj5208 details below

For qdd100's: peak velocities are rated as 3,600 dps at 36 V and 2,300 dps at 24 V. Assuming a linear velocity-voltage relationship (which is a big assumption, for instance the actual maximum velocity will also depend on servo.pwm_rate_hz) leads to 1,650 dps at the 18 V of the RYOBI batteries used on Upkie, or equivalently 28.8 rad/s after conversion and rounding.

For mj5208's: peak velocities from the mj5208 spec are rated as 7,500 rpm, or approximately 785 rad/s. Multiplying by the wheel radius of your typical Upkie (between 5 and 6 cm), we obtain a ground speed comparable to that of a car on a highway. We scale this down a notch! Backtracking from a top ground speed at 20 km/h, we obtain a maximum velocity around 111 rad/s.

Model conventions

There are the conventions used in the URDF description of the robot model. In what follows, we assume you are familiar with the informal URDF standard from the ROS wiki, in particular the urdf/XML/joint and urdf/XML/link pages.

Link and joint names

Links and joints are grouped by "assemblies". We can recognize assemblies in link and joint names:

A link is named <assembly>_<identifier>, for example left_hip_qdd100_stator denotes the stator of the qdd100 of the left hip.
A fixed joint is named <child_link>_fix, for instance the left_hip_qdd100_stator_fix that attaches the qdd100 stator of the left-hip assembly to the torso.
A revolute joint is named directly based on its side and role, for example left_hip or right_wheel.

Note that the moteus convention is that positive angles correspond to clockwise rotations when looking at the rotor / back of the moteus board. This is opposite to the URDF default, so our motor stator-rotor joint axes are aligned with the -z axis of the joint frame. See moteus direction configuration for details.

Virtual links

Virtual links have a net mass of 1 gram. Setting the mass of a virtual link to zero prevents the base link from free-floating in Bullet. Since our description does not account for screws and cables anyway, the additional 1 gram per virtual link should not make a significant difference.

Virtual links should also contain a visual geometry (see this comment).