upkie 9.0.0
Open-source wheeled biped robots
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Observations

Table of Contents

Spines compute observation dictionaries from sensor measurements by applying observers one after the other in a sequence called the observer pipeline. This page lists the outputs of available observers, using shorthands a.b.c for nested dictionary keys observation["a"]["b"]["c"].

Base orientation

The base orientation observer estimates the orientation of the floating base with respect to the world frame.

Observation key Description
base_orientation.angular_velocity Body angular velocity vector of the base frame in rad/s
base_orientation.pitch Pitch angle of the base frame relative to the world frame, in radians

Floor contact

  • Observer: FloorContact
  • Spine observation key: floor_contact

The floor contact observer detects contact between the wheels and the floor. The PID balancer used for testing relies on this observer, for instance, to reset its integrator while the robot is in the air, to avoid fast-spinning wheels at touchdown.

Observation key Description
contact Boolean contact state
left_wheel Wheel contact observation for the left wheel
right_wheel Wheel contact observation for the right wheel
upper_leg_torque Mean squared upper-leg torques in N⋅m

Wheel contact

  • Observer: WheelContact
  • Spine observation key: floor_contact.left_wheel and floor_contact.right_wheel

Internally, the floor contact observer relies on two wheel contact observers, one for each wheel, as listed above.

Observation key Description
abs_acceleration Low-pass filtered absolute wheel acceleration in rad/s²
abs_torque Low-pass filtered absolute wheel torque in N⋅m
contact Current contact state (boolean)

| inertia | Apparent inertia I = |torque| / |acceleration| at the wheel |

History observer

The history observer reports higher-frequency signals from the spine as vectors of observations to lower-frequency agents. It handles floating-point and vector-valued observations. For instance, to report the left-knee torque readings on an Upkie, create a shared-pointer as follows and add it to the observer pipeline of the spine:

auto left_knee_torque_history = std::make_shared<HistoryObserver<double> >(
/* keys = */ std::vector<std::string>{"servo", "left_knee", "torque"},
/* size = */ 10,
/* default_value = */ std::numeric_limits<double>::quiet_NaN());
observer_pipeline.append_observer(left_knee_torque_history);

The same syntax can be used for a vector like the IMU linear acceleration:

auto linear_acceleration_history =
std::make_shared<HistoryObserver<Eigen::Vector3d> >(
/* keys = */ std::vector<std::string>{"imu", "linear_acceleration"},
/* size = */ 10,
/* default_value = */ Eigen::Vector3d::Zero());
observer_pipeline.append_observer(linear_acceleration_history);

IMU

  • Observer: always reported
  • See also: ImuData
  • Spine observation key: imu
Observation key Description
angular_velocity Body angular velocity of the IMU frame in rad/s
linear_acceleration Linear acceleration of the IMU, with gravity filtered out, in m/s²
orientation Orientation of the IMU frame in the ARS frame as a unit quaternion (w, x, y, z)
raw_angular_velocity Raw angular velocity measured by the gyroscope of the IMU, in rad/s
raw_linear_acceleration Raw linear acceleration measured by the accelerometer of the IMU, in m/s²

The inertial measurement unit (IMU) mounted on the pi3hat combines an accelerometer and a gyroscope. These raw measurements are converted onboard by an unscented Kalman filter (based on a standard quasi-static assumption) that outputs observed quantities with respect to an attitude reference system (ARS) frame.

There are three main frames to keep in mind when considering the IMU: the frame of the IMU sensor itself, the world frame, and the attitude reference system (ARS) frame. The world frame is an inertial frame of reference we refer to in various observers. It has an x-axis pointing forward, a y-axis pointing to the left and a z-axis vertical and pointing up (i.e., against the gravity vector).

Servo

  • Observer: always reported
  • Spine observation key: servo
Observation key Description
<servo_name> Observations for a given servo, *e.g. left_hip
<servo_name>.position Angle between the stator and the rotor in radians
<servo_name>.torque Joint torque in N⋅m
<servo_name>.velocity Angular velocity of the rotor w.r.t. stator in rotor, in rad/s

Actuators on the robot are qdd100 beta 3 (hips and knees) and mj5208 brushless motors (wheels). All of them have moteus controller boards that provide the above measurements. They are estimated as follows:

  • Joint angle, sensed by two orthogonal Hall-effect sensors at the back of the moteus controller board (each measuring the magnetic field in one direction; the output angle is then the arc-tangent of the ratio between these two values)
  • Joint velocity, obtained by filtering joint angle measurements (not a direct measurement)
  • Joint torque, estimated from sensed phase currents (with a model that includes stator magnetic saturation)

Simulation-only

  • Observer: when using a simulation interface
  • Spine observation key: sim

Simulation spines may report the following additional observations.

Floating base

  • Spine observation key: sim.base

Positions and velocities of the base frame:

Observation key Description
base.position Position of the base frame in the world frame, in meters
base.orientation Unit quaternion (q, x, y, z) of the orientation of the base frame in the world frame
base.linear_velocity Linear velocity from base to world in world, in m/s
base.angular_velocity Angular velocity from base to world in world, in rad/s

IMU non-observables

  • Spine observation key: sim.imu

Non-observable quantities related to the IMU:

Observation key Description
linear_velocity Linear velocity of the IMU frame in the world frame, in m/s

Rigid bodies

  • Spine observation key: sim.bodies

Coordinates of some rigid bodies in the world frame:

Observation key Description
YYY Positions and velocities of the extra body YYY
YYY.position Position of YYY in the world frame, in meters
YYY.orientation Unit quaternion (q, x, y, z) of the orientation of YYY in the world frame

Wheel odometry

This observer measures the relative motion of the robot with respect to the floor, outputting ground position and velocity estimates. These quantities are used for instance in the PID balancer, which tries to stay around the same spot on the floor.

Observation key Description
position Ground position in meters
velocity Ground velocity in m/s