Examples

The following examples include tasks and limits:

• Arm: UR5
• Flying dual-arm UR3
• Humanoid: Draco 3
• Mobile: Stretch
• Wheeled biped: Upkie

Check out the barriers sub-directory for more examples including control barrier functions.

Arm: UR5

A UR5 arm tracking a moving target:

arm_ur5.mp4

Task	Cost
End-effector	1
Posture	$10^{-3}$

Flying dual-arm UR3

A pair of UR3 arms on a mobile body tracking moving targets:

flying_dual_arm_ur3.mp4

Task	Cost
Mobile base	1
Left end-effector	1
Right end-effector	1
Posture	$10^{-3}$

Humanoid: Draco 3

A Draco 3 humanoid moving its right hand laterally while standing. This model includes a closed kinematic chain, implemented in the example with a JointCouplingTask:

humanoid_draco3.mp4

Task	Cost
Left foot	(1, 1)
Left knee coupling	100
Posture	$10^{-1}$
Right foot	(1, 1)
Right knee coupling	100
Right wrist	(4, 4)
Torso	(1, 0)

Mobile: Stretch

Move a Stretch RE1 with a fixed fingertip target around the origin:

mobile_stretch.mp4

Task	Position cost	Orientation cost
Mobile base	$0.1$	1
Fingertip	1	$10^{-4}$

Wheeled biped: Upkie

An Upkie wheeled biped rolling without slipping:

upkie_rolling_without_slipping.mp4

Task	Position cost	Orientation cost
Floating base	$1$	$1$
Left wheel rolling	$10$	-
Right wheel rolling	$10$	-
Left wheel position	$1$	$0$
Right wheel position	$1$	$0$