Universal Robots (UR)

Cartesian trajectories for Universal Robots (CB3 / e-Series).

Vendor specifics
Teach pendant UR+ / URcaps
Programming / simulation software  
Software  
User interface PolyScope
Programming language UR Script (similar to Python)
Relevant hardware CB3 (UR3, UR5, UR10), e-Series (UR3e, UR5e, UR10e, UR16e)
Further reading

Trajectory composition

Programming is done with move instructions (movement types) that move the robot to specified targets.

  • Linear Cartesian motions

    MoveL

    • tool moves in a straight line. To keep moving linearly between waypoints each joint performs a more complicated motion.

    • parameters (pose, a=1.2, v=0.25, t=0, r=0):

      • pose: target pose
      • a: tool acceleration in m/s2
      • v: tool speed in m/s
      • t: time in s
      • r: blend radius in m
  • Circular motions

    MoveC

    • tool moves on a circular arc segment to from current pose to target pose. Path point pose_via defines the arch’s shape

    • parameters (pose_via, pose_to, a=1.2, v=0.25, r=0, mode=0):

      • pose_via: path point
      • pose_to: target pose
      • a: tool acceleration in m/s2
      • v: tool speed in m/s
      • r: blend radius (of target pose) in m
      • mode: (0: Unconstrained / 1: Fixed mode)
  • Joint space interpolation

    MoveJ

    • tool moves in a curved path interpolated in joint space. Each joint reaches location simultaneously. Preferred motion if a high TCP speed is desired.

    • parameters (q, a=1.4, v=1.05, t=0, r=0):

      • q: joint positions
      • a: joint acceleration of leading axis in rad/s2
      • v: joint speed of leading axisin rad/s
      • t: time in s
      • r: blend radius in m
  • Additional

    MoveP

    • tool moves linearly with constant speed with circular blends. Command can be extendend by a Circle move consisting of two waypoints.

    • parameters (pose, a=1.2, v=0.25, r=0):

      • pose: target pose
      • a: tool acceleration in m/s2
      • v: tool speed in m/s
      • r: blend radius in m

Waypoint representation

Individually taught points have the following representation:

X
Y
Z
Rx (roll)
Ry (pitch)
Rz (yaw)

Trajectory parameterization and execution

Specification of velocity

The robot’s speed is defined in form of an argument by the move command.

  • For MoveJ in deg/s: maximum joint speed
  • For MoveL in mm/s: desired tool speed

Global specification of velocity are done separately for joint and TCP speed. The limits, which depend on the robot version, are stated in the table below. The actual speed limits also depend on the robot configuration.

Function Description Limit
Joint speed Max. angular joint speed 180 ◦/s [1]
TCP speed Max. speed of the robot TCP 5000 mm/s
[1]Wrist joints of UR3 have max. angular speed of 360°/s and shoulder joints of UR10 have max angular speed of 120 °/s.

Specification of acceleration

The acceleration of the robot’s motions is defined in form of an argument by the move command. Depending on the chosen movement type either the joints’ or TCP’s acceleration is definable.

  • For MoveJ in deg/s2: joint acceleration
  • For MoveL in mm/s2: tool acceleration

Blending

  • Circular blending is part of MoveP. The blend radius’ size is by default a shared value between all the waypoints. A smaller blend radius leads to sharper and a biger radius to smoother paths.
  • Blending can also be done by defining a blend radius for waypoints. In this case the trajectory blends around the waypoint, allowing the robot arm not to stop at the point.

Parallel IO operations

Can be triggered at certain points in the robot’s path

Online (real-time) trajectory modifications

  • path offset

    • a robot motion can be superimposed with a Cartesian offset

    • Cartesian path offset is specified by the script function path_offset_set(offset, type)

      • offset: Pose specifying the translational and rotational offset
      • type: Specifies which coordinates to apply (BASE,`TCP`, MOTION, BASE_INVERTED)

    • possible applications:

      • imposing a weaving motion onto a welding task
      • compensating for moving the robot base while following a trajectory

  • dynamic force control (see dynamic_force_control)

    • provides control of the force parameters dynamically at runtime
    • function to set robot to force mode: force_mode(task_frame, selection_vector, wrench, type, limits)

  • conveyor tracking (see conveyor_tracking)

    • adjusts a robot’s trajectory to a moving conveyor
    • available for linear and circular conveyors
    • CB3 and e-Series controller can decode signals at up to 40kHz