Telekinesis Agentic Skill Library

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Forward Kinematics ​

SUMMARY

Forward Kinematics computes the robot tool pose from a given joint configuration.

This skill is used to validate robot poses, generate Cartesian outputs from joint states, and support downstream planning and control tasks.

The Skill ​

python
import numpy as np
from telekinesis.synapse.robots.manipulators import universal_robots

robot = universal_robots.UniversalRobotsUR10E()

q = np.asarray([0, -np.pi / 2 - 0.1, -np.pi / 2, 0, np.pi / 2, 0])

pose = robot.forward_kinematics(q, rot_type="rad")

The Code ​

python
import numpy as np
from telekinesis.synapse.robots.manipulators import universal_robots

# Instantiate the robot model
robot = universal_robots.UniversalRobotsUR10E()

# Define a 6-DOF joint configuration in radians
q = np.asarray([0, -np.pi / 2 - 0.1, -np.pi / 2, 0, np.pi / 2, 0])

# Compute the end-effector pose
pose = robot.forward_kinematics(q, rot_type="rad")

print(pose)

The Explanation of the Code ​

This example shows how to use the forward_kinematics skill to compute the end-effector pose from a joint configuration on a Universal Robots UR10e.

The robot model is instantiated without connecting to physical hardware — forward kinematics is a purely kinematic computation that does not require a live robot connection.

python
from telekinesis.synapse.robots.manipulators import universal_robots

robot = universal_robots.UniversalRobotsUR10E()

The joint configuration q is a NumPy array with one value per joint, ordered from base to end-effector. The UR10e has 6 joints, so q has 6 elements. Values are in radians because rot_type="rad" is specified.

python
q = np.asarray([0, -np.pi / 2 - 0.1, -np.pi / 2, 0, np.pi / 2, 0])

forward_kinematics applies the robot's kinematic chain to q and returns a pose describing the end-effector position and orientation in the robot's base frame.

python
pose = robot.forward_kinematics(q, rot_type="rad")

How to Tune the Parameters ​

q:

  • NumPy array of joint angles, one per joint (base to end-effector)
  • Length must match the robot's DOF count (6 for UR10e)
  • Values must be within the robot's joint limits; out-of-range values will produce poses outside the reachable workspace

rot_type:

  • "rad" — joint values in radians (default; recommended for programmatic use)
  • "deg" — joint values in degrees (useful when values come from a UI or human-readable config)

TIP

Use rot_type="deg" if you are reading joint values from a teach pendant or configuration file that stores angles in degrees, to avoid manual conversion errors.

Where to Use the Skill ​

Forward Kinematics is commonly used in the following scenarios:

  • Pose validation — Confirm that a planned joint configuration reaches the intended Cartesian target before issuing a motion command
  • State logging and analysis — Convert recorded joint trajectories to Cartesian paths for visualization or post-processing
  • Offline planning — Seed task-space planners or grasp pose solvers with Cartesian poses derived from known joint states
  • Simulation cross-checking — Verify that the kinematic model matches expected end-effector positions during development

When Not to Use the Skill ​

Do not use Forward Kinematics when:

  • You need joint values from a target Cartesian pose — use Inverse Kinematics instead
  • You need the live end-effector pose during execution — read it directly from the robot state rather than computing FK on every cycle
  • The joint values are unvalidated — check joint limits before passing values in, as out-of-range inputs will silently produce unreachable poses