AiVibeInverse Kinematics
Inverse kinematics calculates the joint values a robot needs to place its tool at a desired position and orientation. A target may have several solutions, exactly one or none, and is solved analytically or by numerical iteration.
For many six-axis arms with a spherical wrist, closed-form solutions exist that separate the wrist position from its orientation. Other robots use numerical methods that iteratively adjust joint values using the Jacobian matrix until the tool pose matches the target. A target outside the reach, or one that violates joint limits, has no solution, while a reachable target usually has several arm configurations, such as elbow up or elbow down.
Every Cartesian move, every target programmed in a user frame and every path generated from CAD or vision relies on inverse kinematics. Controllers choose configurations consistently, and programmers or offline tools specify the configuration to prevent unexpected flips between solutions.
Near singularities, numerical solutions become ill-conditioned and joint speeds can rise sharply, so paths are planned to avoid them. Redundant robots have infinitely many solutions, which allows secondary objectives such as avoiding obstacles or staying away from joint limits. Learned policies that output tool targets also depend on an inverse kinematics solver to produce joint commands.
Key points
- Maps a desired tool pose to the required joint values
- A target can have multiple solutions, a single solution or none
- Solved in closed form for many six-axis arms or numerically via the Jacobian
- Redundant robots have infinitely many solutions
Where AiVibe comes in
AiVibe designs and manufactures the AiAmbA AI Factory, whose edge devices and AI agents let people talk to robot controllers in plain language. Robotics perception is an AiAmbA use case, and robot safety functions follow ISO 10218 and never depend on the AI layer.