What Is Inverse Kinematics? How Robots Calculate Joint Positions.

What Is Inverse Kinematics?

Inverse kinematics, or IK, is the mathematical process of determining which joint positions will place a robot's tool at a desired position and orientation.

It is a fundamental part of robotic motion planning.

For example, if a robotic arm needs to place its gripper at a particular location above a conveyor, inverse kinematics helps calculate the joint angles required to reach that location.

Depending on the robot's geometry and joint limits, a target may have several possible solutions, one solution, or no feasible solution.

Key Takeaways

• Inverse kinematics calculates joint configurations for a desired tool position or pose.
• A robot may have multiple valid joint configurations for the same target.
• IK calculations must account for the robot's geometry and joint constraints.

How Does Inverse Kinematics Work?

Imagine a simple robotic arm with two rotating joints.

Its gripper needs to reach a particular point on a table.

The robot knows the lengths of its links and the location of its base.

Inverse kinematics uses those relationships to calculate the joint angles that would position the gripper at the target.

For some targets, the arm may reach the point with its elbow raised or lowered.

Both configurations may be mathematically valid.

The system must then determine which solution is appropriate.

For a more complex industrial robot, inverse kinematics may involve six or more joints and additional orientation requirements.

Inverse vs. Forward Kinematics

These calculations address opposite questions.

Forward kinematics: Given the joint positions, where is the robot's tool?

Inverse kinematics: Given the desired tool pose, which joint positions could achieve it?

For example, a robot controller may use forward kinematics to calculate the current gripper position from encoder readings.

It can then use inverse kinematics to find a suitable joint configuration for a new target.

Both are essential to understanding robotic movement.

Why Can IK Have Multiple Solutions?

Robot arms can sometimes reach the same tool position using different arrangements of their joints.

A six-axis industrial robot may approach a target with different elbow or wrist configurations.

A seven-axis arm can have additional flexibility because it has more joint variables than are minimally needed for controlling a six-dimensional tool pose.

The robot's planner can use this flexibility to consider joint limits or avoid unfavorable configurations.

However, inverse kinematics alone does not guarantee that a movement between configurations will be collision-free.

What Happens if a Target Is Unreachable?

A target may lie outside the robot's workspace.

It may also require an orientation that violates joint limits or produces an infeasible configuration.

An IK solver may then report that no solution was found.

Some methods can instead calculate an approximate solution, depending on their objectives and configuration.

Frequently Asked Questions

Does inverse kinematics require artificial intelligence?

No. It is a mathematical robotics problem that can be solved using analytical or numerical methods.

Is inverse kinematics the same as motion planning?

No. IK finds suitable joint configurations. Motion planning determines how to move between configurations while satisfying additional constraints.

The Bottom Line

Inverse kinematics connects desired tool positions with the joint movements needed to reach them. It is fundamental to robotic manipulation, although complete motion planning must also consider constraints and obstacles.