Hardware & control
Inverse kinematics
Inverse kinematics (IK) finds robot configurations that satisfy a desired position, orientation or other geometric constraints. It reverses the question asked by forward kinematics: instead of computing where a hand or foot is from the joint values, it searches for joint values that place it at a target. A target can have multiple solutions or no feasible solution.
Also known as: IK, robot inverse kinematics
Updated
From a target pose to a robot configuration
Forward kinematics computes a link's pose from the robot model and joint configuration. Inverse kinematics asks which configurations could achieve a target pose. For example, a humanoid reaching towards a handle needs joint values that place its hand at the handle with a suitable orientation.
The answer is not necessarily unique. Different elbow positions may place the hand at the same target, while a target outside the robot's reach has no solution. Modern Robotics explains numerical IK as a search for joint values whose forward-kinematics output matches the requested configuration.
Numerical solutions depend on the starting configuration
A common numerical method starts from an initial guess, measures the remaining pose error and uses a Jacobian to update the joint values. It repeats until the error is within a chosen tolerance or the solver stops. A Jacobian pseudoinverse can provide a local least-squares update when an ordinary matrix inverse is unavailable.
As Modern Robotics shows, the initial guess affects convergence and which solution is found. A failed local solve is therefore not, by itself, proof that the target is unreachable. When targets change gradually, the previous solution can be a useful starting guess for the next one.
Humanoid IK needs more than a hand target
A hand pose alone does not specify an acceptable whole-body posture. Joint limits, foot placement, self-collision and the surrounding geometry may also matter. These constraints must be included explicitly or checked separately; a basic pose solver does not enforce them automatically.
Tedrake's Robotic Manipulation notes describe IK as optimisation with geometric constraints and posture preferences. The humanoid examples add joint-centering objectives and static stability constraints alongside end-effector targets. This can help select a useful posture from several possible solutions.
A feasible posture is not a complete motion plan. It does not establish that the route to that posture is collision-free, or that the robot can execute the motion within its torque and contact limits. Trajectory planning and whole-body control address additional parts of that problem.
Keep IK-generated targets distinct from measurements
For motion retargeting, IK can translate human hand or foot targets into configurations of a robot with different proportions. The resulting joint values depend on the robot model, target frames, constraints, solver tolerances and starting guess.
When storing these results as training data, record those choices and distinguish requested poses, IK solutions and measured robot states. Include solver success and residual errors where available. A computed configuration is a proposed geometric solution, not evidence that the physical robot reached it safely.
Sources
Related terms
Hardware & control
Robot kinematics
Robot kinematics describes the geometric relationship between a robot’s joint configuration and the position, orientation and velocity of its links or end-effector, without modelling the forces that cause the motion. Forward kinematics computes pose from joint values; inverse kinematics searches for joint values that achieve a requested pose.
Hardware & control
End effector
An end effector is a task-specific device attached to a robot manipulator’s mechanical interface so the robot can act on its environment, such as a gripper, hand or welding tool. It is distinct from the wrist or mounting flange, and from the tool centre point, which is only a coordinate frame used to plan the device’s motion.
Hardware & control
Degree of freedom
A degree of freedom (DoF) is one independent parameter needed to specify a robot’s configuration; equivalently, a robot’s DoF is the dimension of its configuration space. It describes possible motion, not the number of motors. Joint constraints, closed kinematic chains and environmental contacts can make joint count, actuator count and controllable motion differ.
Simulation & transfer
Motion retargeting
Motion retargeting is the adaptation of a recorded or generated motion from one body to another with different proportions, joints or limits. For humanoid robots, it maps source poses or trajectories into robot configurations while preserving task-relevant relationships such as contacts and end-effector paths and satisfying kinematic, balance, collision and actuator constraints.
Hardware & control
Whole-body control
Whole-body control coordinates a humanoid’s full multibody state, actuated joints and environmental contacts to pursue several motion or force objectives while respecting constraints such as balance, joint limits and friction. It is a family of hierarchical or optimisation-based methods, not one algorithm; implementations may output joint positions, accelerations or torques.