forward kinematics
In plain wordsThe math that works out where a robot's hand or tool ends up, given the angles of all its joints, by chaining together the movement each joint adds.
The calculation that turns known joint variables — angles for revolute joints, extensions for prismatic ones — into the pose (position and orientation) of a robot's end effectorend effector, n.: The tool at the end of a robot arm that actually touches the world, such as a gripper, suction cup, welding torch, paint sprayer or robotic hand. or of any other link. For a serial chain it is a composition of rigid-body transformations — each joint and link contributes a 4×4 homogeneous transformation matrix, and multiplying them from base to tip gives the end-effector frame. Link geometry is conventionally encoded either with the four Denavit–Hartenberg parameters per joint or with the product-of-exponentials formula from screw theory. For serial arms the computation is straightforward and has a unique answer, unlike inverse kinematicsinverse kinematics, n.: Working backward from where you want a robot's hand to be to the joint angles that will put it there, like working out how to bend your arm to touch your nose.; for parallel mechanisms such as delta robots the roles reverse and forward kinematics becomes the hard direction. Differentiating it with respect to the joint variables gives the manipulator JacobianJacobian, n.: A table listing how each output of a process responds to a small change in each input. It describes how a transformation locally stretches, squeezes and turns space., which maps joint velocities to end-effector velocities and is central to control, singularity analysis and inverse kinematics. The same computation poses animated skeletons in computer graphics.
Run forward kinematics on the logged joint angles to see where the gripper actually was.
Origin
Matrix methods for linkage kinematics were introduced by Jacques Denavit and Richard Hartenberg in 1955 in the Journal of Applied Mechanics; the forward/inverse terminology for manipulators was standard in robotics textbooks by the 1980s, and Roger Brockett's product-of-exponentials formulation appeared in 1984.
Related
- inverse kinematicsinverse kinematics, n.: Working backward from where you want a robot's hand to be to the joint angles that will put it there, like working out how to bend your arm to touch your nose.
- degrees of freedomdegrees of freedom, n.: The number of independent ways something can move. A robot arm with six motorized joints has six; a free-floating object can slide three ways and turn three ways.
- end effectorend effector, n.: The tool at the end of a robot arm that actually touches the world, such as a gripper, suction cup, welding torch, paint sprayer or robotic hand.
- JacobianJacobian, n.: A table listing how each output of a process responds to a small change in each input. It describes how a transformation locally stretches, squeezes and turns space.
- configuration spaceconfiguration space, n.: An imaginary space in which a robot's whole body position is a single point, which turns 'move this many-jointed robot without hitting things' into 'find a path for a dot'.
- motion planningmotion planning, n.: Working out how a robot should move from where it is to where it needs to be, without hitting anything and within the limits of what its body can do.
- inverse kinematicsinverse kinematics, n.: Working backward from where you want a robot's hand to be to the joint angles that will put it there, like working out how to bend your arm to touch your nose.
Sources
- Denavit, J. & Hartenberg, R. S. (1955). A kinematic notation for lower-pair mechanisms based on matrices. Journal of Applied Mechanics 22, 215–221.
- Lynch, K. M. & Park, F. C. (2017). Modern Robotics: Mechanics, Planning, and Control. Cambridge University Press.
Mentioned in
roboticsrobotics, n.: The science and engineering of building robots and making them work: designing their bodies, sensors and motors, and writing the software that lets them see, plan and move safely., degrees of freedomdegrees of freedom, n.: The number of independent ways something can move. A robot arm with six motorized joints has six; a free-floating object can slide three ways and turn three ways., end effectorend effector, n.: The tool at the end of a robot arm that actually touches the world, such as a gripper, suction cup, welding torch, paint sprayer or robotic hand., inverse kinematicsinverse kinematics, n.: Working backward from where you want a robot's hand to be to the joint angles that will put it there, like working out how to bend your arm to touch your nose., configuration spaceconfiguration space, n.: An imaginary space in which a robot's whole body position is a single point, which turns 'move this many-jointed robot without hitting things' into 'find a path for a dot'.