Robot kinematics
Encyclopedia
Robot kinematics is the study of the motion (kinematics
) of robot
s. In a kinematic analysis the position, velocity
and acceleration
of all the links are calculated without considering the forces that cause this motion. The relationship between motion, and the associated forces and torques is studied in robot dynamics. One of the most active areas within robot kinematics is the screw theory
.
Robot kinematics deals with aspects of redundancy, collision avoidance and singularity avoidance. While dealing with the kinematics used in the robots we deal each parts of the robot by assigning a frame of reference to it and hence a robot with many parts may have many individual frames assigned to each movable parts. For simplicity we deal with the single manipulator arm of the robot. Each frames are named systematically with numbers, for example the immovable base part of the manipulator is numbered 0, and the first link joined to the base is numbered 1, and the next link 2 and similarly till n for the last nth link.
Robot kinematics are mainly of the following two types: forward kinematics and inverse kinematics. Forward kinematics is also known as direct kinematics. In forward kinematics, the length of each link and the angle of each joint is given and we have to calculate the position of any point in the work volume of the robot. In inverse kinematics, the length of each link and position of the point in work volume is given and we have to calculate the angle of each joint.
Robot kinematics can be divided in serial manipulator kinematics, parallel manipulator kinematics, mobile robot kinematics and humanoid kinematics.
Often robot kinematics are described in reference to a simplified kinematic diagram
that applies to a large category of physical robots.
"Given the joint positions, what is the corresponding end effector's pose?"
Methods for a forward kinematic analysis:
there are 40 poses possible which can be real for some design examples. Computation is intensive but solved in closed form with the help of algebraic geometry
.
In contrast to the forward problem, the solution of the inverse problem is not always unique: the same end effector pose can be reached in several configurations, corresponding to distinct joint position vectors.
A 6R manipulator (a serial chain with six revolute joint
s) with a completely general geometric structure has sixteen different inverse kinematics solutions, found as the solutions of a sixteenth order polynomial for best result.
Kinematics
Kinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
) of robot
Robot
A robot is a mechanical or virtual intelligent agent that can perform tasks automatically or with guidance, typically by remote control. In practice a robot is usually an electro-mechanical machine that is guided by computer and electronic programming. Robots can be autonomous, semi-autonomous or...
s. In a kinematic analysis the position, velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
and acceleration
Acceleration
In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...
of all the links are calculated without considering the forces that cause this motion. The relationship between motion, and the associated forces and torques is studied in robot dynamics. One of the most active areas within robot kinematics is the screw theory
Screw theory
Screw theory refers to the algebra and calculus of pairs of vectors, such as forces and moments and angular and linear velocity, that arise in the kinematics and dynamics of rigid bodies....
.
Robot kinematics deals with aspects of redundancy, collision avoidance and singularity avoidance. While dealing with the kinematics used in the robots we deal each parts of the robot by assigning a frame of reference to it and hence a robot with many parts may have many individual frames assigned to each movable parts. For simplicity we deal with the single manipulator arm of the robot. Each frames are named systematically with numbers, for example the immovable base part of the manipulator is numbered 0, and the first link joined to the base is numbered 1, and the next link 2 and similarly till n for the last nth link.
Robot kinematics are mainly of the following two types: forward kinematics and inverse kinematics. Forward kinematics is also known as direct kinematics. In forward kinematics, the length of each link and the angle of each joint is given and we have to calculate the position of any point in the work volume of the robot. In inverse kinematics, the length of each link and position of the point in work volume is given and we have to calculate the angle of each joint.
Robot kinematics can be divided in serial manipulator kinematics, parallel manipulator kinematics, mobile robot kinematics and humanoid kinematics.
Often robot kinematics are described in reference to a simplified kinematic diagram
Kinematic diagram
|- style="text-align:center;"| || |- style="text-align:center;"| PUMA robot || and its kinematic diagramKinematic diagram or kinematic scheme is diagram of a mechanism or machine that shows its moving parts and their relationships to each other....
that applies to a large category of physical robots.
Forward position kinematics
The forward position kinematics (FPK) solves the following problem:"Given the joint positions, what is the corresponding end effector's pose?"
Serial chains
The solution is always unique: one given joint position vector always corresponds to only one single end effector pose. The FK problem is not difficult to solve, even for a completely arbitrary kinematic structure.Methods for a forward kinematic analysis:
- using straightforward geometry
- using transformation matrices
Parallel chains (Stewart Gough Manipulators)
The solution is not unique: one set of joint coordinates has more different end effector poses. In case of a Stewart platformStewart platform
A Stewart platform is a type of parallel robot that incorporates six prismatic actuators, commonly hydraulic jacks. These actuators are mounted in pairs to the mechanism's base, crossing over to three mounting points on a top plate. Devices placed on the top plate can be moved in the six degrees...
there are 40 poses possible which can be real for some design examples. Computation is intensive but solved in closed form with the help of algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
.
Forward velocity kinematics
The forward velocity kinematics (FVK) solves the following problem: "Given the vectors of joint positions and joint velocities, what is the resulting end effector twist?" The solution is always unique: one given set of joint positions and joint velocities always corresponds to only one single end effector twist.Inverse position kinematics
The inverse position kinematics (IPK) solves the following problem: "Given the actual end effector pose, what are the corresponding joint positions?"In contrast to the forward problem, the solution of the inverse problem is not always unique: the same end effector pose can be reached in several configurations, corresponding to distinct joint position vectors.
A 6R manipulator (a serial chain with six revolute joint
Revolute joint
A revolute joint is a one degree of freedom kinematic pair used in mechanisms. Revolute joints provide single-axis rotation function used in many places such as door hinges, folding mechanisms, and other uni-axial rotation devices. -See also:* Cylindrical joint* Kinematics* Degrees of freedom *...
s) with a completely general geometric structure has sixteen different inverse kinematics solutions, found as the solutions of a sixteenth order polynomial for best result.
Inverse velocity kinematics
Assuming that the inverse position kinematics problem has been solved for the current end effector pose, the inverse velocity kinematics (IVK) then solves the following problem: "Given the end effector twist, what is the corresponding vector of joint velocities?"Forward force kinematics
The forward force kinematics (FFK) solves the following problem: "Given the vectors of joint force/torques, what is the resulting static wrench that the end effector exerts on the environment?" (If the end effector is rigidly fixed to a rigid environment.)Inverse force kinematics
Assuming that the inverse position kinematics problem has been solved for the current end effector pose, the inverse force kinematics (IFK) then solves the following problem: "Given the wrench that acts on the end effector, what is the corresponding vector of joint forces/torques?"See also
- Robotics conventionsRobotics conventionsThere are many conventions used in the robotics research field. This article summarises these conventions.-Line representations:Lines are very important in robotics because:...
- Degrees of freedom (engineering)Degrees of freedom (engineering)In mechanics, degrees of freedom are the set of independent displacements and/or rotations that specify completely the displaced or deformed position and orientation of the body or system...
- Humanoid robotHumanoid robotA humanoid robot or an anthropomorphic robot is a robot with its overall appearance, based on that of the human body, allowing interaction with made-for-human tools or environments. In general humanoid robots have a torso with a head, two arms and two legs, although some forms of humanoid robots...
- Inverse kinematicsInverse kinematicsInverse kinematics is a subdomain of kinematics, which is of particular interest in robotics and computer animation. In contrast to forward kinematics, which calculates the position of a body after a series of motions, inverse kinematics calculates the motions necessary to achieve a desired...
- Parallel manipulatorParallel manipulatorParallel robots and parallel manipulators are articulated robots that use similar mechanisms for the movement of either the robot on its base, or one or more manipulator arms...
- Serial manipulatorSerial manipulatorSerial manipulators are by far the most common industrial robots. Often they have an anthropomorphic mechanical arm structure, i.e. a serial chain of rigid links, connected by joints, forming a "shoulder", an "elbow", and a "wrist"....
- KinematicsKinematicsKinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces that cause the motion....
- Mobile robotMobile robotA mobile robot is an automatic machine that is capable of movement in a given environment.-Overview:Mobile robots have the capability to move around in their environment and are not fixed to one physical location...
- Robot locomotionRobot locomotionRobot locomotion is the collective name for the various methods that robots use to transport themselves from place to place. Although wheeled robots are typically quite energy efficient and simple to control, other forms of locomotion may be more appropriate for a number of reasons...