geometricJacobian
Geometric Jacobian for robot configuration
Description
computes the geometric Jacobian relative to the base for the specified end-effector
name and configuration for the robot model.jacobian
= geometricJacobian(robot
,configuration
,endeffectorname
)
Examples
Geometric Jacobian for Robot Configuration
Calculate the geometric Jacobian for a specific end effector and configuration of a robot.
Load a PUMA 560 robot from the Robotics System Toolbox™ loadrobot
, specified as a rigidBodyTree
object.
puma = loadrobot("puma560");
Calculate the geometric Jacobian of body "link7"
on the Puma robot for a random configuration.
geoJacob = geometricJacobian(puma,randomConfiguration(puma),"link7")
geoJacob = 6×6
-0.0000 -0.5752 -0.5752 -0.4266 -0.7683 -0.5213
0.0000 0.8180 0.8180 -0.3000 -0.3776 0.8377
1.0000 -0.0000 -0.0000 0.8533 -0.5168 0.1629
0.1696 0.0823 0.3087 -0.0407 0.0198 0
-0.5577 0.0578 0.2171 -0.0200 0.0210 0
0.0000 0.5538 0.2224 -0.0274 -0.0448 0
Input Arguments
robot
— Robot model
rigidBodyTree
object
Robot model, specified as a rigidBodyTree
object.
configuration
— Robot configuration
vector | structure
Robot configuration, specified as a vector of joint positions or a structure with joint names and positions for all the bodies in the robot model. You can generate a configuration using homeConfiguration(robot)
, randomConfiguration(robot)
, or by specifying your own joint positions in a structure. To use the vector form of configuration
, set the DataFormat
property for robot
to either "row"
or "column"
.
endeffectorname
— End-effector name
string scalar | character vector
End-effector name, specified as a string scalar or character vector. An end effector can be any body in the robot model.
Data Types: char
| string
Output Arguments
jacobian
— Geometric Jacobian
6-by-n matrix
Geometric Jacobian of the end effector with the specified configuration
,
returned as a 6-by-n matrix, where n
is the number of degrees of freedom of the robot. The Jacobian maps the
joint-space velocity to the end-effector velocity, relative to the base
coordinate frame. The end-effector velocity equals:
ω is the angular velocity, υ is the linear velocity, and is the joint-space velocity.
More About
Dynamics Properties
When working with robot dynamics, specify the information for individual bodies of your manipulator robot using these properties of the rigidBody
objects:
Mass
— Mass of the rigid body in kilograms.CenterOfMass
— Center of mass position of the rigid body, specified as a vector of the form[x y z]
. The vector describes the location of the center of mass of the rigid body, relative to the body frame, in meters. ThecenterOfMass
object function uses these rigid body property values when computing the center of mass of a robot.Inertia
— Inertia of the rigid body, specified as a vector of the form[Ixx Iyy Izz Iyz Ixz Ixy]
. The vector is relative to the body frame in kilogram square meters. The inertia tensor is a positive definite matrix of the form:The first three elements of the
Inertia
vector are the moment of inertia, which are the diagonal elements of the inertia tensor. The last three elements are the product of inertia, which are the off-diagonal elements of the inertia tensor.
For information related to the entire manipulator robot model, specify these rigidBodyTree
object properties:
Gravity
— Gravitational acceleration experienced by the robot, specified as an[x y z]
vector in m/s2. By default, there is no gravitational acceleration.DataFormat
— The input and output data format for the kinematics and dynamics functions, specified as"struct"
,"row"
, or"column"
.
Dynamics Equations
Manipulator rigid body dynamics are governed by this equation:
also written as:
where:
— is a joint-space mass matrix based on the current robot configuration. Calculate this matrix by using the
massMatrix
object function.— are the Coriolis terms, which are multiplied by to calculate the velocity product. Calculate the velocity product by using by the
velocityProduct
object function.— is the gravity torques and forces required for all joints to maintain their positions in the specified gravity
Gravity
. Calculate the gravity torque by using thegravityTorque
object function.— is the geometric Jacobian for the specified joint configuration. Calculate the geometric Jacobian by using the
geometricJacobian
object function.— is a matrix of the external forces applied to the rigid body. Generate external forces by using the
externalForce
object function.— are the joint torques and forces applied directly as a vector to each joint.
— are the joint configuration, joint velocities, and joint accelerations, respectively, as individual vectors. For revolute joints, specify values in radians, rad/s, and rad/s2, respectively. For prismatic joints, specify in meters, m/s, and m/s2.
To compute the dynamics directly, use the forwardDynamics
object function. The function calculates the joint accelerations for the specified combinations of the above inputs.
To achieve a certain set of motions, use the inverseDynamics
object function. The function calculates the joint torques required to achieve the specified configuration, velocities, accelerations, and external forces.
References
[1] Featherstone, Roy. Rigid Body Dynamics Algorithms. Springer US, 2008. DOI.org (Crossref), doi:10.1007/978-1-4899-7560-7.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
When creating the rigidBodyTree
object, use the syntax that specifies the
MaxNumBodies
as an upper bound for adding bodies to the robot model.
You must also specify the DataFormat
property as a name-value pair. For
example:
robot = rigidBodyTree("MaxNumBodies",15,"DataFormat","row")
To minimize data usage, limit the upper bound to a number close to the expected number of bodies in the model. All data formats are supported for code generation. To use the dynamics functions, the data format must be set to "row"
or "column"
.
The show
and showdetails
functions do not support code generation.
Version History
Introduced in R2016bR2024a: Static memory allocation support
geometricJacobian
now supports code generation with disabled dynamic memory allocation. For more information about disabling dynamic memory allocation, see Set Dynamic Memory Allocation Threshold (MATLAB Coder).
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