Joint accelerations given joint torques and states
Compute Forward Dynamics Due to External Forces on Rigid Body Tree Model
Calculate the resultant joint accelerations for a given robot configuration with applied external forces and forces due to gravity. A wrench is applied to a specific body with the gravity being specified for the whole robot.
Load a predefined KUKA LBR robot model, which is specified as a
load exampleRobots.mat lbr
Set the data format to
'row'. For all dynamics calculations, the data format must be either
lbr.DataFormat = 'row';
Set the gravity. By default, gravity is assumed to be zero.
lbr.Gravity = [0 0 -9.81];
Get the home configuration for the
q = homeConfiguration(lbr);
Specify the wrench vector that represents the external forces experienced by the robot. Use the
externalForce function to generate the external force matrix. Specify the robot model, the end effector that experiences the wrench, the wrench vector, and the current robot configuration.
wrench is given relative to the
'tool0' body frame, which requires you to specify the robot configuration,
wrench = [0 0 0.5 0 0 0.3]; fext = externalForce(lbr,'tool0',wrench,q);
Compute the resultant joint accelerations due to gravity, with the external force applied to the end-effector
lbr is at its home configuration. The joint velocities and joint torques are assumed to be zero (input as an empty vector
qddot = forwardDynamics(lbr,q,,,fext);
robot — Robot model
Robot model, specified as a
rigidBodyTree object. To
forwardDynamics function, set the
DataFormat property to either
configuration — Robot configuration
Robot configuration, specified as a vector with positions for all nonfixed joints in the robot
model. You can generate a configuration using
randomConfiguration(robot), or by specifying your own
joint positions. To use the vector form of
configuration, set the
DataFormat property for the
robot to either
jointVel — Joint velocities
Joint velocities, specified as a vector. The number of joint velocities is equal to the
degrees of freedom of the robot. To use the vector form of
jointVel, set the
property for the
robot to either
jointTorq — Joint torques
Joint torques, specified as a vector. Each element corresponds to a torque applied to a
specific joint. To use the vector form of
DataFormat property for the
robot to either
fext — External force matrix
n-by-6 matrix | 6-by-n matrix
External force matrix, specified as either an n-by-6 or
6-by-n matrix, where n is the
number of bodies of the robot. The shape depends on the
DataFormat property of
'row' data format uses an n-by-6
'column' data format uses a
The matrix lists only values other than zero at the locations relevant to the body specified. You can add force matrices together to specify multiple forces on multiple bodies.
To create the matrix for a specified force or torque, see
When working with robot dynamics, specify the information for individual bodies of your manipulator robot using these properties of the
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. The
centerOfMassobject 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
Inertiavector 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:
Manipulator rigid body dynamics are governed by this equation:
also written as:
— is a joint-space mass matrix based on the current robot configuration. Calculate this matrix by using the
— is the coriolis terms, which are multiplied by to calculate the velocity product. Calculate the velocity product by using by the
— is the geometric Jacobian for the specified joint configuration. Calculate the geometric Jacobian by using the
— is a matrix of the external forces applied to the rigid body. Generate external forces by using the
— 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.
 Featherstone, Roy. Rigid Body Dynamics Algorithms. Springer US, 2008. DOI.org (Crossref), doi:10.1007/978-1-4899-7560-7.
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
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