Main Content

externalForce

Compose external force matrix relative to base

Description

example

fext = externalForce(robot,bodyname,wrench) composes the external force matrix, which you can use as inputs to inverseDynamics and forwardDynamics to apply an external force, wrench, to the body specified by bodyname. The wrench input is assumed to be in the base frame.

example

fext = externalForce(robot,bodyname,wrench,configuration) composes the external force matrix assuming that wrench is in the bodyname frame for the specified configuration. The force matrix fext is given in the base frame.

Examples

collapse all

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 RigidBodyTree object.

load exampleRobots.mat lbr

Set the data format to 'row'. For all dynamics calculations, the data format must be either 'row' or 'column'.

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 lbr robot.

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, q.

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 'tool0' when 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);

Use the externalForce function to generate force matrices to apply to a rigid body tree model. The force matrix is an m-by-6 vector that has a row for each joint on the robot to apply a six-element wrench. Use the externalForce function and specify the end effector to properly assign the wrench to the correct row of the matrix. You can add multiple force matrices together to apply multiple forces to one robot.

To calculate the joint torques that counter these external forces, use the inverseDynamics function.

Load a predefined KUKA LBR robot model, which is specified as a RigidBodyTree object.

load exampleRobots.mat lbr

Set the data format to 'row'. For all dynamics calculations, the data format must be either 'row' or 'column'.

lbr.DataFormat = 'row';

Set the Gravity property to give a specific gravitational acceleration.

lbr.Gravity = [0 0 -9.81];

Get the home configuration for lbr.

q = homeConfiguration(lbr);

Set external force on link1. The input wrench vector is expressed in the base frame.

fext1 = externalForce(lbr,'link_1',[0 0 0.0 0.1 0 0]);

Set external force on the end effector, tool0. The input wrench vector is expressed in the tool0 frame.

fext2 = externalForce(lbr,'tool0',[0 0 0.0 0.1 0 0],q);

Compute the joint torques required to balance the external forces. To combine the forces, add the force matrices together. Joint velocities and accelerations are assumed to be zero (input as []).

tau = inverseDynamics(lbr,q,[],[],fext1+fext2);

Input Arguments

collapse all

Robot model, specified as a rigidBodyTree object. To use the externalForce function, set the DataFormat property to either "row" or "column".

Name of body to which the external force is applied, specified as a string scalar or character vector. This body name must match a body on the robot object.

Data Types: char | string

Torques and forces applied to the body, specified as a [Tx Ty Tz Fx Fy Fz] vector. The first three elements of the wrench correspond to the moments around xyz-axes. The last three elements are linear forces along the same axes. Unless you specify the robot configuration, the wrench is assumed to be relative to the base frame.

Robot configuration, specified as a vector with positions for all nonfixed joints in the robot model. You can generate a configuration using homeConfiguration(robot), 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 "row" or "column" .

Output Arguments

collapse all

External force matrix, returned as either an n-by-6 or 6-by-n matrix, where n is the velocity number (degrees of freedom) of the robot. The shape depends on the DataFormat property of robot. The "row" data format uses an n-by-6 matrix. The "column" data format uses a 6-by-n .

The composed 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. Use the external force matrix to specify external forces to dynamics functions inverseDynamics and forwardDynamics.

References

[1] Featherstone, Roy. Rigid Body Dynamics Algorithms. Springer US, 2008. DOI.org (Crossref), doi:10.1007/978-1-4899-7560-7.

Extended Capabilities

Introduced in R2017a