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inverseDynamics

Required joint torques for given motion

Description

jointTorq = inverseDynamics(robot) computes joint torques required for the robot to statically hold its home configuration with no external forces applied.

jointTorq = inverseDynamics(robot,configuration) computes joint torques to hold the specified robot configuration.

example

jointTorq = inverseDynamics(robot,configuration,jointVel) computes joint torques for the specified joint configuration and velocities with zero acceleration and no external forces.

jointTorq = inverseDynamics(robot,configuration,jointVel,jointAccel) computes joint torques for the specified joint configuration, velocities, and accelerations with no external forces. To specify the home configuration, zero joint velocities, or zero accelerations, use [] for that input argument.

jointTorq = inverseDynamics(robot,configuration,jointVel,jointAccel,fext) computes joint torques for the specified joint configuration, velocities, accelerations, and external forces. Use the externalForce function to generate fext.

Examples

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Use the inverseDynamics function to calculate the required joint torques to statically hold a specific robot configuration. You can also specify the joint velocities, joint accelerations, and external forces using other syntaxes.

Load an Omron eCobra-600 from the Robotics System Toolbox™ loadrobot, specified as a rigidBodyTree object. Set the gravity property and ensure the data format is set to "row". For all dynamics calculations, the data format must be either "row" or "column".

robot = loadrobot("omronEcobra600", DataFormat="row", Gravity=[0 0 -9.81]);

Generate a random configuration for robot.

q = randomConfiguration(robot);

Compute the required joint torques for robot to statically hold that configuration.

tau = inverseDynamics(robot,q)
tau = 1×4

    0.0000    0.0000  -19.6200         0

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 Universal Robots UR5e from the Robotics System Toolbox™ loadrobot, specified as a rigidBodyTree object. Update the gravity and set the data format to "row". For all dynamics calculations, the data format must be either "row" or "column"

manipulator = loadrobot("universalUR5e", DataFormat="row", Gravity=[0 0 -9.81]);
showdetails(manipulator)
--------------------
Robot: (10 bodies)

 Idx                Body Name                         Joint Name                         Joint Type                Parent Name(Idx)   Children Name(s)
 ---                ---------                         ----------                         ----------                ----------------   ----------------
   1                     base         base_link-base_fixed_joint                              fixed                    base_link(0)   
   2        base_link_inertia        base_link-base_link_inertia                              fixed                    base_link(0)   shoulder_link(3)  
   3            shoulder_link                 shoulder_pan_joint                           revolute            base_link_inertia(2)   upper_arm_link(4)  
   4           upper_arm_link                shoulder_lift_joint                           revolute                shoulder_link(3)   forearm_link(5)  
   5             forearm_link                        elbow_joint                           revolute               upper_arm_link(4)   wrist_1_link(6)  
   6             wrist_1_link                      wrist_1_joint                           revolute                 forearm_link(5)   wrist_2_link(7)  
   7             wrist_2_link                      wrist_2_joint                           revolute                 wrist_1_link(6)   wrist_3_link(8)  
   8             wrist_3_link                      wrist_3_joint                           revolute                 wrist_2_link(7)   flange(9)  
   9                   flange                     wrist_3-flange                              fixed                 wrist_3_link(8)   tool0(10)  
  10                    tool0                       flange-tool0                              fixed                       flange(9)   
--------------------

Get the home configuration for manipulator.

q = homeConfiguration(manipulator);

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

fext1 = externalForce(manipulator,"shoulder_link",[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(manipulator,"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(manipulator,q,[],[],fext1+fext2)
tau = 1×6

   -0.0233  -52.4189  -14.4896   -0.0100    0.0100   -0.0000

Input Arguments

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

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'.

Joint velocities, specified as a vector. The number of joint velocities is equal to the velocity degrees of freedom of the robot. To use the vector form of jointVel, set the DataFormat property for the robot to either 'row' or 'column'.

Joint accelerations, returned as a vector. The dimension of the joint accelerations vector is equal to the velocity degrees of freedom of the robot. Each element corresponds to a specific joint on the robot. To use the vector form of jointAccel, set the DataFormat property for the robot to either 'row' or 'column'.

External force matrix, specified as either an n-by-6 or 6-by-n matrix, where n is the velocity 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 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 externalForce.

Output Arguments

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Joint torques, returned as a vector. Each element corresponds to a torque applied to a specific joint.

More About

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References

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

Extended Capabilities

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Version History

Introduced in R2017a

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