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Model rigid body tree motion given task-space reference inputs

Since R2019b


The taskSpaceMotionModel object models the closed-loop task-space motion of a manipulator, specified as a rigid body tree object. The motion model behavior is defined by the MotionType property.

For more details about the equations of motion, see Task-Space Motion Model.



motionModel = taskSpaceMotionModel creates a motion model for a default two-joint manipulator.

motionModel = taskSpaceMotionModel("RigidBodyTree",tree) creates a motion model for the specified rigidBodyTree object.


motionModel = taskSpaceMotionControlModel(Name,Value) sets additional properties specified as name-value pairs. You can specify multiple properties in any order.


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Rigid body tree robot model, specified as a rigidBodyTree object that defines the inertial and kinematic properties of the manipulator.

This property defines the body that will be used as the end effector, and for which the task-space motion is defined. The property must correspond to a body name in the rigidBodyTree object of the RigidBodyTree property. If the rigid body tree is updated without also updating the end effector, the body with the highest index becomes the end-effector body by default.

Proportional gain for PD control, specified as a 6-by-6 matrix.

Derivative gain for proportional-derivative (PD) control, specified as a 6-by-6 matrix.

Joint damping constant, specified as an n-element vector, where n is the number of non-fixed joints in the robot model specified by the RigidBodyTree property. Joint damping units are N/(m/s) or N/(rad/s) for prismatic and revolute joints, respectively.

Type of motion, specified as "PDControl", which uses proportional-derivative (PD) control mapped to the joints via a Jacobian-Transpose controller. The control is based on the specified Kp and Kd properties.

To use computed torque control or independent joint motion, use the jointSpaceMotionModel object.

Object Functions

derivativeTime derivative of manipulator model states
updateErrorDynamicsFromStepUpdate values of NaturalFrequency and DampingRatio properties given desired step response


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This example shows how to create and use a taskSpaceMotionModel object for a manipulator robot arm in task-space.

Create the Robot

robot = loadrobot("kinovaGen3","DataFormat","column","Gravity",[0 0 -9.81]);

Set Up the Simulation

Set the time span to be 1 second with a timestep size of 0.02 seconds. Set the initial state to the home configuration of the robot, with a velocity of zero.

tspan = 0:0.02:1;
initialState = [homeConfiguration(robot);zeros(7,1)];

Define a reference state with a target position and zero velocity.

refPose = trvec2tform([0.6 -.1 0.5]);
refVel = zeros(6,1);

Create the Motion Model

Model the behavior as a system under proportional-derivative (PD) control.

motionModel = taskSpaceMotionModel("RigidBodyTree",robot,"EndEffectorName","EndEffector_Link");

Simulate the Robot

Simulate the behavior over 1 second using a stiff solver to more efficiently capture the robot dynamics. Using ode15s enables higher precision around the areas with a high rate of change.

[t,robotState] = ode15s(@(t,state)derivative(motionModel,state,refPose,refVel),tspan,initialState);

Plot the Response

Plot the robot's initial position and mark the target with an X.

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Observe the response by plotting the robot in a 5 Hz loop.

r = rateControl(5);
for i = 1:size(robotState,1)


[1] Craig, John J. Introduction to Robotics: Mechanics and Control. Upper Saddle River, NJ: Pearson Education, 2005.

[2] Spong, Mark W., Seth Hutchinson, and Mathukumalli Vidyasagar. Robot Modeling and Control. Hoboken, NJ: Wiley, 2006.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2019b

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