Model rigid body tree motion given task-space reference inputs
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
For more details about the equations of motion, see Task-Space Motion Model.
a motion model for a default two-joint manipulator.
motionModel = taskSpaceMotionModel
creates a motion model for the specified
motionModel = taskSpaceMotionModel("RigidBodyTree",tree)
sets additional properties specified as name-value pairs. You can specify multiple
properties in any order.
motionModel = taskSpaceMotionControlModel(Name,Value)
RigidBodyTree — Rigid body tree robot model
Rigid body tree robot model, specified as a
rigidBodyTree object that defines the inertial and kinematic properties of
EndEffectorName — End-effector body
'tool' (default) | string scalar | character vector
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
Kp — Proportional gain for PD Control
500*eye(6) (default) | 6-by-6 matrix
Proportional gain for PD control, specified as a 6-by-6 matrix.
Kd — Derivative gain for PD control
100*eye(6) (default) | 6-by-6 matrix
Derivative gain for proportional-derivative (PD) control, specified as a 6-by-6 matrix.
JointDamping — Joint damping constant
ones(1,n) (default) | n-element vector
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.
MotionType — Type of motion computed by the motion model
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
To use computed torque control or independent joint motion, use the
Create Task-Space Motion Model
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
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.
figure show(robot,initialState(1:7)); hold all plot3(refPose(1,4),refPose(2,4),refPose(3,4),"x","MarkerSize",20)
Observe the response by plotting the robot in a 5 Hz loop.
r = rateControl(5); for i = 1:size(robotState,1) show(robot,robotState(i,1:7)',"PreservePlot",false); waitfor(r); end
 Craig, John J. Introduction to Robotics: Mechanics and Control. Upper Saddle River, NJ: Pearson Education, 2005.
 Spong, Mark W., Seth Hutchinson, and Mathukumalli Vidyasagar. Robot Modeling and Control. Hoboken, NJ: Wiley, 2006.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Introduced in R2019b