Joint Space Motion Model

Model rigid body tree motion given joint-space inputs

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Libraries:
Robotics System Toolbox / Manipulator Algorithms

Description

The Joint Space Motion Model block models the closed-loop joint-space motion of a manipulator robot, specified as a rigidBodyTree object. The motion model behavior is defined by the Motion Type parameter.

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

Examples

Follow Joint Space Trajectory in Simulink

Use a Task Space Motion Model to follow a task space trajectory in Simulink^®.

• Open Live Script

Ports

Input

qRef — Joint positions

n-element vector

n-element vector representing the desired joint positions of radians, where n is the number of nonfixed joints in the rigidBodyTree object of the Rigid body tree parameter.

Dependencies

To enable this port, set the Motion Type parameter to Computed Torque Control, PD Control, or Independent Joint Motion.

qRefDot — Joint velocities

n-element vector

n-element vector representing the desired joint velocities of radians per second, where n is the number of nonfixed joints in the rigidBodyTree object of the Rigid body tree parameter.

Dependencies

To enable this port, set the Motion Type parameter to Computed Torque Control, or Independent Joint Motion.

qRefDDot — Joint accelerations

n-element vector

n-element vector representing the desired joint velocities of radians per second squared, where n is the number of nonfixed joints in the rigidBodyTree object of the Rigid body tree parameter.

Dependencies

To enable this port, set the Motion Type parameter to Computed Torque Control, PD Control, or Independent Joint Motion.

FExt — External forces acting on system

6-by-m matrix

A 6-by-m matrix of external forces for the m bodies in the rigidBodyTree object of the Rigid body tree parameter.

Dependencies

To enable this port, set the Show external force input parameter to on.

Output

q — Joint positions

n-element vector

Joint positions output as an n-element vector in radians or meters, where n is the number of nonfixed joints in the rigidBodyTree object of the Rigid body tree parameter.

qd — Joint velocities

n-element vector

Joint velocities output as an n-element vector in radians per second or meters per second, where n is the number of nonfixed joints in the rigidBodyTree object of the Rigid body tree parameter

qdd — Joint accelerations

n-element vector

Joint accelerations output as an n-element vector in radians per second squared or meters per second squared, where n is the number of nonfixed joints in the rigidBodyTree object of the Rigid body tree parameter

Parameters

Rigid body tree — Robot model

twoJointRigidBodyTree (default) | RigidBodyTree object

Robot model, specified as a rigidBodyTree object. You can also import a robot model from an URDF (Unified Robot Description Formation) file using importrobot.

The default robot model, twoJointRigidBodyTree, is a manipulator with revolute joints and two degrees of freedom.

Motion Type — Type of motion computed by motion model

Computed Torque Control (default) | Independent Joint Motion | PD Control | Open Loop Dynamics

Type of motion, specified as a string scalar or character vector that defines the closed-loop joint-space behavior that the object models. Options are:

• Computed Torque Control — Compensates for full-body dynamics and assigns the error dynamics specified in the Natural frequency and Damping ratio parameters.

• Independent Joint Motion — Models each joint as an independent second order system using the error dynamics specified by the Natural frequency and Damping ratio parameters.

• PD Control — Uses proportional-derivative (PD) control on the joints based on the specified Proportional gain and Derivative gain parameters.

• Open Loop Dynamics — Disables inputs except for FExt if Show external force input is enabled. This is an open-loop configuration.

Specification format — Inputs to control robot

Damping Ratio / Natural Frequency (default) | Step Response

Inputs to control the robot system. Options are:

• Damping Ratio / Natural Frequency — Setting the natural frequency using the Natural frequency parameter of the system in Hz, and the damping ratio using the Damping ratio parameter.

• Step Response — Model at discrete time-steps with a fixed settling time and overshoot using the Settling time and the Overshoot parameters.

Dependencies

To enable this parameter, set the Motion Type parameter to Computed Torque Control or Independent Joint Motion.

Damping ratio — Damping ratio of system

1 (default) | numeric scalar

Damping ratio use to decay system oscillations. A value of 1 results in no damping, whereas 0 fully dampens the system.

Dependencies

To enable this parameter, set the Specification format parameter to Damping Ratio / Natural Frequency.

Natural frequency — Natural frequency of system

10 (default) | numeric scalar

Frequency of the system oscillations if unimpeded, specified in Hz.

Dependencies

To enable this parameter, set the Specification format parameter to Damping Ratio / Natural Frequency.

Settling time — Settling time of system

0.59 (default) | numeric scalar

The time taken for each joint to reach steady state, measured in seconds.

Dependencies

To enable this parameter, set the Specification format parameter to Step Response.

Overshoot — System overshoot

0.0 (default) | numeric scalar

The maximum value that the system exceeds the target position.

Dependencies

To enable this parameter, set the Specification format parameter to Step Response.

Proportional gain — Proportional gain for PD Control

100 (default) | n-by-n matrix | scalar

Proportional gain for proportional-derivative (PD) control, specified as a scalar or n-by-n matrix, where n is the number of nonfixed joints in the rigidBodyTree object of the Rigid body tree parameter.

Dependencies

To enable this parameter, set the Specification format parameter to PD Control.

Derivative gain — Derivative gain for PD control

10 (default) | n-by-n matrix | scalar

Derivative gain for proportional-derivative (PD) control, specified as a scalar or n-by-n matrix, where n is the number of nonfixed joints in the rigidBodyTree object of the Rigid body tree parameter

Dependencies

To enable this parameter, set the Specification format parameter to PD Control.

Show external force input — Display FExt port

off (default) | on

Enable this parameter to input external forces using the FExt port.

Dependencies

To enable this parameter, set the Motion Type parameter to Computed Torque Control, PD Control, or Open Loop Dynamics.

Initial joint configuration — Initial joint positions

0 (default) | n-element vector | scalar

Initial joint positions, specified as a n-element vector or scalar in radians. n is the number of nonfixed joints in the rigidBodyTree object in the Rigid body tree parameter.

Initial joint velocities — Initial joint velocities

0 (default) | n-element vector | scalar

Initial joint velocities, specified as a n-element vector or scalar in radians per second. n is the number of nonfixed joints in the rigidBodyTree object in the Rigid body tree parameter.

Simulate using — Type of simulation to run

Interpreted execution (default) | Code generation

• Interpreted execution — Simulate model using the MATLAB^® interpreter. For more information, see Interpreted Execution vs. Code Generation (Simulink).

• Code generation — Simulate model using generated C code. The first time you run a simulation, Simulink generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change.

Tunable: No

References

[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 Simulink® Coder™.

Version History

Introduced in R2019b

R2024a: Static memory allocation support

Joint Space Motion Model now supports code generation with disabled dynamic memory allocation. For more information about disabling dynamic memory allocation, see Set Dynamic Memory Allocation Threshold (MATLAB Coder).