manipulabilityIndex

Calculate manipulability index of robot at specified joint configuration

Since R2024b

Syntax

manipIndex = manipulabilityIndex(robot,configuration)

manipIndex = manipulabilityIndex(robot,configuration,eeName)

manipIndex = manipulabilityIndex(___,Name=Value)

Description

manipIndex = manipulabilityIndex(robot,configuration) calculates the manipulability index of the specified robot at the specified joint configuration. This syntax uses last rigid body in the robot model as the end effector.

manipIndex = manipulabilityIndex(robot,configuration,eeName) specifies the rigid body to use as the end effector for manipulability calculations.

manipIndex = manipulabilityIndex(___,Name=Value) specifies options using one or more name-value arguments in addition to any combination of input arguments from previous syntaxes. For example, IndexType="asada" uses the Asada approach for manipulability calculations.

Examples

Find Inverse Kinematics Solutions with High-Manipulability

Load the robot model for the ABB IRB 120 manipulator, and use an analytical inverse kinematics solver to generate an IK solver for the robot.

robot = loadrobot("abbIrb120",DataFormat="row");
eeName = "tool0";
aik = analyticalInverseKinematics(robot);
generateIKFunction(aik,"robotIK");

Use the IK solver to find joint configurations in which the end effector of the manipulator reaches the xyz-position (0.2, 0.5, 0.5). The solver finds multiple configurations that satisfy this condition.

eePosition = [0.2 0.5 0.5];
eePose = trvec2tform(eePosition);
ikConfig = robotIK(eePose)

ikConfig = 8×6

   -1.8214   -1.4863   -0.7791    1.7650    1.4114    0.6790
   -1.8214   -0.8824   -1.9070    1.6589    1.3359    1.2082
    1.3202    0.8824   -0.7791   -1.5972    1.3215    1.6774
    1.3202    1.4863   -1.9070   -1.4666    1.3424    1.1382
   -1.8214   -1.4863   -0.7791   -1.3766   -1.4114    3.8206
   -1.8214   -0.8824   -1.9070   -1.4827   -1.3359    4.3498
    1.3202    0.8824   -0.7791    1.5444   -1.3215   -1.4641
    1.3202    1.4863   -1.9070    1.6750   -1.3424    4.2798

Calculate the manipulability index for each of the joint configuration solutions.

mValues = manipulabilityIndex(robot,ikConfig,eeName)

mValues = 8×1

    0.0228
    0.0225
    0.0224
    0.0225
    0.0228
    0.0225
    0.0224
    0.0225

Find the highest manipulability index, and get the corresponding joint configuration.

[~,argMax] = max(mValues);
highManipConfig = ikConfig(argMax,:)

highManipConfig = 1×6

   -1.8214   -1.4863   -0.7791   -1.3766   -1.4114    3.8206

Input Arguments

robot — Robot model

rigidBodyTree object

Robot model, specified as a rigidBodyTree object.

configuration — Robot configuration

N-element vector | M-by-N matrix

Robot configuration, specified as an N-element vector, or an M-by-N matrix, where each row is a configuration. N is the number of nonfixed joints in the robot model and M is the number of joint configurations. You can generate a configuration using homeConfiguration(robot), randomConfiguration(robot), or by specifying your own joint positions as a vector.

eeName — Name of end effector

string scalar | character vector

Name of the end effector, specified as a string scalar or character vector. A body with this name must be on the robot model specified by robot.

By default, the last body of robot is the end effector.

Data Types: char | string

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: manipulabilityIndex(robot,config,IndexType="yoshikawa",MotionComponent="linear") specifies to use the Yoshikawa approach for manipulability calculations, and consider only linear motion.

IndexType — Manipulability index type to calculate

"yoshikawa" (default) | "inverse-condition" | "asada"

Manipulability index type to calculate, specified as one of these options:

• "yoshikawa" — Use the volume of the velocity ellipsoid at each configuration as the measure of manipulability [1]. High Yoshikawa manipulability index values indicate that the robot has good dexterity and can move in multiple directions from the corresponding configurations. Low manipulability index values indicate that corresponding configurations are less dexterous and more susceptible to singularities.

• "asada" — Use the geometric representation of the manipulator as the measure of manipulability [2]. A high Asada manipulability index indicates that a configuration is efficient for transmitting forces and velocities from the actuators to the end effector. Low Asada index values imply that the configuration is less efficient at force and velocity transmission, potentially hindering the ability of the robot to perform tasks requiring precise force application or rapid movements.

• "inverse-condition" — Use the inverse of condition number of the robot's Jacobian matrix as the measure of manipulability [3]. High inverse condition index values indicate a low condition number, suggesting that the configuration is stable and capable of moving well in many directions, indicating uniform manipulability. Low inverse condition index values signify a high condition number, meaning the configuration is poorly conditioned, leading to sensitivity to input variations and potentially unstable or unpredictable movement, especially near singularities.

Example: manipulabilityIndex(robot,config,IndexType="asada")

MotionComponent — Type of motion to consider for manipulability index calculation

"combined" (default) | "angular" | "linear" | six-element vector of logical values

Type of motion to consider for manipulability index calculation, specified as one of these options:

• "combined" — Consider both linear and angular motions on the xyz-axes.

• "linear" — Consider only linear motion along the xyz-axes.

• "angular" — Consider only angular motion about the xyz-axes.

• six-element vector of logical values — Consider motion components specified by a logical vector in the form [rx ry rz x y z]. Each element in the vector corresponds to a motion component along or about the xyz-axes, where a value of 0 (false) ignores the corresponding motion component, and 1 (true) considers the corresponding motion component for manipulability index calculation. For example, [0 0 1 1 1 0] specifies that the function only considers the z angular motion, along with the x and y linear motions, for the manipulability index calculation.

Example: manipulabilityIndex(robot,config,MotionComponent="angular")

Example: manipulabilityIndex(robot,config,MotionComponent=[1 1 0 0 0 1])

Output Arguments

manipIndex — Manipulability index

numeric scalar | M-element vector

Manipulability index, returned as a numeric scalar or M-element vector. M is the number of specified joint configurations.

References

[1] Yoshikawa, T. "Analysis and Control of Robot Manipulators with Redundancy." In Robotics Research: The First International Symposium, 735–47. Cambridge: MIT Press, 1984.

[2] Asada, Haruhiko. “A Geometrical Representation of Manipulator Dynamics and Its Application to Arm Design.” Journal of Dynamic Systems, Measurement, and Control 105, no. 3, (September 1, 1983): 131–42. https://doi.org/10.1115/1.3140644.

[3] Togai, Masaki. “An Application of the Singular Value Decomposition to Manipulability and Sensitivity of Industrial Robots.” SIAM Journal on Algebraic Discrete Methods 7, no. 2, (April 1986): 315–20. https://doi.org/10.1137/0607034.

Extended Capabilities

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

Version History

Introduced in R2024b