Arm Type Robots - ETS¶

Code author: Jesse Haviland

ETS¶

Created on Tue Apr 24 15:48:52 2020 @author: Jesse Haviland

class ropy.robot.ETS.ETS(elinks, name='noname', base_link=None, ee_link=None, manufacturer='', base=None, tool=None, gravity=array([0.0, 0.0, 9.81]))[source]¶

Bases: object

The Elementary Transform Sequence (ETS). A superclass which represents the kinematics of a serial-link manipulator

Parameters

et_list (ET list) – List of elementary transforms which represent the robot kinematics
name (str, optional) – Name of the robot
manufacturer (str, optional) – Manufacturer of the robot
base (SE3, optional) – Location of the base is the world frame
tool (SE3, optional) – Offset of the flange of the robot to the end-effector
gravity – The gravity vector

References

Kinematic Derivatives using the Elementary Transform Sequence, J. Haviland and P. Corke

bfs_link(func)[source]¶

dfs_path(l1, l2)[source]¶

to_dict()[source]¶

fk_dict()[source]¶

static urdf_to_ets_args(file_path)[source]¶

property qlim¶

property ets¶

property n¶

property M¶

property q_idx¶

property name¶

property manuf¶

property gravity¶

property q¶

property qd¶

property qdd¶

property control_type¶

property base¶

property tool¶

property base_link¶

property ee_link¶

fkine(q=None)[source]¶

Evaluates the forward kinematics of a robot based on its ETS and joint angles q.

T = fkine(q) evaluates forward kinematics for the robot at joint configuration q.

T = fkine() as above except uses the stored q value of the robot object.

Trajectory operation: Calculates fkine for each point on a trajectory of joints q where q is (nxm) and the returning SE3 in (m)

Parameters

q (float ndarray(n)) – The joint angles/configuration of the robot (Optional, if not supplied will use the stored q values).

Returns

The transformation matrix representing the pose of the end-effector

Return type

SE3

Notes

The robot’s base or tool transform, if present, are incorporated into the result.

References

Kinematic Derivatives using the Elementary Transform Sequence, J. Haviland and P. Corke

allfkine(q=None)[source]¶

Tall = allfkine(q) evaluates fkine for each joint within a robot and returns a trajecotry of poses.

Tall = allfkine() as above except uses the stored q value of the robot object.

Parameters

q (float ndarray(n)) – The joint angles/configuration of the robot (Optional, if not supplied will use the stored q values).

Return T

Homogeneous transformation trajectory

Rtype T

SE3 list

Notes

The robot’s base transform, if present, are incorporated into the result.

References

Kinematic Derivatives using the Elementary Transform Sequence, J. Haviland and P. Corke

jacob0(q=None)[source]¶

J0 = jacob0(q) is the manipulator Jacobian matrix which maps joint velocity to end-effector spatial velocity. v = J0*qd in the base frame.

J0 = jacob0() as above except uses the stored q value of the robot object.

Parameters

q (float ndarray(n)) – The joint angles/configuration of the robot (Optional, if not supplied will use the stored q values).

Return J

The manipulator Jacobian in ee frame

Return type

float ndarray(6,n)

References

Kinematic Derivatives using the Elementary Transform Sequence, J. Haviland and P. Corke

jacobe(q=None)[source]¶

Je = jacobe(q) is the manipulator Jacobian matrix which maps joint velocity to end-effector spatial velocity. v = Je*qd in the end-effector frame.

Je = jacobe() as above except uses the stored q value of the robot object.

Parameters: q (float ndarray(n)) – The joint angles/configuration of the robot (Optional, if not supplied will use the stored q values).
Return J: The manipulator Jacobian in ee frame
Return type: float ndarray(6,n)

hessian0(q=None, J0=None)[source]¶

The manipulator Hessian tensor maps joint acceleration to end-effector spatial acceleration, expressed in the world-coordinate frame. This function calulcates this based on the ETS of the robot. One of J0 or q is required. Supply J0 if already calculated to save computation time

Parameters

q (float ndarray(n)) – The joint angles/configuration of the robot (Optional, if not supplied will use the stored q values).
J0 (float ndarray(6,n)) – The manipulator Jacobian in the 0 frame

Returns

The manipulator Hessian in 0 frame

Return type

float ndarray(6,n,n)

References

Kinematic Derivatives using the Elementary Transform Sequence, J. Haviland and P. Corke

manipulability(q=None, J=None)[source]¶

Calculates the manipulability index (scalar) robot at the joint configuration q. It indicates dexterity, that is, how isotropic the robot’s motion is with respect to the 6 degrees of Cartesian motion. The measure is high when the manipulator is capable of equal motion in all directions and low when the manipulator is close to a singularity. One of J or q is required. Supply J if already calculated to save computation time

Parameters

q (float ndarray(n)) – The joint angles/configuration of the robot (Optional, if not supplied will use the stored q values).
J (float ndarray(6,n)) – The manipulator Jacobian in any frame

Returns

The manipulability index

Return type

float

References

Analysis and control of robot manipulators with redundancy, T. Yoshikawa,
Robotics Research: The First International Symposium (M. Brady and R. Paul, eds.), pp. 735-747, The MIT press, 1984.

jacobm(q=None, J=None, H=None)[source]¶

Calculates the manipulability Jacobian. This measure relates the rate of change of the manipulability to the joint velocities of the robot. One of J or q is required. Supply J and H if already calculated to save computation time

Parameters

q (float ndarray(n)) – The joint angles/configuration of the robot (Optional, if not supplied will use the stored q values).
J (float ndarray(6,n)) – The manipulator Jacobian in any frame
H (float ndarray(6,n,n)) – The manipulator Hessian in any frame

Returns

The manipulability Jacobian

Return type

float ndarray(n)

References

Kinematic Derivatives using the Elementary Transform Sequence, J. Haviland and P. Corke

jacobev(q=None)[source]¶

Jv = jacobev(q) is the spatial velocity Jacobian, at joint configuration q, which relates the velocity in the base frame to the velocity in the end-effector frame.

Jv = jacobev() as above except uses the stored q value of the robot object.

Parameters: q (float ndarray(n)) – The joint angles/configuration of the robot (Optional, if not supplied will use the stored q values).
Returns J: The velocity Jacobian in ee frame
Rtype J: float ndarray(6,6)

jacob0v(q=None)[source]¶

Jv = jacob0v(q) is the spatial velocity Jacobian, at joint configuration q, which relates the velocity in the end-effector frame to velocity in the base frame

Jv = jacob0v() as above except uses the stored q value of the robot object.

Parameters: q (float ndarray(n)) – The joint angles/configuration of the robot (Optional, if not supplied will use the stored q values).
Returns J: The velocity Jacobian in 0 frame
Rtype J: float ndarray(6,6)

ET¶

@author: Jesse Haviland

class ropy.robot.ET.ET(axis_func, axis, eta=None, joint=None)[source]¶

Bases: object

This class implements a single elementary transform (ET)

Parameters

axis_func (static et.T__ function) – The function which calculates the transform of the ET.
eta (float, optional) – The coordinate of the ET. If not supplied the ET corresponds to a variable ET which is a joint
joint (int, optional) – If this ET corresponds to a joint, this corresponds to the joint number within the robot

References

Kinematic Derivatives using the Elementary Transform Sequence, J. Haviland and P. Corke

property eta¶

property eta_deg¶

property axis_func¶

property axis¶

property jtype¶

property j¶

T(q=None)[source]¶

Calculates the transformation matrix of the ET

Parameters: q (float (radians), required for variable ET's) – Is used if this ET is variable (a joint)
Returns: The transformation matrix of the ET
Return type: SE3

classmethod TRx(eta=None)[source]¶

An elementary transform (ET). A pure rotation of eta about the x-axis.

L = TRx(eta) will instantiate an ET object which represents a pure rotation about the x-axis by amount eta.

L = TRx() as above except this ET representation a variable rotation, i.e. a joint

Parameters

eta (float (radians)) – The amount of rotation about the x-axis
joint (int) – The joint number within the robot

Returns

An ET object

Return type

ET

classmethod TRy(eta=None)[source]¶

An elementary transform (ET). A pure rotation of eta about the y-axis.

L = TRy(eta) will instantiate an ET object which represents a pure rotation about the y-axis by amount eta.

L = TRy() as above except this ET representation a variable rotation, i.e. a joint

Parameters

eta (float (radians)) – The amount of rotation about the y-axis
joint (int) – The joint number within the robot

Returns

An ET object

Return type

ET

classmethod TRz(eta=None)[source]¶

An elementary transform (ET). A pure rotation of eta about the z-axis.

L = TRz(eta) will instantiate an ET object which represents a pure rotation about the z-axis by amount eta.

L = TRz() as above except this ET representation a variable rotation, i.e. a joint

Parameters: eta (float (radians)) – The amount of rotation about the z-axis
Returns: An ET object
Return type: ET

classmethod Ttx(eta=None)[source]¶

An elementary transform (ET). A pure translation of eta along the x-axis

L = Ttx(eta) will instantiate an ET object which represents a pure translation along the x-axis by amount eta.

L = Ttx() as above except this ET representation a variable translation, i.e. a joint

Parameters: eta (float (metres)) – The amount of translation along the x-axis
Returns: An ET object
Return type: ET

classmethod Tty(eta=None)[source]¶

An elementary transform (ET). A pure translation of eta along the x-axis

L = Tty(eta) will instantiate an ET object which represents a pure translation along the y-axis by amount eta.

L = Tty() as above except this ET representation a variable translation, i.e. a joint

Parameters: eta (float (metres)) – The amount of translation along the x-axis
Returns: An ET object
Return type: ET

classmethod Ttz(eta=None)[source]¶

An elementary transform (ET). A pure translation of eta along the z-axis

L = Ttz(eta) will instantiate an ET object which represents a pure translation along the z-axis by amount eta.

L = Ttz() as above except this ET representation a variable translation, i.e. a joint

Parameters: eta (float (metres)) – The amount of translation along the x-axis
Returns: An ET object
Return type: ET