WOLFRAM SYSTEMMODELER

KinematicPTP2

Move as fast as possible from start to end position within given kinematic constraints with output signals q, qd=der(q), qdd=der(qd)

Wolfram Language

In[1]:=
SystemModel["Modelica.Blocks.Sources.KinematicPTP2"]
Out[1]:=

Information

This information is part of the Modelica Standard Library maintained by the Modelica Association.

The goal is to move as fast as possible from start position q_begin to end position q_end under given kinematical constraints. The positions can be translational or rotational definitions (i.e., q_begin/q_end is given). In robotics such a movement is called PTP (Point-To-Point). This source block generates the position q(t), the speed qd(t) = der(q), and the acceleration qdd = der(qd) as output. The signals are constructed in such a way that it is not possible to move faster, given the maximally allowed velocity qd_max and the maximally allowed acceleration qdd_max:

KinematicPTP2.png

If vectors q_begin/q_end have more than 1 element, the output vectors are constructed such that all signals are in the same periods in the acceleration, constant velocity and deceleration phase. This means that only one of the signals is at its limits whereas the others are synchronized in such a way that the end point is reached at the same time instant.

This element is useful to generate a reference signal for a controller which controls, e.g., a drive train, or to drive a flange according to a given acceleration.

Parameters (6)

q_begin

Value: {0}

Type: Real[:]

Description: Start position

q_end

Value: {1}

Type: Real[:]

Description: End position

qd_max

Value: {1}

Type: Real[:]

Description: Maximum velocities der(q)

qdd_max

Value: {1}

Type: Real[:]

Description: Maximum accelerations der(qd)

startTime

Value: 0

Type: Time (s)

Description: Time instant at which movement starts

nout

Value: max([size(q_begin, 1); size(q_end, 1); size(qd_max, 1); size(qdd_max, 1)])

Type: Integer

Description: Number of output signals (= dimension of q, qd, qdd, moving)

Outputs (1)

endTime

Type: Time (s)

Description: Time instant at which movement stops

Connectors (4)

q

Type: RealOutput[nout]

Description: Reference position of path planning

qd

Type: RealOutput[nout]

Description: Reference speed of path planning

qdd

Type: RealOutput[nout]

Description: Reference acceleration of path planning

moving

Type: BooleanOutput[nout]

Description: = true, if end position not yet reached; = false, if end position reached or axis is completely at rest

Used in Examples (1)

PositionControlledDCPM

Modelica.Electrical.Machines.Examples.ControlledDCDrives

Position controlled DC PM drive with H-bridge from battery

Used in Components (2)

PathPlanning1

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components

Generate reference angles for fastest kinematic movement

PathPlanning6

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components

Generate reference angles for fastest kinematic movement