WOLFRAM SYSTEM MODELER

# Wolfram Language

In[1]:=
`SystemModel["Aircraft.Utilities.Trajectories.ReferenceTrajectories"]`
Out[1]:=

# Information

Planar trajectory introduces reference pre-defined path shapes for the quadrotor model. It calculate the the path based on the simple equations for the circular and lemniscate (infinity and eight) trajectory and set up as output the x, y and z position. The trajectroty is planar means that after take off to the final amplitude and hover it starts to create an specific path is x-y plane. the path is parametrized so that, the user can set it up. When choosing the trajectory type, the necessary path parameters will be displayed and can be configured.

###### Circular trajectory

Figure 1: Circular motion trajectory.

The circular path encompasses three phases: takeoff, lateral movement to point "3" by a distance equal to the radius, and planar circular motion. The required parameters for configuration are as follows:

• heightAmplitude: As illustrated in Figure 1, the heightAmplitude defines the maximum height at which planar circular motion can be performed.
• heightStartTime: It specifies the start time of the take off.
• radius: As depicted in Figure 1, this parameter determines the radius of the circular motion.
• period: It specifies the time reuired to complete the generation of a circular path. Consequently, a lower period implies a faster generation of the path
• circularElapseTime: The start time to move laterally for a distance equal to a radius.
• circularStartTime: The start time to start a counter-clockwise circular motion.
###### Lemniscate Trajectory (infinity and eight)

Figure 2: Lemniscate motion (infinity) trajectory.

Both infinity and eight paths adhere to the lemniscate path algorithm. The only difference lies in the exchange of the x and y path equations between them. Lemniscate path consits of two phases: takeoff, lemniscate motion. The required parameters for configuration are as follows:

• heightAmplitude: As illustrated in Figure 2, the heightAmplitude defines the maximum height at which planar lemniscate motion can be performed.
• heightStartTime: It specifies the start time of the take off.
• radius: As depicted in Figure 2, this parameter determines the radius of the lemniscate motion.
• period: It specifies the time reuired to complete the generation of a circular path. Consequently, a lower period implies a faster generation of the path.
• startTime: The start time to start a lemniscate motion.

Note: The period of both movements is determined by the quadrotor and controller speeds,and this period should be adjusted according to the specific quadrotor design.

# Parameters (7)

trajectoryType Value: Type: TrajectoryType Description: Type of the trajectory Value: 2.0 Type: Length (m) Description: Final vertical height Value: 1.0 Type: Time (s) Description: Take off start time Value: 2.0 Type: Length (m) Description: Radius of the circular trajectory Value: 10 Type: Period (s) Description: Time required to trace one complete shape (cycle) Value: 7.0 Type: Time (s) Description: Time to move from the center to the starting position for circular motion Value: 5.0 Type: Time (s) Description: Start time of the circular trajectory after hover

# Connectors (1)

positionRef Type: RealOutput[3] Description: Reference position of the selected trajectory

# Used in Examples (1)

 CircularTrajectoryTracking Aircraft.Examples Circular path tracking by a quadrotor