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.