Collaboration diagram for Cable attachment:

A point mass that is held to a connection point by a PID-type spring-damper when it is attached, and falls freely under gravity when it is not. The mass moves with

\[ \dot v = \frac{a F_{reg} + F_{ext}}{m} + g \hat z \]

where \( a \) is the AttachState input, \( F_{ext} \) the ForceNED input, and \( F_{reg} = K_p (P_1 - P_0) + K_d (V_1 - V_0) + K_i e \) with \( P_0, V_0 \) the mass state, \( P_1, V_1 \) the connection point inputs, and \( e \) the integrated position error. \( F_{reg} \) is zero when the distance \( |P_1 - P_0| \) is at least AttachRadius. When AttachState is 0, a drag \( -0.1 v \) is added to the acceleration, and the error state decays with rate 2.

Input ports

Name	Width	Description
ForceNED	3	External (cable) force on the mass in the NED frame
PositionNED	3	Position of the connection point in the NED frame
VelocityNED	3	Velocity of the connection point in the NED frame
AttachState	1	Attached when not 0 (the force of the regulator is multiplied by this value; the integral error grows only when greater than 0)

Output ports

Name	Width	Description
PositionNED	3	Position of the mass in the NED frame
VelocityNED	3	Velocity of the mass in the NED frame
ForceNED	3	ForceNED input times AttachState, as computed at the last evaluation of the derivatives

Configuration parameters

Name	Width	Description
Mass	1	Mass of the point. Default 10. Unit not stated in the code
Kp	1	Proportional gain on the position error. Default 0
Kd	1	Gain on the velocity error. Default 0
Ki	1	Gain on the integrated position error. Default 0
AttachRadius	1	The regulator acts only when the distance to the connection point is less than this. Default 1.0

States

Name	Width	Description
Position	3	Position of the mass in the NED frame. No default: set it as an initial condition
Velocity	3	Velocity of the mass. Initial value 0
Error	3	Integrated position error. Initial value 0