From CW Motion to Controlled Docking
A chaser spacecraft begins near a target in circular orbit. In the previous CW problem, natural relative motion could oscillate or drift depending on initial conditions. Now the goal changes: can we design a controller that brings the chaser safely to the target?
The core question is whether the chaser can dock without overshoot, oscillation, or excessive control effort.
Radial relative position.
Along-track relative position.
Relative velocity components.
Control acceleration commands.
Docking Is Not Straight-Line Motion
Docking is not the same as flying directly toward the target. If the chaser commands motion directly toward the target, orbital coupling can make it overshoot, loop around, or drift along-track.
In orbit, “go toward the target” is not automatically a safe docking strategy.
Adding Control to Relative Motion
The controller enters the CW equations as acceleration commands in the radial and along-track directions.
The controller must overcome the natural coupling between radial and along-track motion.
PD Control for Docking
The first controller is a simple PD law. Position feedback pulls the chaser toward the target, while velocity feedback damps the closing motion.
Oscillation around the target.
Aggressive approach, overshoot, or saturation.
Slow drift and poor docking.
Docking Controller Tuning
Adjust the initial condition, controller gains, orbit altitude, control limit, and simulation time. Watch the trajectory, velocity, separation, control commands, effort, and docking status update.
Docking Is More Than Reaching Zero Position
Docking is successful only if the chaser reaches the target slowly, safely, and without excessive control demand.
final separation < 1 m
final relative velocity < 0.05 m/s
saturation percentage is not excessive
trajectory remains inside the safety corridor
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Docking vs Oscillation Scenarios
Use the preset buttons to compare four control behaviours: clean convergence, underdamped oscillation, aggressive overshoot, and weak control drift.
Moderate Kp and good Kd produce clean convergence.
High Kp and low Kd repeatedly cross the target.
Very high gain reaches fast but can violate safety limits.
Low gains cannot overcome relative dynamics quickly enough.
The Path Must Be Safe Too
A controller may reduce separation eventually but still be unsafe if it leaves the docking corridor. The corridor here represents a simple approach rule: while approaching along-track, radial deviation should remain within a bounded safety envelope.
Reaching the target is not enough. The path to the target must also be safe.
When the Controller Asks for More Than the Thruster Can Give
The controller may command more acceleration than the vehicle can physically apply. Saturation clips the commanded acceleration.
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Docking Also Has a Propellant Cost
A simple control-effort metric estimates how much total acceleration the controller used. Lower control effort suggests less propellant usage, but too little effort may mean slow or unsafe docking.
Kp–Kd Gain Map
Controller tuning is not about one magic value. It is about finding a safe stability region. The map classifies gain combinations as successful, oscillatory, slow, or failed/unsafe.
No Control vs PD vs Saturated PD
This overlay links the previous CW page to control design: no control drifts, PD converges, and saturated PD may converge more slowly or fail if control authority is too low.
What the Controller Is Really Doing
The chaser must remove both relative position and relative velocity.
Kp pulls toward the target. Kd damps closing speed. Good docking needs both.
The plant is not flat-space motion. It is shaped by CW orbital dynamics.
A stable controller can still be unsafe if it overshoots, violates the corridor, or uses too much effort.
What This Problem Shows
Position control alone can create oscillation around the target.
Low final separation is not enough if closing speed is too high.
Control saturation can turn a good theoretical controller into a poor practical one.
The trajectory must remain inside an acceptable approach corridor.