Rafi Nasrallah
EN FR
Advanced Control & Systems

Luenberger-Based Rendezvous Control with Angle-Only Data

Output-feedback rendezvous controller for a chaser satellite using only line-of-sight angle measurement, with state reconstruction through a Luenberger observer and MATLAB/Simulink validation.

Academic project | Observer design, normalized state feedback, orbital simulation

Download Full Simulation Report (PDF)

Measurement

y = theta

Angle-only sensing.

State vector

4 states

r, r_dot, theta, theta_dot.

Estimator

Luenberger

Full-state reconstruction.

Toolchain

MATLAB

Simulation and gain validation.

Engineering problem

Output-feedback rendezvous

The controller needs the full relative state x = [r, r_dot, theta, theta_dot]^T, but the available sensor output is only the angle y = theta. The missing radial position and velocity states must be estimated before feedback control can work.

Numerical conditioning issue

The physical model in meters and seconds produced unrealistic gains around 10^15. The project therefore used normalization before controller and observer design to obtain usable numerical behavior.

Control architecture

STEP 1

Feasibility analysis

Verified controllability and observability from y = theta, proving that the reduced sensing problem is mathematically solvable.

Achieved
STEP 2

Normalized gain design

Designed stable K_norm and L_norm gains after non-dimensionalization, with observer dynamics set faster than controller dynamics.

Achieved
STEP 3

Observer validation

Confirmed estimation error convergence e_x(t) -> 0, showing that estimated states track real states reliably.

Achieved
STEP 4

Closed-loop validation

Validated that the real satellite state x(t) converges to zero and that the control input settles as the rendezvous completes.

Achieved

Simulation evidence

What the plots confirm

The observer estimates converge to the true states, the estimation error goes to zero, the physical satellite states converge to the rendezvous target, and the control effort settles as the maneuver completes.

Plot comparing real satellite states with Luenberger observer estimated states.
Observer validation: estimated states converge toward real states.
Plot of Luenberger observer estimation error versus time.
Observer performance: all four estimation errors converge to zero.
Plot of real satellite rendezvous state convergence versus time.
Closed-loop validation: real states are driven to the rendezvous target.
Phase plot of the rendezvous trajectory converging to the origin.
Trajectory phase plot: the chaser converges toward the origin.
Plot of rendezvous control effort converging over time.
Control effort: commanded input converges as rendezvous is reached.

Conclusion and next steps

Result

The simulation demonstrates that an observer-controller rendezvous architecture can stabilize a 2D relative-motion model using only angular measurement. Normalization was the key step that made the numerical design physically usable.

Logical extension

  • Extend the model to a 13-state 6-DOF formulation.
  • Replace the linear observer with EKF or UKF sensor fusion.
  • Control translation forces F and attitude torques tau together.

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