Leader-Follower

Problem Statement

Leader-follower architectures simplify coordination by assigning one trajectory source and distributed tracking controllers for followers.

Model and Formulation

Follower error in leader frame:

$$e_i=p_i-(p_L+{\mathrm{\Delta }}_i)$$

Control law:

$$u_i=-K_p{e}_i-K_d{\dot{e}}_i$$

Practical Notes

• Differentiate the leader's trajectory analytically. Differencing its position against the previous value works everywhere except the first step, where "previous" is the initialisation — the atlas demo produced a 250 m/s velocity spike on step 0 and blew the formation apart before it began.

• The leader velocity term is what lets followers hold station on a moving leader at all; without it they trail by an offset proportional to leader speed. Follower error on the atlas demo: 1.90 m mean before, 0.64 m after.

• Seed the RNG that places the followers. Drawing from the global np.random state makes the run irreproducible and couples it to whatever else in the process touched that state.

• Robust leader estimation is critical for formation stability.

• Follower chain topologies are simple but vulnerable to upstream failure.

• Relative-sensing noise can cause accordion oscillations.

Implementation and Execution

python -m uav_sim.simulations.swarm.leader_follower

Evidence

References

• Desai et al., Modeling and Control of Formations of Nonholonomic Mobile Robots (2001)
• Oh, Park, Ahn, Survey of Multi-Agent Formation Control (2015)

Related Algorithms

• Virtual Structure
• Consensus Formation