[Paper Review] Distributed Average Tracking for Double-integrator Multi-agent Systems with Reduced Requirement on Velocity Measurements

Sheida Ghapani, Wei Ren+2 more|arXiv (Cornell University)|Jul 16, 2015

Distributed Control Multi-Agent Systems14 references3 citations

TL;DR

This paper proposes two distributed discontinuous control algorithms for double-integrator multi-agent systems to achieve average tracking of time-varying input signals with reduced velocity measurement requirements. The first algorithm eliminates both absolute and relative velocity measurements by using relative positions and filter outputs, requiring correct initialization but handling bounded acceleration deviations. The second algorithm removes communication and initialization constraints by using only local position and velocity measurements, with all signals bounded, achieving robust tracking without relative velocity sensing or precise initialization.

ABSTRACT

This paper addresses distributed average tracking for a group of physical double-integrator agents under an undirected graph with reduced requirement on velocity measurements. The idea is that multiple agents track the average of multiple time-varying input signals, each of which is available to only one agent, under local interaction with neighbors. We consider two cases. First, a distributed discontinuous algorithm and filter are proposed, where each agent needs the relative positions between itself and its neighbors and its neighbors' filter outputs obtained through communication but the requirement for either absolute or relative velocity measurements is removed. The agents' positions and velocities must be initialized correctly, but the algorithm can deal with a wide class of input signals with bounded acceleration deviations. Second, a distributed discontinuous algorithm and filter are proposed to remove the requirement for communication and accurate initialization. Here each agent needs to measure the relative position between itself and its neighbors and its own velocity but the requirement for relative velocity measurements between itself and its neighbors is removed. The algorithm can deal with the case where the input signals and their velocities and accelerations are all bounded. Numerical simulations are also presented to illustrate the theoretical results.

Motivation & Objective

• To address distributed average tracking in double-integrator multi-agent systems under reduced velocity measurement requirements.
• To eliminate the need for relative velocity measurements, which are costly and inaccurate in practice.
• To develop control algorithms that rely only on relative positions and local velocity sensing, minimizing communication and initialization dependencies.
• To ensure robust tracking performance under bounded input accelerations and without requiring precise agent state initialization.
• To extend existing distributed average tracking methods to physical agents with double-integrator dynamics while minimizing sensing complexity.

Proposed method

• A distributed discontinuous controller and a distributed filter are designed, using only relative positions between agents and neighbors’ filter outputs, eliminating the need for absolute or relative velocity measurements.
• The control law incorporates a filter state that evolves based on local information, enabling estimation of the average input signal without velocity feedback.
• The first algorithm requires correct initialization of agent positions and velocities and uses control parameters α, γ, and β to ensure convergence under bounded acceleration deviations.
• The second algorithm replaces communication with local velocity measurements and removes the need for initialization accuracy, relying only on local sensing of position, velocity, and input signal derivatives.
• Control parameters κ, α, γ, and β are tuned to ensure bounded tracking error and convergence in the absence of relative velocity measurements.
• Theoretical analysis proves bounded tracking error and convergence to the average of time-varying input signals under the specified conditions.

Experimental results

Research questions

• RQ1 Can distributed average tracking be achieved in double-integrator multi-agent systems without requiring relative velocity measurements between agents?
• RQ2 How can the need for accurate initialization and inter-agent communication be eliminated while maintaining tracking performance?
• RQ3 What control structure enables robust average tracking under bounded input accelerations and without velocity feedback?
• RQ4 Can a discontinuous control and filtering framework achieve distributed average tracking with minimal sensing requirements?
• RQ5 What trade-offs exist between communication, initialization accuracy, and velocity measurement reduction in distributed average tracking?

Key findings

• The first algorithm achieves distributed average tracking without any velocity measurements—neither absolute nor relative—by using relative positions and filter outputs, provided agent states are correctly initialized.
• The algorithm ensures bounded tracking error for input signals with bounded acceleration deviations, even when input signals are time-varying and non-steady-state.
• The second algorithm removes the need for communication between agents and correct initialization, relying only on local position and velocity measurements and bounded input derivatives.
• Numerical simulations confirm that both algorithms successfully track the average of time-varying input signals in 2D space with ten agents, achieving convergence in both position and velocity states.
• The simulation results demonstrate that tracking is achieved in the absence of velocity measurements and without accurate initialization, validating the robustness of the proposed approach.
• The control design effectively reduces sensing and communication costs by eliminating relative velocity measurements and inter-agent communication in the second algorithm.