Coordinated Multi-Robot Trajectory Tracking Control over Sampled Communication

TL;DR

The paper tackles coordinated multi-robot trajectory tracking under sampled communication by introducing an inverse-kinematics controller that combines a sampled proportional feedback with a continuous-time feedforward to linearize around a precomputed reference. It develops the SIKM framework, enabling distributed implementation with a single broadcast per sample and derives explicit stability and convergence bounds in terms of the gain $k$ and sampling period $T$, including stability regions and optimal gain/sampling time pairs. A data-driven procedure estimates auxiliary parameters $(\mu,\alpha,\gamma_1,\gamma_2)$ to bound the convergence rate, and the approach is validated through Fly-Crane simulations comparing against centralized online-gain heuristics, showing comparable performance with distributed robustness. The work lays groundwork for reliable, communication-efficient multi-robot trajectory tracking and suggests directions for real-system experiments and latency/packet-loss analyses.

Abstract

In this paper, we propose an inverse-kinematics controller for a class of multi-robot systems in the scenario of sampled communication. The goal is to make a group of robots perform trajectory tracking in a coordinated way when the sampling time of communications is much larger than the sampling time of low-level controllers, disrupting theoretical convergence guarantees of standard control design in continuous time. Given a desired trajectory in configuration space which is precomputed offline, the proposed controller receives configuration measurements, possibly via wireless, to re-compute velocity references for the robots, which are tracked by a low-level controller. We propose joint design of a sampled proportional feedback plus a novel continuous-time feedforward that linearizes the dynamics around the reference trajectory: this method is amenable to distributed communication implementation where only one broadcast transmission is needed per sample. Also, we provide closed-form expressions for instability and stability regions and convergence rate in terms of proportional gain $k$ and sampling period $T$. We test the proposed control strategy via numerical simulations in the scenario of cooperative aerial manipulation of a cable-suspended load using a realistic simulator (Fly-Crane). Finally, we compare our proposed controller with centralized approaches that adapt the feedback gain online through smart heuristics, and show that it achieves comparable performance.

Figures (10)

• Figure 4: Controller architectures for trajectory tracking. The pivot is colored in gray, each robot (equipped with a dynamical controller which converts $\mathbf{u}$ to forces) in blue, sensor measurements in red, and the reference trajectory in green. The wireless symbol refers to sampled communication.
• Figure 5: Representation of the quantities $\tau_s(k)$, $\tau_o(k)$, $\tau(k_o)$ defined in Propositions \ref{['prop:tau_s']}--\ref{['prop:k_o_tau_fixed']}.
• Figure 6: Estimated convergence rate $\rho_0$ as a function of the gain $k$ and of the sampling time $\tau$.
• Figure 7: The Fly-Crane system in the Gazebo simulator.
• Figure 8: Architecture used to perform simulations: a global planner generates the desired trajectory $\mathbf{q}^r, \mathbf{\dot{q}}^r$ and sends it to the local planner which generates the desired robot velocities. The blue rectangle on the right represents a realistic environment where the robotic system is simulated.

Theorems & Definitions (19)

• Proposition 1
• Proposition 2
• Definition 3
• Lemma 4
• Proposition 5
• Remark 6: Stability limitations on $T$ and $k$
• Proposition 7
• Remark 8: Stability
• Proposition 9
• Remark 10: Constant reference