A Globally Exponential, Convergent, Adaptive Velocity Observation for Multiple Nonholonomic Mobile Robots with Discrete-Time Communications

The widespread application of multi-agent robotic systems in domains such as agricultural collaboration and automation has accentuated the challenges faced in seeking to achieve rapid synchronization and sustain high-performance control under conditions where velocity states remain unmeasurable. To relieve these challenges, a synchronization control framework is proposed for multi-agent systems, employing non-uniform sampling communication protocols. Initially, a state-variable transformation is applied to construct a composite Lyapunov function that integrates a sampling term. An explicit relation is then derived between the communication interval and the global exponential synchronization rate, thereby establishing a theoretical foundation for the design of non-periodic sampling-based control strategies. Second, a linear-state feedback controller is introduced, which balances convergence speed with the limited frequency of information updates, ensuring asymptotic stability even under prolonged sampling intervals. Third, a velocity observer was designed based on Immersion and Invariance (I&I) theory to solve the problem of unmeasurable velocity states, ensuring the exponential convergence of the estimation error. Finally, the simulation results demonstrate that, with sampling intervals of h∈[0.03,0.08] s, the position errors ∥qi−qd,i∥ of all six robots converge to below 10−2 within 7 s; meanwhile, the velocity estimation errors decay to nearly zero within 7 s, confirming the effectiveness of the proposed method. The main contributions of this work can be summarized as follows: (1) a new I&I velocity observer is tailored for discrete-time communication; (2) rigorous proof of global exponential convergence is provided via a composite Lyapunov energy function; (3) a reproducible MATLAB simulation framework is presented that enhances both the verifiability and applicability of the proposed approach.