| Summary: | This paper presents a navigation strategy for a platoon of <i>n</i> non-holonomic mobile robots with a time-varying spacing policy between each pair of successive robots at the platoon, such that a safe trailing distance is maintained at any speed, avoiding the robots getting too close to each other. It is intended that all the vehicles in the formation follow the trajectory described by the leader robot, which is generated by bounded input velocities. To establish a chain formation among the vehicles, it is required that, for each pair of successive vehicles, the (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula>)-th one follows the trajectory executed by the former <i>i</i>-th one, with a delay of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>τ</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> units of time. An observer is proposed to estimate the trajectory, velocities, and positions of the <i>i</i>-th vehicle, delayed <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>τ</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula> units of time, consequently generating the desired path for the (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula>)-th vehicle, avoiding numerical approximations of the velocities, rendering robustness against noise and corrupted or missing data as well as to external disturbances. Besides the time-varying gap, a constant-time gap is used to get a secure trailing distance between each two successive robots. The presented platoon formation strategy is analyzed and proven by using Lyapunov theory, concluding asymptotic convergence for the posture tracking between the (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>i</mi><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula>)-th robot and the virtual reference provided by the observer that corresponds to the <i>i</i>-th robot. The strategy is evaluated by numerical simulations and real-time experiments.
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