Control of one-dimensional guided formations using coarsely quantized information

Abstract

Abstract-Motivated by applications of platoon formations, the paper studies the problem of guiding mobile agents in a onedimensional formation to their desired relative positions. Only coarsely quantized information is used which is communicated from a guidance system that monitors in real time the agents' motions. The desired relative positions are defined by the given distance constraints between the agents under which the overall formation is rigid in shape and thus admits locally a unique realization. It is firstly shown that even when the guidance system can only transmit at most four bits of information to each agent, it is still possible to design control laws to guide the agents to their desired positions. We further delineate the thin set of initial conditions for which the proposed control law may fail using the example of a three-agent formation. Tools from non-smooth analysis are utilized for the convergence analysis.

Cooperative Coordination and Formation Control for Multi-agent Systems

“…Here we extend such controllers to stabilize general undirected formation which are minimally and infinitesimally rigid. The above controller (7.17) can also be seen as a highdimensional extension of the one-dimensional formation controller studied in [De Persis et al, 2010]. Also, note that the right-hand side of (7.17) is composed of the sum of a unit vector multiplied by a signum function.…”

“…Formation control with quantized measurements has been discussed in e.g. [De Persis et al, 2010;Liu et al, 2014;Jafarian and De Persis, 2015], while a complete analysis of the quantization effects on rigid formation control system is still lacking. This motivates us to further investigate the dynamics and convergence property for rigid formation control systems with quantized measurements.…”

Quantization effects and convergence properties of rigid formation control systems with quantized distance measurements

“…Here, we extend such controllers to stabilize a general undirected formation, which is minimally and infinitesimally rigid. The aforementioned controller can also be seen as a high‐dimensional extension of the 1D formation controller studied in the work of De Persis et al…”

“…Here, we extend such controllers to stabilize a general undirected formation, which is minimally and infinitesimally rigid. The aforementioned controller (21) can also be seen as a high-dimensional extension of the 1D formation controller studied in the work of De Persis et al 39 Remark 6. (Boundedness of the control input (21)) Note that (since b ij ∈ { − 1, 0, 1}) the right-hand side of (21) is composed of the sum of a number of unit vectors multiplied by a signum function.…”

“…Lemma 6. Consider the two-agent formation control system (38) and (39) with the asymmetric quantization function (37).…”