Study of the local controllability of a non-holonomic truck-type mobile robot system

Vincent KANGBE; Adama COULIBALY

doi:10.61383/ejam.202641118

Authors

Vincent KANGBE Félix Houphouet Boigny University, Abidjan, Ivory Coast Corresponding Author https://orcid.org/0009-0008-3467-2821
Adama COULIBALY Félix Houphouet Boigny University, Abidjan, Ivory Coast https://orcid.org/0000-0002-3029-9125

DOI:

https://doi.org/10.61383/ejam.202641118

Keywords:

Lie algebra, controllability, Kalman criterion, Lie bracket, linearization, non-holonomic autonomous mobile robot, optimal control theory

Abstract

In this article, we studied the local controllability of a truck-type mobile robot modeled as a nonlinear, non-holonomic system. After presenting the system’s kinematic model and identifying the vector fields associated with the control inputs, two complementary analysis methods were developed. The first approach is based on the study of the Lie algebra generated by the system’s vector fields, using the Chow–Rashevskii theorem. This approach allows us to rigorously characterize the system’s accessibility by explicitly calculating the Lie brackets and analyzing their rank. The second method involves linearizing the system around an equilibrium trajectory and applying the Kalman controllability criterion to the linearized system. The results obtained, formulated as propositions and accompanied by detailed proofs, highlight the robot’s local controllability properties and underscore the fundamental role of non-holonomic constraints in generating additional movement directions.

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