Trajectory Control of Wheeled Mobile Robots Not Satisfying Ideal Velocity Constraints by Using Slipping and Skidding Variations: A Singular Perturbation Approach

Control of wheeled mobile robots singularly perturbed by using the slipping and skidding variations: curvilinear coordinates approach (Part II)**The authors would like to thank Instituto Federal de Educação, Ciência e Tecnologia da Bahia (IFBA) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), all of them of Brazil, for the research grant, financial support and study fellowship.

“…However, the chattering phenomena associated with the sliding control makes of these methodologies rather impracticable [see Chwa (2004); Aithal and Janardhanan (2013)]. Instead, in this paper the technique used is based on methods in Fernández et al (2015).…”

“…�A T (q)A(q)εµ� ≤ ξ * , where ξ * > 0, for ∀t, is a known function that depends on slipping, skidding and deformation of the wheel. A singular perturbation model for a WMR can be write as the following space-state [see Fernández et al (2015Fernández et al ( , 2014 …”

“…(21) The equation (21) will be called the dynamic condition of appropriate rolling [see Fernández et al (2015)]. …”

“…(Appropriate rolling conditions). For motion of a WMR on a trajectory there are N conditions, corresponding to N wheels [see Fernández et al (2015)], defined by: δ x,i =δ x,i = 0 and s i =ṡ i = 0, for i = 1, . .…”

“…In addition, several phenomena contribute with that violation, such as sliding, deformability or flexibility. Thus, the trajectory tracking control of WMRs and its stabilization have given rise to an abundant literature in recent years due to its challenging theoretical nature [see Chwa (2004); Aithal and Janardhanan (2013); Song and Boo (2004); Fernández et al (2015)]. It is well-known that there does not exist a smooth pure state feedback control law such that the state of a WMR converges to the origin [see Dong (2010); Fernández et al (2014); Bloch et al (2000)].…”