Berkane, Soulaimane

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Scholarship@Western

Global Exponential Stabilization on SO(3)Background:The attitude control on the Special Orthogonal Group SO(3) is a long lastingproblem that has received a broad interest during the last decades. Recentinvestigations focus on using differential geometric tools to design attitudecontrol systems directly on the attitude configuration space SO(3); wherethe orientation of the rigid body is uniquely and globally rep- resented by arotation matrix in SO(3). The available results obtained via smooth feedbackare limited to almost global asymptotic stability, with slow convergence ratesnear some critical points. These limitations are mainly due to the topologicalnature of the closed compact manifold SO(3).Methods:An interesting hybrid framework involving synergistic potential functions hasbeen developed by A. Teel and his collaborators, overcoming the topologicalobstruction to global stabilization on SO(3) and leading to global asymptoticstability results.Results and Discussions:Recently, we extended the synergistic hybrid control design approach andproposed a comprehensive framework for the design of hybrid control and es-timation schemes providing stronger global exponential stability results. Ourframework encompasses the use of either differentiable or non-differentiableattitude potential functions. A hybrid switching mechanism is employed toavoid the critical points or the singular points of each individual control law,when using smooth or non-smooth attitude potential functions, respectively.We provide new results on the design of the hysteresis gap that is neces-sary for the implementation the switching mechanism. We show that thesecontrol strategies guarantee global exponential stability results on SO(3); aresult that was considered as the holy grail for many years.Conclusion and Interdisciplinary reflection:We strongly believe that our developed tools will not only benefit the area of1aerial vehicles engineering but also the robotics and biomedical engineeringcommunity. In fact, hybrid systems modelling arise from natural phenomenawhere both continuous and discrete events can be present.2

P26. Global Exponential Stabilization on SO(3)

https://ir.lib.uwo.ca/cgi/viewcontent.cgi?article=1041&amp;context=wrf

P26. Global Exponential Stabilization on SO(3)

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Scholarship@Western