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Investigates the problem of almost asymptotic stabilization for a class of uncertain driftless systems in power chained form. The main obstacles for the control of this new type of driftless systems are: i) nonexistence of any time-invariant smooth (or even continuous) state feedback control law; ii) lack of affineness in the control input; and iii) high-order nonlinearities that make most of the nonlinear design methods inapplicable. To overcome these difficulties we propose a constructive approach that combines a discontinuous change of coordinates and the recent adding a power integrator technique. Sufficient conditions are given under which discontinuous robust and adaptive controllers can be explicitly constructed, achieving almost stabilization and adaptive regulation. Solutions to the problems of global robust regulation and adaptive regulation are also obtained by using switching control schemes.