We analyze the case of run-and-tumble particles pushed through a rugged channel both in the continuum and on the lattice. The current characteristic is non-monotone in the external field with the appearance of a current and nontrivial density profile even at zero field for asymmetric obstacles. If an external field is exerted against the direction of that zero-field current, then the resulting current decreases with persistence at small field and increases with persistence at large field. Activity in terms of self-propulsion increases the maximal current and postpones dying. We give an effective theoretical description with wider validity. I. INTRODUCTIONA nonequilibrium system, be it transient or stationary driven, is very sensitive to time-symmetric constraints and obstacles. Kinetic constraints or disorder indeed influence relaxation, diffusion and transport even for independent particles. For transport in out-ofequilibrium systems, even at small (and even zero) external driving, the frenetic contribution complements entropic considerations (as in the fluctuation-dissipation relation) to enter crucially in the current characteristic [1,2]. Examples where the response to external fields, temperature or chemical affinities show negative differential susceptibility include [3][4][5][6][7][8][9]. In the present paper we revisit the set up of [3,4] but for active particles as studied before e.g. also in [10][11][12][13][14][15]: how does the current characteristic change as a function of the persistence?Active matter consists of self-propelled particles, characterized by a coupling between motion and an internal degree of freedom, quantified by persistence [16][17][18][19][20]. Their dynamics model bacteria-motion and nanomotors or active colloids for their locomotion, possibly showing collective effects such as flocking or phase separation [21][22][23][24][25][26]. Also individually they