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This paper exploits a nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors subject to thrust constraint and inertial parameter uncertainty to accomplish trajectory tracking missions. Because of under-actuated nature of the quadrotor, a hierarchical control strategy is available; and position and attitude loop controllers are synthesized according to adaptive sliding mode control projects, where adaptive updates with projection algorithm are developed to ensure bounded estimations for uncertain inertial parameters. Further, during the position loop controller development, an auxiliary dynamic system is introduced, and selection criteria for controller parameters are established to maintain the thrust constraint and to ensure the non-singular requirement of command attitude extraction. It has demonstrated that, the asymptotically stable trajectory tracking can be realized by the asymptotically stable cascaded closed-loop system and auxiliary dynamic system. Simulations validate and highlight the proposed control approach.ROBUST ADAPTIVE HIERARCHICAL SLIDING MODE CONTROL FOR QUADROTORS 927 with 1 2 R n and 2 2 R n . Positive parameters˛,ˇ, k, and l can guarantee that the system (1) is asymptotically stable. Attitude representationThe quadrotor system is described in two frames: the inertial frame I D ¹O I x I y I´I º whose origin is located at a fixed point on the earth, and the body frame B D ¹O b x b y b´b º whose origin is in accordance with the quadrotor center of gravity (c.g.). To begin with, it is necessary to specify the relative attitude between these two frames. The rotation matrix R 2 SO.3/ D ¹R 2 R 3 3 j det R D 1; RR T D R T R D I 3 º describes a rotation of the frame B by an Euler angle ' with respect to an Euler vector k to the frame I, which can be determined with the Euler's formula [26] Given the reference acceleration R p c and the control parameters k˛, kˇ, the resulting control thrust T is bounded and satisfies

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