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A new approach is proposed for an adaptive robust three-dimensional 3D trajectory-tracking controller design. The controller is modeled for actively articulated tracked vehicles AATVs. These vehicles have active sub-tracks, called flippers, linked to the ends of the main tracks, to extend the locomotion capabilities in hazardous environments, such as rescue scenarios. The proposed controller adapts the flippers configuration and simultaneously generates the track velocities, to allow the vehicle to autonomously follow a given feasible 3D path. The approach develops both a direct and differential kinematic model of the AATV for traversal task execution correlating the robot body motion to the flippers motion. The benefit of this approach is to allow the controller to flexibly manage all the degrees of freedom of the AATV as well as the steering. The differential kinematic model integrates a differential drive robot model, compensating the slippage between the vehicle tracks and the traversed terrain. The underlying feedback control law dynamically accounts for the kinematic singularities of the mechanical vehicle structure. The designed controller integrates a strategy selector too, which has the role of locally modifying the rail path of the flipper end points. This serves to reduce both the effort of the flipper servo motors and the traction force on the robot body, recognizing when the robot is moving on a horizontal plane surface. Several experiments have been performed, in both virtual and real scenarios, to validate the designed trajectory-tracking controller, while the AATV negotiates rubble, stairs, and complex terrain surfaces. Results are compared with both the performance of an alternative control strategy and the ability of skilled human operators, manually controlling the actively articulated components of the robot.