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Abstract-A continuous robust adaptive control method is designed for a class of uncertain nonlinear systems with unknown constant time-delays in the states. Specifically, a robust adaptive control method and a delay-free gradient-based desired compensation adaptation law (DCAL) are utilized to compensate for unknown time-delays, linearly parameterizable uncertainties, and additive bounded disturbances for a general nonlinear system. Despite these disturbances, a Lyapunov Krasovskii-based analysis is used to conclude that the system output asymptotically tracks a desired time varying bounded trajectory.

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In this paper, the non-holonomic characteristic of a free-floating space robotic system is used to plan the path of the manipulator joints, by whose motion the base attitude and the manipulator joints attain the desired states. Here, we parameterize the joint trajectory using sinusoidal functions, whose arguments are high-order polynomials. Then, we define the cost function for optimization according to the constraint conditions and the accuracy of the space robot. Finally, genetic algorithms (GAs) are used to search for the solutions of the parameters. Compared with others, our approach has advantages as follows. (i) The motion of the manipulator and the disturbance on the base are practically constrained. (ii) The dynamic singularities cannot affect the algorithm since only the direct kinematic equations are utilized. (iii) The planned path is smooth and more applicable for the control of the manipulator. (iv) The convergence of the algorithm is not affected by the attitude singularity since the orientation error is represented by quaternion, which is globally singularity-free. The simulation results of the spacecraft with a 6-d.o.f. manipulator verify the performance and the validity of the proposed method.

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