This letter investigates the direct trajectory optimization of the free-floating space manipulator (FFSM). The main purpose is to plan the joint space trajectories to reduce the spacecraft motion due to the joint rotation during the FFSM performing tasks. To improve the calculation efficiency, the adaptive Radau pseudospectral method (A-RPM) is applied to discretize the system dynamics and transform the formulated optimal problem into a nonlinear programming problem (NLP). By adaptively subdividing the current segment and assigning collocation points according to the solution error, high-degree interpolation polynomials are avoided. To verify the effectiveness of the proposed method, a ground micro-gravity platform of the FFSM system is designed by using the air-bearing technique, on which experiments are carried out. The results show that the variation of the base spacecraft is dramatically reduced if the joints rotate along the optimized trajectories.

This article investigates the zero-sum game-based secure control problem for cyber-physical systems (CPS) under the actuator false data injection attacks. The physical process is described as a linear time-invariant discrete-time model. Both the process noise and the measurement noise are addressed in the design process. An optimal Kalman filter is given to estimate the system states. The adversary and the defender are modeled as two players. Under the zero-sum game framework, an optimal infinite-horizon quadratic cost function is defined. Employing the dynamic programming approach, the optimal defending policy and the attack policy are derived. The convergence of the cost function is proved. Moreover, the critical attack probability is derived, beyond which the cost cannot be bounded. Finally, simulation results are provided to validate the proposed secure scheme.