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Development of time-optimal strategy for non-linear problem of planetary landing mission by using perturbation technique is investigated on two scenarios in this study. The first scenario includes finding an optimal control policy for descent in the variable gravitational field of the target planet analytically. In the second scenario, the optimal policy is derived by considering the effect of spacecraft mass variations in an analytic solution. To validate the accuracy of each generated policy, a numeric method such as steepest descent is employed. Afterwards, the fuzzy algorithm is followed to achieve the closed-loop guidance strategy for this non-linear system. The training process of the fuzzy system is based on the achieved perturbation solution of variable mass landing problem by utilizing a set of states-related non-dimensional variables for faster convergence rate. Finally, the lunar landing mission is demonstrated as a viable example of the non-linear planetary landing mission. Simulation results show that the presented optimal guidance laws are so effective which can be utilized in the real world spacecraft applications.

In this paper, the homotopy perturbation method (HPM) is used to investigate the effect of the Casimir force on the pull-in instability of electrostatic actuators at nano-scale separations. The proposed HPM is employed to solve nonlinear constitutive equations of cantilever beam-type nanoactuators. An analytical solution is obtained in terms of convergent series with easily computable components. Basic design parameters such as critical cantilever tip deflection and pull-in voltage of the nano-cantilevers are computed. As special cases of this work, freestanding nanoactuators and electrostatic micro-actuators are investigated. The analytical HPM results agree well with numerical solutions and those from the literature.

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In this article, a novel guidance law derivation and new synchronization strategy are proposed for a virtual structure-based formation flight. These are designed using both aerodynamic and dynamics equations of aerial robots to facilitate implementation of the guidance and control laws. The guidance commands are derived in the form of acceleration based on a new analytical approach. These acceleration commands are converted to suitable inputs for the control system in the form of velocity, roll and pitch angles by employing an innovative strategy. In addition, a new synchronization strategy for virtual structure formation control is proposed. In this strategy, each agent utilizes the other agents’ actual position rather than their position errors. The proposed strategy is capable of shape formation flight using a passive sensor, such as vision sensors, for position detection of neighbour agents. This ability makes the proposed strategy more reliable than conventional synchronization methods. The mentioned strategy is further improved by self-tuning of the synchronization gain based on a fuzzy inference. The simulation of formation flight for a group of three fixed-wing aerial robots using six degrees of freedom models for each one reveals the merits of the proposed strategy. In fact, this approach significantly decreases the number of oscillations and corresponding amplitudes of position/orientation error for each agent. This is a crucial aspect of the mission performance for formation flight control.