A new optimal robust control strategy is designed based on the modified backstepping method in this paper. Using this strategy, stable, accurate and real-time trajectory tracking for the wheeled ...mobile robot in the presence of unavoidable disturbances is achieved. The control strategy consists of a kinematic controller, a dynamical controller and an online optimization algorithm. The kinematic controller, which considers non-holonomic constraint and the resulting under-actuated nature, has fewer gains and reduces the computational burden. The dynamical controller introduces a saturation function for error compensation and effectively suppresses disturbances. The optimization algorithm is used to achieve online tuning of controllers, thus achieving fast and accurate convergence of the trajectory tracking error. The stability of the control strategy is proved theoretically. Various numerical simulation scenarios with different types of disturbances and the experiment test verify the superiority of the trajectory tracking effect.
Low-energy bi-impulsive Earth-Moon transfers are investigated by using periodic orbits. Two Earth-Moon transfer design strategies in the CR3BP are proposed, termed direct and indirect design ...strategy. In the direct design strategy, periodic orbits which approach both vicinities of the Earth and Moon are selected as candidate periodic orbits, which can provide an initial guess of bi-impulsive Earth-Moon transfers. In the indirect design strategy, new bi-impulsive Earth-Moon transfers can be designed by patching together a bi-impulsive Earth-Moon transfer and a candidate periodic orbit which can approach the vicinity of the Moon. Optimizations in the CR3BP are undertaken based on the Gradient Descent method. Finally, bi-impulsive Earth-Moon transfer design and optimizations in the Sun-Earth-Moon bi-circular model (BCM) are carried out, using bi-impulsive Earth-Moon transfers in the CR3BP as initial guesses. Results show that the bi-impulsive Earth-Moon transfer in the CR3BP can serve as a good approximation for the BCM. Moreover, numerical results indicate that the optimal transfers in the BCM have the potential to be of lower cost in terms of velocity impulse than optimal transfers in the CR3BP.
Near-Earth asteroids have attracted attention for both scientific and commercial mission applications. Due to the fact that the Earth–Moon
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and
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points are candidates for gateway stations for ...lunar exploration, and an ideal location for space science, capturing asteroids and inserting them into periodic orbits around these points is of significant interest for the future. In this paper, we define a new type of lunar asteroid capture, termed direct capture. In this capture strategy, the candidate asteroid leaves its heliocentric orbit after an initial impulse, with its dynamics modeled using the Sun–Earth–Moon restricted four-body problem until its insertion, with a second impulse, onto the
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stable manifold in the Earth–Moon circular restricted three-body problem. A Lambert arc in the Sun-asteroid two-body problem is used as an initial guess and a differential corrector used to generate the transfer trajectory from the asteroid’s initial obit to the stable manifold associated with Earth–Moon
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point. Results show that the direct asteroid capture strategy needs a shorter flight time compared to an indirect asteroid capture, which couples capture in the Sun–Earth circular restricted three-body problem and subsequent transfer to the Earth–Moon circular restricted three-body problem. Finally, the direct and indirect asteroid capture strategies are also applied to consider capture of asteroids at the triangular libration points in the Earth–Moon system.
Cooperative guidance issues with desired impact angles against a target are studied in a leader-follower system in this article. Different from the existing achievements, the attackers and the target ...are modeled as the participants of a pursuit-evasion game in the cooperative guidance scenario. Specifically, the leader's differential game guidance law is first formulated by using optimal control theory, while the cooperative guidance law of the follower is designed to ensure the simultaneous attack on the target with the desired impact angles by using model predictive control (MPC) and robust sliding mode control. Compared to methods using time-to-go as the consensus variable, the proposed guidance law has the potential to achieve higher performance. Simulation validation shows that simultaneous attacks can be accomplished at the desired impact angles for different targets with stationary, classical maneuvers, and game maneuvers.
Distant retrograde orbit (DRO), serving for future astrophysical observatories and communications, has received much attention, including those around the Moon. Instead of high-order analytical ...approximate solutions, a numerical algorithm is deduced to find DRO, with a given Jacobi value or given amplitude. The goal is to determine the DRO around the Moon and the Lyapunov orbits which are tangential to the DRO. Considering the force of Sun׳s gravity, the long term DRO remains bounded at some moments which are expropriated as the launch window. After determining the launch window of a long term DRO, two different types of transfers to the DRO are obtained, namely interior transfers and exterior transfers. Numerical results indicate that exterior transfers need less fuel consumption while interior transfers always achieve quicker transfers. By the comparison of these transfer strategies, the interior transfers with non-tangential injection can be accomplished with as less fuel consumption as the exterior transfers approximately, about 549m/s less than the transfers in the previous works.
•A numerical algorithm for finding DRO without approximations is investigated.•The launch window and the zone of a long term DRO are proposed.•Two different types of transfers to a long term DRO around the Moon are designed.•Interior transfers can also achieve low energy transfers like exterior transfers.
The single impulsive planar Earth–Moon transfer strategy is investigated by analyzing the energy change of the lunar capture. A planar bicircular model of the restricted four-body problem is applied ...to define the single impulsive trajectory to the Moon from the Earth. Then analytical expressions are derived to describe the energy changes of the lunar capture in the Sun–Earth rotating frame. Accordingly, the eccentricity at the perilune of the single impulsive transfer trajectory can be calculated analytically to explore the lunar escape and capture conditions. The error analysis shows that the theoretical solutions serve as good approximations of the energy changes of the single impulsive transfer. Furthermore, it has been found that the perilune angle and the perilune radius are the critical factors for lunar capture. Finally, the theoretical results are successfully employed to find a series of single impulsive planar Earth–Moon transfers.
•A single impulsive strategy for the Earth–Moon transfer is proposed.•Analytical expressions of the energy changes of the transfer are derived.•Linear approximations of energy changes and eccentricity values are obtained.•The perilune angle and the radius play a significant role in the lunar capture.
•The strategy of capturing asteroids using a lunar flyby and station-keeping maneuvers is proposed.•Station-keeping maneuvers of LPOs with different amplitudes and durations are ...investigated.•Analytic expressions of the non-planar Hohmann transfer are used to select candidate asteroids.•A lunar flyby can reduce the fuel consumption of capturing asteroids, even when the station-keeping maneuvers are considered.
Long-term capture of near-Earth asteroids to Sun-Earth L1/L2 libration point orbits using a lunar flyby and station-keeping maneuvers is investigated in this paper. The model of the circular restricted three-body problem (CR3BP) provides reference L1/L2 libration point orbits and stable manifolds to capture asteroids. A station-keeping method using target points is employed to maintain the final periodic orbits under the Moon’s perturbation. Then the stable manifold with the Moon’s perturbation is applied to achieve transfers for capturing candidate asteroids. After candidate asteroids are selected using the non-planar Hohmann transfer, optimizations of capturing asteroids are carried out by minimizing the sum of transfer costs and station-keeping maneuvers. Simulation results show that the lunar flyby can reduce the fuel consumption of capturing asteroids, even when the station-keeping maneuvers are taken into account.
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