International audienceAutonomous soft, safe and precise landing on celestial bodies like the Moon, planets and asteroids is still a challenging task for future exploration missions. To achieve a maximum of payload mass landed on the target body the trajectories of landing vehicles need to be (fuel) optimized. In order to allow an adjustability of the trajectory and a compensation of disturbances for all vehicles so far a thrust modulation is required. The drawback is that currently no main engine is available which allows the needed thrust modulation for an efficient, robust and safe landing on a celestial body like the Moon. The technology of the Apollo missions is not available anymore.Most planned lunar missions rely on the modulation capability of multiple engines where in some cases the thrust of the auxiliary engines for modulation is in the order of main engine thrust. This approach requires a large number of smaller engines to achieve the needed thrust modulation adding complexity and increasing the probability of failure. This paper shows a different approach to compute and control optimal trajectories for landing vehicles. It provides a new method for computing fuel efficient optimal trajectories which require minimal thrust modulation. A corresponding tracking control scheme is presented which allows the pre-computed optimal trajectory to be followed. The robustness of the method is discussed with results of a simulation

No abstract

For the use of container cranes in high rack warehouses, reference trajectories can be obtained from optimal control problems in order to control the swinging of the crane system during the fast movement and in order to reach an equilibrium position at the end of the trajectory. Safety requirements extend these problems to bilevel optimal control problems, where the existence of alternative stop trajectories has to be guaranteed. A method as to how these complex problems can be reduced to conventional optimal control problems, even under control and state constraints, is presented together with numerical examples.

No abstract

No abstract