Search results for: divine commands

Authors: Loyd R. Hook, Maryam Moharek

Abstract:

With the envisioned future growth of low altitude urban aircraft operations for airborne delivery service and advanced air mobility, strategies to coordinate and deconflict aircraft flight paths must be prioritized. Autonomous coordination and planning of flight trajectories is the preferred approach to the future vision in order to increase safety, density, and efficiency over manual methods employed today. Difficulties arise because any conflict resolution must be constrained by all other aircraft, all airspace restrictions, and all ground-based obstacles in the vicinity. These considerations make pair-wise tactical deconfliction difficult at best and unlikely to find a suitable solution for the entire system of vehicles. In addition, more traditional methods which rely on long time scales and large protected zones will artificially limit vehicle density and drastically decrease efficiency. Instead, strategic planning, which is able to respond to highly dynamic conditions and still account for high density operations, will be required to coordinate multiple vehicles in the highly constrained low altitude urban environment. This paper develops and evaluates such a planning algorithm which can be implemented autonomously across multiple aircraft and situations. Data from this evaluation provide promising results with simulations showing up to 10 aircraft deconflicted through a relatively narrow low-altitude urban canyon without any vehicle to vehicle or obstacle conflict. The algorithm achieves this level of coordination beginning with the assumption that each vehicle is controlled to follow an independently constructed flight path, which is itself free of obstacle conflict and restricted airspace. Then, by preferencing speed change deconfliction maneuvers constrained by the vehicles flight envelope, vehicles can remain as close to the original planned path and prevent cascading vehicle to vehicle conflicts. Performing the search for a set of commands which can simultaneously ensure separation for each pair-wise aircraft interaction and optimize the total velocities of all the aircraft is further complicated by the fact that each aircraft's flight plan could contain multiple segments. This means that relative velocities will change when any aircraft achieves a waypoint and changes course. Additionally, the timing of when that aircraft will achieve a waypoint (or, more directly, the order upon which all of the aircraft will achieve their respective waypoints) will change with the commanded speed. Put all together, the continuous relative velocity of each vehicle pair and the discretized change in relative velocity at waypoints resembles a hybrid reachability problem - a form of control reachability. This paper proposes two methods for finding solutions to these multi-body problems. First, an analytical formulation of the continuous problem is developed with an exhaustive search of the combined state space. However, because of computational complexity, this technique is only computable for pairwise interactions. For more complicated scenarios, including the proposed 10 vehicle example, a discretized search space is used, and a depth-first search with early stopping is employed to find the first solution that solves the constraints.

Keywords: strategic planning, autonomous, aircraft, deconfliction

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Authors: Anne Schattel, Mitja Echim, Christof Büskens

Abstract:

Trajectory planning for deep space missions has become a recent topic of great interest. Flying to space objects like asteroids provides two main challenges. One is to find rare earth elements, the other to gain scientific knowledge of the origin of the world. Due to the enormous spatial distances such explorer missions have to be performed unmanned and autonomously. The mathematical field of optimization and optimal control can be used to realize autonomous missions while protecting recourses and making them safer. The resulting algorithms may be applied to other, earth-bound applications like e.g. deep sea navigation and autonomous driving as well. The project KaNaRiA ('Kognitionsbasierte, autonome Navigation am Beispiel des Ressourcenabbaus im All') investigates the possibilities of cognitive autonomous navigation on the example of an asteroid mining mission, including the cruise phase and approach as well as the asteroid rendezvous, landing and surface exploration. To verify and test all methods an interactive, real-time capable simulation using virtual reality is developed under KaNaRiA. This paper focuses on the specific challenge of the guidance during the cruise phase of the spacecraft, i.e. trajectory optimization and optimal control, including first solutions and results. In principle there exist two ways to solve optimal control problems (OCPs), the so called indirect and direct methods. The indirect methods are being studied since several decades and their usage needs advanced skills regarding optimal control theory. The main idea of direct approaches, also known as transcription techniques, is to transform the infinite-dimensional OCP into a finite-dimensional non-linear optimization problem (NLP) via discretization of states and controls. These direct methods are applied in this paper. The resulting high dimensional NLP with constraints can be solved efficiently by special NLP methods, e.g. sequential quadratic programming (SQP) or interior point methods (IP). The movement of the spacecraft due to gravitational influences of the sun and other planets, as well as the thrust commands, is described through ordinary differential equations (ODEs). The competitive mission aims like short flight times and low energy consumption are considered by using a multi-criteria objective function. The resulting non-linear high-dimensional optimization problems are solved by using the software package WORHP ('We Optimize Really Huge Problems'), a software routine combining SQP at an outer level and IP to solve underlying quadratic subproblems. An application-adapted model of impulsive thrusting, as well as a model of an electrically powered spacecraft propulsion system, is introduced. Different priorities and possibilities of a space mission regarding energy cost and flight time duration are investigated by choosing different weighting factors for the multi-criteria objective function. Varying mission trajectories are analyzed and compared, both aiming at different destination asteroids and using different propulsion systems. For the transcription, the robust method of full discretization is used. The results strengthen the need for trajectory optimization as a foundation for autonomous decision making during deep space missions. Simultaneously they show the enormous increase in possibilities for flight maneuvers by being able to consider different and opposite mission objectives.

Keywords: deep space navigation, guidance, multi-objective, non-linear optimization, optimal control, trajectory planning.

Procedia PDF Downloads 383