Bi-level programming based real-time path planning for unmanned aerial vehicles
Introduction
Real-time path planning for unmanned aerial vehicles (UAVs) in unknown complex environments has been considered as a fundamental and necessary mission in diverse applications, such as reconnaissance, surveillance, rescue, navigation and guidance of air, combat and precision strikes (see e.g. [1], [2], [3], [4], [5], [6]). The basic objective of real-time path planning is to find a convergent flight path along which a UAV can safely reach a specified target in the presence of potential opposition obstacles. Besides the basic objective, a significant challenge is how to further optimize the flight path in additional valuable aspects, for instance, shortening the path length, keeping the UAV away from obstacles as far as possible, alleviating the computing load, smoothing the trajectory, increasing flight path navigability, and improving the method’s adaptability to a UAV with performances fluctuation.
There is already an extensive literature on the path planning subject, and plenty of methods have been developed to plan path in real time, for example, Voronoi diagram method [7], directed graph based method [8], A∗ algorithms [9], [10], probabilistic roadmaps methods (PRMs) [11], [12], rapidly-exploring random trees (RRTs) based methods [13], [14], [15], [16], mixed-integer linear programming (MILP) based methods [2], [17], potential field approaches [18], bouncing algorithms [19], [23], etc. All these methods have been successfully applied to classic path planning applications [6], [20], but most of them only consider the basic objective without sufficient significance for the aforementioned additional aspects. Against this situation, we present an integrated demand on real-time path planning for a UAV, which requires five abilities of a satisfactory method:
- (i)
planning a path that is convergent to the specified target;
- (ii)
ensuring absolute obstacle avoidance;
- (iii)
planning an optimal or near-optimal path in terms of flight distance, safety and planning frequency;
- (iv)
planning a smooth path that a UAV is able to easily track under the constraints of kinematic properties;
- (v)
planning a navigable path for a UAV when its kinematic performances or sensory capability change, including turning capability, sensory range and possible flight velocity.
In response to these desired abilities, we dedicate to developing an optimization based approach capable of designing feasible safe flight paths for a single UAV with varying properties, which are also trackable and navigable in realistic flight processes. It is unpractical to develop an all-purpose real-time path planning method for any type of UAVs due to the wide variety of flight tasks and the advent of new UAVs with diverse sensors and control models [3], [4]. In this study, we particularly aim at a generic fixed-wing UAV described with a unicycle model in two-dimension space. In particular, for ability (v) some methods have handled specific subsets of the adaptability to UAV’s maneuver degradation caused by weather deterioration (such as unanticipated wind vectors or ice accumulation on aerofoil) [45], [46], or to sensor module change [47]. We in this paper lay emphasis upon the applicability to a UAV when more performances fluctuate, including turning capability, sensory range and maximal flight velocity.
In order to plan short and smooth flight path for a UAV, an improved leader–follower decision model embedded with discrete decision rule sets has been studied in our previous work [21]. We advance this idea by extending the path length and smoothness considerations to an integrated demand on the aforementioned multiple abilities by adopting a leader–follower hierarchical optimization structure. Consequently, a novel real-time path planning approach for a UAV is put forward on the basis of bi-level programming (BLP) model and its heuristic solution algorithm.
The BLP based real-time path planning model consists of decision variables, optimal objectives, and constraints in leader and follower levels. Yaw rate and flight time, as decision variables, are determined to generate new reference waypoints repeatedly in real time. The leader’s and follower’s objectives are defined as the deviation angle from a target and the distance to destination respectively, which are optimized to guarantee the realization of abilities (i) and (iii). Relevant kinematic and detection performances of the UAV and threat environment are formulated as constraints to fulfill ability (ii) and optimize abilities (iii)–(v). Variable planning time interval is introduced as follower’s decision variable to smooth the holistic flight path, and also optimize ability (iii) by updating the path only when necessary. Moreover, the interdependence and interaction between the leader and follower levels tend to broaden the applicability to a UAV with varying performances. Due to the NP-hard property of BLP [36], [38], a highly efficient solution algorithm with several heuristic strategies embedded is specially developed. The path planning effects are evaluated by numerous simulations and comparisons with four typical methods [2], [14], [19], [22], during which the effectiveness and efficiency of the proposed approach in the integrated realization and optimization of abilities (i)–(v) are witnessed.
The paper is organized as follows. After this introduction, the related works are investigated. The addressed real-time path planning problem for UAVs is described in Section 3. Section 4 presents a novel real-time path planning approach based on BLP model. Section 5 elucidates a solution algorithm embedded with heuristic strategies and analyzes its performances. Simulations in a large number of scenarios and comparisons among different methods are carried out in Section 6. In Section 7, the extensions to three-dimension scenarios and relaxed conditions, as well as the applicability to diverse environments, are discussed. Section 8 concludes the paper.
Section snippets
Related works
Existing researches on path planning generally addresses a subset of the five desired abilities, which is insufficient in practice when performing complex missions. For example, it is common that a long-distance flight task may demand several special concerns together, like fuel saving, physical limits of controlling organization, safety issues, maneuverability fluctuation due to weather conditions, and smoothness requirement for sensitive loads or security critical equipment [4], [5], [25],
Problem statement
This section develops the real-time path planning problem statement for UAVs. The purpose of the path planning addressed in this paper is to find an optimal (or near-optimal), navigable and obstacle-free flight path for a single UAV with fluctuating control and sensor properties. The formulation and assumptions below adapt to, but are not limited to, fixed-wing UAVs’ routing problem in two-dimension space. The generalization of the problem for extended applications will be discussed in Section 7
Overall solution
An overall solution is illustrated in Fig. 1 to clarify the BLP based real-time path planning approach for UAVs. Details are elaborated in the rest of this section.
As illustrated in Fig. 1, after the input of initial flight state and target information, s will be updated in real time by solving the BLP based path planning model under the constraints of threat environment and UAV’s control performances. The decisions of the model include yaw rate (ω) and flight time (t), which compose the
Solution algorithm and performance analysis
The work on path planning have been surveyed and considered as NP-Complete in the presence of obstacles [1], [6]. In addition, the BLP problem has been confirmed to be NP-hard in many literatures [35], [36], [38]. In our BLP model, both the decision objective functions in leader and follower levels are nonlinear continuous functions including inverse trigonometric expressions, and the constraints on decision variables involve diverse forms. All these properties bring great difficulties and high
Simulations
In order to validate the effectiveness and efficiency of the BLP based approach in solving the real-time path planning problem for UAVs, we perform simulations in 1000 stochastic scenarios with various obstacle distributions. Highly complex scenarios are also taken to test the feasibility of approach in the extreme. Furthermore, we draw comparisons between our approach and other classic methods in representative and challenging scenarios to highlight the advantages of ours in realizing the
Extension to three-dimensional scenarios
The presented approach can be extended from two-dimension space executions to realistic missions based on three-dimensional scenarios, by way of introducing more components into the BLP model, including pitching angle control, flight altitude decision, three-dimension threat environment modeling and dynamic controller utilization. Actually, extensive research on representative methods generally lays emphasis upon conventional two-dimensional cases at first, and then takes advantage of
Conclusion
Real-time path planning is a significant issue in the applications of UAVs. This paper presents an integrated demand on a satisfactory method concerning five realistic abilities. To realize them, a BLP based approach is proposed, including a BLP model and a solution algorithm embedded with heuristic strategies. The model divides the planning objective into two levels to improve the presented abilities in a cooperative and competitive manner. In the planning process, threat environment is
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grants 60904066. The authors are sincerely grateful to the anonymous reviewers for their meticulous reviews and valuable suggestions, as well as to the editor for the efficient and professional processing of this paper. Many thanks also go to Ms. Xin Liu for her language polishing efforts.
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