Trajectory planning using Mixed Integer Linear Programming (MILP) is a powerful approach because vehicle dynamics and other constraints can be taken into account. However, it is currently severely limited by poor scalability. This paper presents a new approach which improves the scalability regarding the amount of obstacles and the distance between the start and goal positions. While previous approaches hit computational limits when the problem contains tens of obstacles, our approach can handle tens of thousands of polygonal obstacles successfully on a typical consumer computer. This performance is achieved by dividing the problem into many smaller MILP subproblems using two sets of heuristics. Each subproblem models a small part of the trajectory. The subproblems are solved in sequence, gradually building the desired trajectory. The first set of heuristics generate each subproblem in a way that minimizes its difficulty, while preserving stability. The second set of heuristics select a limited amount obstacles to be modeled in each subproblem, while preserving consistency. To demonstrate that this approach can scale enough to be useful in real, complex environments, it has been tested on maps of two cities with trajectories spanning over several kilometers.
In this paper we present the use of linear programming to systematically create control software for choreographed UAVs. This application requires the control of multiple UAVs where each UAV follows a predefined trajectory while simultaneously maintaining safety properties, such as keeping a safe distance between each other and geofencing. Modeling and incorporating safety requirements into the movement behavior of UAVs is the main motivation of our research. First, we describe an approach where the movement behavior of each UAV is formulated as a linear program. Second, we compare and analyze two different modeling techniques to implement the safe distance and geofencing requirements. Our approach was validated by doing experiments with Parrot Bebop UAVs. Besides being tested in the laboratory, our approach was validated in real life conditions in more than 30 performances of a dance show where five UAVs perform choreographed movements as part of the show introduction.1 Parrot Bebop UAV is a lightweight commercial UAV platform that counts with a 14 Mega pixels fisheye lens camera and a simple to use Software Development Kit (SDK).
Discrete decision making is a crucial software component of autonomous systems. Since many autonomous systems are safety-critical, it is important to have their decision making formally verified. Model checking is a well-known technique in computer science that can automatically verify the correctness of a system. In this paper we report our experience on applying different model checkers, including ProB, SPIN, TLC, Alloy and NuSMV, on verifying the discrete decision making of an autonomous UAV in an industrial application: pylon inspection. We study how the decision making logic of the UAV and the assumptions on its operating environment can be represented in each model checker and conduct a performance evaluation. The results demonstrate that only model checkers based on bounded model checking and symbolic model checking, that is, Alloy and NuSMV, are able to verify the decision making of the UAV in our case study.
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