Protected areas (PAs) are designated spaces where human activities are restricted to preserve critical habitats. Decision-makers are challenged with balancing a trade-off of financial feasibility with ecological benefit when establishing PAs. Given the long-term ramifications of these decisions and the constantly shifting environment, it is crucial that PAs are carefully selected with long-term viability in mind. Using AI tools like simulation and optimization is common for designating PAs, but current decision models are primarily linear. In this paper, we propose a derivative-free optimization framework paired with a nonlinear component, population viability analysis (PVA). Formulated as a mixed integer nonlinear programming (MINLP) problem, our model allows for linear and nonlinear inputs. Connectivity, competition, crowding, and other similar concerns are handled by the PVA software, rather than expressed as constraints of the optimization model. In addition, we present numerical results that serve as a proof of concept, showing our models yield PAs with similar expected risk to that of preserving every parcel in a habitat, but at a significantly lower cost. The overall goal is to promote interdisciplinary work by providing a new mathematical programming tool for conservationists that allows for nonlinear inputs and can be paired with existing ecological software. The code and data are available at https://github.com/cassiebuhler/conservation-dfo.

Mixed Integer Nonlinear Programming (MINLP) techniques are increasingly used to address challenging problems in robotics, especially Multi-Vehicle Motion Planning (MVMP). A particular challenge in using this framework is encoding stochastic phenomena such as communication connectivity in the form of MINLP constraints. The main contribution of this paper is an analytical formulation of communication connectivity constraints using stochastic physical layer communication models. These constraints account for the log-normal channel shadowing in noisy communication environments and specify inter-vehicle connectivity in terms of the outage probability of communication. A method is developed to provably accord robustness to communication failure by specifying an upper bound on the outage probability in terms of the inter-vehicle communication range. Finally, we demonstrate the utility of this formulation in the context of a realistic decentralized Multi-Vehicle Path Coordination (MVPC) scenario in which multiple robotic vehicles travel along predetermined fixed paths and are required to maintain communication connectivity during their transit. Conditions that affect the feasibility of the MVPC problem are formalized. Examples that assist in visualizing these conditions are provided.

Real world Multi-Vehicle Motion Planning (MVMP) problems require the optimization of suitable performance measures under an array of complex and challenging constraints involving kinematics, dynamics, communication connectivity, target tracking, and collision avoidance. The general MVMP problem can thus be formulated as a mathematical program (MP). In this paper we present a mathematical programming (MP) framework that captures the salient features of the general MVMP problem. To demonstrate the use of this framework for the formulation and solution of MVMP problems, we examine in detail four representative works and summarize several other related works. As MP solution algorithms and associated numerical solvers continue to develop, we anticipate that MP solution techniques will be applied to an increasing number of MVMP problems and that the framework and formulations presented in this paper may serve as a guide for future MVMP research.

We present a mathematical programming based decentralized framework to generate time optimal velocity profiles for a group of path constrained mobile vehicle robots subject to communication connectivity constraints. Each vehicle robot starts from a fixed start point and moves towards a goal point along a fixed path so as to avoid collisions with other robots, and remain in communication connectivity with other robots. The main contribution of this paper is the discrete time decentralized Receding Horizon Mixed Integer Nonlinear Programming (RH-MINLP) formulation of the multi-vehicle path coordination problem with constraints on kinematics, dynamics, collision avoidance, and communication connectivity, and the application of state-of-the-art MINLP solution techniques. We test scenarios involving up to ten (10) robots to demonstrate (i) the effect of communication connectivity requirements on robot velocity profiles; and (ii) the dependence of the solution computation time on communication connectivity requirements.

This paper presents a framework for generating time-optimal velocity profiles for a group of path-constrained vehicle robots that have fixed and known initial and goal locations and are required to maintain communication connectivity. Each robot must follow a fixed and known path, arrive at its goal as quickly as possible (or at least not increase the time for the last robot to arrive at its goal) and stay in communication with other robots in the arena throughout its journey. The main contribution of this paper is the formulation of the problem as a discrete time nonlinear programming problem (NLP) with constraints on robot kinematics, dynamics, collision avoidance, and communication connectivity. We develop partition elimination constraints that assist in ensuring that the communication network is fully connected (no network partitions). These constraints are enforced only when network partitions would otherwise occur, an approach which significantly reduces the problem size and the required computational effort. In addition, we introduce path-constrained jammer robots with known paths and velocity profiles into the scenario. These jammer robots have an effective jamming range and disrupt all communications within this range. Except for the jammers, all robots must remain outside this jamming range at all times. We investigate the scalability of the proposed approach by testing scenarios involving up to fifty (50) robots. Solutions demonstrate (i) the trade off between the arrival time and the communication connectivity requirements in scenarios with and without jamming; and (ii) the dependence of computation time on the number of robots.