This paper considers the problem of finding the shortest tour to cover a given set of inverted cone views with apex angle α and height H when their apex points lie on a planar surface. This is a novel variant of the 3D Traveling Salesman Problem with intersecting Neighborhoods (TSPN) called Cone-TSPN. When the cones are allowed to tilt by an angle c we have the tilted Cone-TSPN problem, to which we present an algorithm that returns a solution with an approximation ratio of O (1+tan α/1-tan ϵ tan α (1 + log max(H)/min(H)). We demonstrate through simulations that our algorithm can be implemented in a practical way and by exploiting the structure of the cones we can achieve shorter tours. Finally, we present results from covering a reflective surface (lake area) that shows the importance of selecting different view angles under strong sunlight specularities.

We present algorithms for environment exploration in the context of a habitat monitoring task, where the goal is to track radio-tagged invasive fish with autonomous surface or ground robots. The first task is navigation around an unknown obstacle using an input from a front-facing sonar. This capability is important for navigation on inland lakes, because plants and shallow shorelines are hard to map in advance. The second task involves energy harvesting for long-term operation. We address the problem of exploring the solar map of the environment which is used for energy-efficient navigation. For both problems, we present online algorithms and examine their performance using competitive analysis. In competitive analysis, the performance of an online algorithm is compared against the optimal offline algorithm. For obstacle avoidance, the offline algorithm knows the shape of the obstacle. For solar exploration, the offline algorithm knows the geometry of the shadow-casting objects. We obtain an $O(1)$ competitive ratio for obstacle avoidance and an $O(\log n)$ competitive ratio for solar exploration, where $n$ is the number of critical points to observe. The strategies for obstacle avoidance are validated through extensive field experiments, and the strategies for exploration are validated with simulations.

Energy harvesting using solar panels can significantly increase the operational life of mobile robots. If a map of expected solar power is available, energy efficient paths can be computed. However, estimating this map is a challenging task, especially in complex environments. In this paper, we show how the problem of estimating solar power can be decomposed into the steps of magnitude estimation and solar classification. Then, we provide two methods to classify a position as sunny or shaded: a simple data-driven Gaussian Process method and a method that estimates the geometry of the environment as a latent variable. Both of these methods are practical when the training measurements are sparse, such as with a simple robot that can only measure solar power at its own position. We demonstrate our methods on simulated randomly generated environments. We also justify our methods with measured solar data by comparing the constructed height maps with satellite images of the test environments, and in a cross-validation step where we examine the accuracy of predicted shadows and solar current.

In this paper, we study the problem of quickly building the 3D model of an outdoor environment from measurements obtained by a robot equipped with a solar panel. The robot knows the angle of the sun and the locations of the objects in the environment. It does not know, however, the height of the objects. For example, it might be possible to use satellite images to obtain locations of trees in a field but not their heights. In order to compute the height of an object, the robot must find the projection of the object's highest point. This is where the shadow of the object ends. The robot can find it by tracing the shadow (moving parallel to the sun) until the measurement switches from shadow to sun or vice versa. The robot's goal is to compute the height of every object as quickly as possible using only solar measurements. We formulate this as an online optimization problem. The optimal offline algorithm is given by the Traveling Salesman path of the transition points. The robot does not know these locations a priori. It must search for each of them. We present an algorithm with the property that for n objects, our distance traveled is guaranteed to be within a factor O(log n) of this optimal offline tour. In addition to analytical proofs, we demonstrate the algorithm with simulations using solar data collected from field experiments, and examine its performance for uniformly distributed sites.

Robotic routers (mobile robots with wireless communication capabilities) can create an adaptive wireless network and provide communication services for mobile users on-demand. Robotic routers are especially appealing for applications in which there is a single mobile user whose connectivity to a base station must be maintained in an environment that is large compared to the wireless range. In this paper, we study the problem of computing motion strategies for robotic routers in such scenarios, as well as the minimum number of robotic routers necessary to enact our motion strategies. Assuming that the routers are as fast as the user, we present an optimal solution for cases where the environment is a simply-connected polygon, a constant factor approximation for cases where the environment has a single obstacle, and an O(h) approximation for cases where the environment has h circular obstacles. The O(h) approximation also holds for cases where the environment has h arbitrary polygonal obstacles, provided they satisfy certain geometric constraints - e.g. when the set of their minimum bounding circles is disjoint.