Design of Planar Collision-free Trochoidal Paths for a Multi-robot Swarm

In the literature, a distributed consensus protocol by which a connected swarm of agents can generate artistic patterns in 2-dimensional space is proposed. Motivated by this protocol, in this paper, we design the parameters of this protocol for a 3-agent swarm of non-holonomic robots of finite size that results in the generation of periodic trochoidal trajectories that satisfy a set of geometric and speed constraints; this design also includes selecting the initial positions of the robots. This problem finds applications in persistent surveillance and coverage, guarding a region of interest, and target detection. While the trajectories may be self-intersecting, imposing geometric constraints i. eliminates collisions between robots; ii. ensures minimum and maximum separation distance between any robot and a fixed point, thus ensuring the robots are in communication range. Imposing speed constraints ensure that tracking these trajectories becomes feasible. It is also shown that robots can be injected to these paths at specific locations, in order to increase the refresh rate, without violating any of the geometric constraints. The designs are implemented in an indoor mobile robot platform.

Classification with Trust: A Supervised Approach based on Sequential Ellipsoidal Partitioning

Standard metrics of performance of classifiers, such as accuracy and sensitivity, do not reveal the trust or confidence in the predicted labels of data. While other metrics such as the computed probability of a label or the signed distance from a hyperplane can act as a trust measure, these are subjected to heuristic thresholds. This paper presents a convex optimization-based supervised classifier that sequentially partitions a dataset into several ellipsoids, where each ellipsoid contains nearly all points of the same label. By stating classification rules based on this partitioning, Bayes' formula is then applied to calculate a trust score to a label assigned to a test datapoint determined from these rules. The proposed Sequential Ellipsoidal Partitioning Classifier (SEP-C) exposes dataset irregularities, such as degree of overlap, without requiring a separate exploratory data analysis. The rules of classification, which are free of hyperparameters, are also not affected by class-imbalance, the underlying data distribution, or number of features. SEP-C does not require the use of non-linear kernels when the dataset is not linearly separable. The performance, and comparison with other methods, of SEP-C is demonstrated on the XOR-problem, circle dataset, and other open-source datasets.

Cooperative Collision Avoidance in Mobile Robots using Dynamic Vortex Potential Fields

In this paper, the collision avoidance problem for non-holonomic robots moving at constant linear speeds in the 2-D plane is considered. The maneuvers to avoid collisions are designed using dynamic vortex potential fields (PFs) and their negative gradients; this formulation leads to a reciprocal behaviour between the robots, denoted as being cooperative. The repulsive field is selected as a function of the velocity and position of a robot relative to another and introducing vorticity in its definition guarantees the absence of local minima. Such a repulsive field is activated by a robot only when it is on a collision path with other mobile robots or stationary obstacles. By analysing the kinematics-based engagement dynamics in polar coordinates, it is shown that a cooperative robot is able to avoid collisions with non-cooperating robots, such as stationary and constant velocity robots, as well as those actively seeking to collide with it. Conditions on the PF parameters are identified that ensure collision avoidance for all cases. Experimental results acquired using a mobile robot platform support the theoretical contributions.