Mahathi Anand

Diana Cuervo Espinosa, Mahathi Anand, Angela P. Schoellig

Learning from demonstratins (LfD) is usually performed over Euclidean spaces, while the robot state, e.g. orientation, naturally evolves over curved spaces. Therefore, to ensure natural, complex motion generation, we investigate learning from demonstrations over Riemannian manifolds that are capable of encoding both position and orientation data. Here, geodesic paths provide for natural motion between two arbitrary points within the manifold. We propose to numerically estimate geodesics via neural ordinary differential equations, mitigating large computational overhead of existing approaches. Finally, these geodesics can be decoded back into the original task space before deploying on the robot. In this extended abstract, we discuss the architecture of our framework, provide some initial insights from our simulation experiments, including comparison to other geodesic computation mechanisms, and discuss the challenges and prospects for future work.

Maria Mannone, Mahathi Anand, Peppino Fazio et al.

In a robotic swarm, parameters such as position and proximity to the target can be described in terms of probability amplitudes. This idea led to recent studies on a quantum approach to the definition of the swarm, including a block-matrix representation. However, the size of such matrix-based representation increases drastically with the swarm size, making them impractical for large swarms. Hence, in this work, we propose a new approach for modeling robotic swarms and robotic networks by considering them as mixed quantum states that can be represented mathematically via density matrices. The size of such an approach only depends on the available degrees of freedom of the robot, and not its swarm size and thus scales well to large swarms. Moreover, it also enables the extraction of local information of the robots from the global swarm information contained in the density matrices, facilitating decentralized behavior that aligns with the collective swarm behavior. Our approach is validated on several simulations including large-scale swarms of up to 1000 robots. Finally, we provide some directions for future research that could potentially widen the impact of our approach.