Collision Avoidance using Iterative Dynamic and Nonlinear Programming with Adaptive Grid Refinements

Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods struggle when adopted separately, their combination enabled by a penalty approach was found capable of handling highly nonlinear systems while overcoming the curse of dimensionality. Nevertheless, using dynamic programming with a fixed state space discretization limits the set of reachable solutions, hindering convergence or requiring enormous memory resources for uniformly spaced grids. In this work we solve this issue by incorporating an adaptive refinement of the state space grid, splitting cells where needed to better capture the problem structure while requiring less discretization points overall. Numerical results on a space manipulator demonstrate the improved robustness and efficiency of the combined method with respect to the single components.

Relativistic Digital Twin: Bringing the IoT to the Future

Complex IoT ecosystems often require the usage of Digital Twins (DTs) of their physical assets in order to perform predictive analytics and simulate what-if scenarios. DTs are able to replicate IoT devices and adapt over time to their behavioral changes. However, DTs in IoT are typically tailored to a specific use case, without the possibility to seamlessly adapt to different scenarios. Further, the fragmentation of IoT poses additional challenges on how to deploy DTs in heterogeneous scenarios characterized by the usage of multiple data formats and IoT network protocols. In this paper, we propose the Relativistic Digital Twin (RDT) framework, through which we automatically generate general purpose DTs of IoT entities and tune their behavioral models over time by constantly observing their real counterparts. The framework relies on the object representation via the Web of Things (WoT), to offer a standardized interface to each of the IoT devices as well as to their DTs. To this purpose, we extended the W3C WoT standard in order to encompass the concept of behavioral model and define it in the Thing Description (TD) through a new vocabulary. Finally, we evaluated the RDT framework over two disjoint use cases to assess its correctness and learning performance, i.e. the DT of a simulated smart home scenario with the capability of forecasting the indoor temperature, and the DT of a real-world drone with the capability of forecasting its trajectory in an outdoor scenario.