Rakesh

Sushant Veer, Rakesh, Ioannis Poulakakis · princeton

In this paper we investigate the relation between robustness of periodic orbits exhibited by systems with impulse effects and robustness of their corresponding Poincaré maps. In particular, we prove that input-to-state stability (ISS) of a periodic orbit under external excitation in both continuous and discrete time is equivalent to ISS of the corresponding 0-input fixed point of the associated \emph{forced} Poincaré map. This result extends the classical Poincaré analysis for asymptotic stability of periodic solutions to establish orbital input-to-state stability of such solutions under external excitation. In our proof, we define the forced Poincaré map, and use it to construct ISS estimates for the periodic orbit in terms of ISS estimates of this map under mild assumptions on the input signals. As a consequence of the availability of these estimates, the equivalence between exponential stability (ES) of the fixed point of the 0-input (unforced) Poincaré map and ES of the corresponding orbit is recovered. The results can be applied naturally to study the robustness of periodic orbits of continuous-time systems as well. Although our motivation for extending classical Poincaré analysis to address ISS stems from the need to design robust controllers for limit-cycle walking and running robots, the results are applicable to a much broader class of systems that exhibit periodic solutions.

Varun Murali, Han-Pang Chiu, Supun Samarasekera et al.

This paper presents a new approach for integrating semantic information for vision-based vehicle navigation. Although vision-based vehicle navigation systems using pre-mapped visual landmarks are capable of achieving submeter level accuracy in large-scale urban environment, a typical error source in this type of systems comes from the presence of visual landmarks or features from temporal objects in the environment, such as cars and pedestrians. We propose a gated factor graph framework to use semantic information associated with visual features to make decisions on outlier/ inlier computation from three perspectives: the feature tracking process, the geo-referenced map building process, and the navigation system using pre-mapped landmarks. The class category that the visual feature belongs to is extracted from a pre-trained deep learning network trained for semantic segmentation. The feasibility and generality of our approach is demonstrated by our implementations on top of two vision-based navigation systems. Experimental evaluations validate that the injection of semantic information associated with visual landmarks using our approach achieves substantial improvements in accuracy on GPS-denied navigation solutions for large-scale urban scenarios