We propose a novel quadratic programming formulation for estimating the corruption levels in group synchronization, and use these estimates to solve this problem. Our objective function exploits the cycle consistency of the group and we thus refer to our method as detection and estimation of structural consistency (DESC). This general framework can be extended to other algebraic and geometric structures. Our formulation has the following advantages: it can tolerate corruption as high as the information-theoretic bound, it does not require a good initialization for the estimates of group elements, it has a simple interpretation, and under some mild conditions the global minimum of our objective function exactly recovers the corruption levels. We demonstrate the competitive accuracy of our approach on both synthetic and real data experiments of rotation averaging.

Mobile robots in unstructured, mapless environments must rely on an obstacle avoidance module to navigate safely. The standard avoidance techniques estimate the locations of obstacles with respect to the robot but are unaware of the obstacles’ identities. Consequently, the robot cannot take advantage of semantic information about obstacles when making decisions about how to navigate. We propose an obstacle avoidance module that combines visual instance segmentation with a depth map to classify and localize objects in the scene. The system avoids obstacles differentially, based on the identity of the objects: for example, the system is more cautious in response to unpredictable objects such as humans. The system can also navigate closer to harmless obstacles and ignore obstacles that pose no collision danger, enabling it to navigate more efficiently. We validate our approach in two simulated environments: one terrestrial and one underwater. Results indicate that our approach is feasible and can enable more efficient navigation strategies.