Lagrangian systems represent a wide range of robotic systems, including manipulators, wheeled and legged robots, and quadrotors. Inverse dynamics control and feedforward linearization techniques are typically used to convert the complex nonlinear dynamics of Lagrangian systems to a set of decoupled double integrators, and then a standard, outer-loop controller can be used to calculate the commanded acceleration for the linearized system. However, these methods typically depend on having a very accurate system model, which is often not available in practice. While this challenge has been addressed in the literature using different learning approaches, most of these approaches do not provide safety guarantees in terms of stability of the learning-based control system. In this paper, we provide a novel, learning-based control approach based on Gaussian processes (GPs) that ensures both stability of the closed-loop system and high-accuracy tracking. We use GPs to approximate the error between the commanded acceleration and the actual acceleration of the system, and then use the predicted mean and variance of the GP to calculate an upper bound on the uncertainty of the linearized model. This uncertainty bound is then used in a robust, outer-loop controller to ensure stability of the overall system. Moreover, we show that the tracking error converges to a ball with a radius that can be made arbitrarily small. Furthermore, we verify the effectiveness of our approach via simulations on a 2 degree-offreedom (DOF) planar manipulator and experimentally on a 6 DOF industrial manipulator.

Unmanned Aerial Vehicles (UAVs) have opened a wide range of opportunities and applications in different sectors including construction. Such applications include: 3D mapping from 2D images and video footage, automated site inspection, and performance monitoring. All of the above-mentioned applications perform well outdoors where GPS is quite reliable for localization and navigation of UAV's. Indoor localization and consequently indoor navigation have remained relatively untapped, because GPS is not sufficiently reliable and accurate in indoor environments. This paper presents a method for localization of aerial vehicles in GPSdenied indoor construction environments. The proposed method employs AprilTags that are linked to previously known coordinates in the 3D building information model (BIM). Using cameras on-board the UAV and extracting the transformation from the tag to the camera's frame, the UAV can be localized on the site. It can then use the previously computed information for navigation between critical locations on construction sites. We use an experimental setup to verify and validate the proposed method by comparing with an indoor localization system as the ground truth. Results show that the proposed method is sufficiently accurate to perform indoor navigation. Moreover, the method does not intensify the complexity of the construction execution as the tags are simply printed and placed on available surfaces at the construction site.

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