This paper considers the problem of online optimal trajectory design under time-varying environments. Of particular interest is the design of energy-efficient trajectories under strong and uncertain disturbances in ocean environments and time-varying goal location. We formulate the problem within the constrained online convex optimization formalism, and a modified online gradient descent algorithm is motivated. The mobility constraints are met using a carefully chosen stepsize, and the proposed algorithm is shown to incur sublinear regret. Different from the state-of-the-art algorithms that entail planning and re-planning the full trajectory using forecast data at each time instant, the proposed algorithm is entirely online and relies mostly on the current ocean velocity measurements at the vehicle locations. The trade-off between excess delay incurred in reaching the goal and the overall energy consumption is examined via numerical tests carried out on real data obtained from the regional ocean modelling system. As compared to the state-of-the-art algorithms, the proposed algorithm is not only energy-efficient but also several orders of magnitude computationally efficient.

Robotic calibration allows for the fusion of data from multiple sensors such as odometers, cameras, etc., by providing appropriate relationships between the corresponding reference frames. For wheeled robots equipped with camera/lidar along with wheel encoders, calibration entails learning the motion model of the sensor or the robot in terms of the data from the encoders and generally carried out before performing tasks such as simultaneous localization and mapping (SLAM). This work puts forward a novel Gaussian Process-based non-parametric approach for calibrating wheeled robots with arbitrary or unknown drive configurations. The procedure is more general as it learns the entire sensor/robot motion model in terms of odometry measurements. Different from existing non-parametric approaches, our method relies on measurements from the onboard sensors and hence does not require the ground truth information from external motion capture systems. Alternatively, we propose a computationally efficient approach that relies on the linear approximation of the sensor motion model. Finally, we perform experiments to calibrate robots with un-modelled effects to demonstrate the accuracy, usefulness, and flexibility of the proposed approach.