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Assistive mobile robots that can navigate autonomously can greatly benefit people with mobility impairments. Since an assistive mobile robot transports a human user from one place to another, its motion should be comfortable for human users. Moreover, it should be possible for users to customize the motion according to their comfort. While there exists a large body of work on motion planning for mobile robots, very little attention has been paid to characterizing comfort and planning comfortable trajectories. In this paper, we first characterize comfortable motion by formulating a measure of discomfort as a weighted sum of the total travel time and time integrals of various kinematic quantities. We then present a method for factoring the weights such that once a user has customized the weights for one task, the same choice of weights leads to similar average value of the discomfort measure in other tasks. We seek trajectories that minimize the discomfort and satisfy boundary conditions on pose, velocity and acceleration. Such a problem can naturally be formulated as a variational optimization problem. Unlike previous work, we present a comprehensive formulation that allows the travel time to be unspecified and includes boundary conditions on position, orientation, velocity and acceleration. This makes the formulation very general as it can be used to compute trajectories for various kinds of tasks, such as starting from rest, coming to rest, moving from one specified velocity to another, arriving at a goal with a specified orientation etc. Finally, we present a fast and robust numerical method for solving the minimization problem.

This paper describes the 2008 and 2009 Antarctic deployments of the National Aeronautics and Space Administration ENDURANCE autonomous underwater vehicle (AUV). The goal of this project was to conduct three autonomous tasks beneath the ice cap 4 m thick of West Lake Bonney: first, to measure the three-dimensional (3D) water chemistry of the lake at prespecified coordinates; second, to map the underwater face of the Taylor Glacier; third, to chart the bathymetry of the lake bottom. At the end of each mission the AUV had to locate and return through a hole in the ice slightly larger than the outer diameter of the vehicle. During two 10-week deployments to Antarctica, in the austral summers of 2008 and 2009, ENDURANCE logged 243 h of sub-ice operational time, conducted 275 aqueous chemistry sonde casts, completed a 3D bathymetry survey over an area of 1.06 km 2 at a resolution of 22 cm, and traversed 74 km beneath the ice cap of West Lake Bonney. Many of the characteristics and capabilities of ENDURANCE are similar to the behaviours that will be needed for sub-ice autonomous probes to Europa, Enceladus, and other outer-planet icy moons. These characteristics are also of great utility for terrestrial operations in which there is a need for an underwater vehicle to manoeuvre precisely to desired positions in 3D space or to manoeuvre and explore complicated 3D environments.