Shilpa Gulati. 2011.
A Framework for Characterization and Planning of Safe, Comfortable, and
Customizable Motion of Assistive Mobile Robots
Doctoral dissertation, Mechanical Engineering Department, University of Texas at Austin.
Assistive mobile robots, such as intelligent wheelchairs, that can navigate autonomously in response to high level commands from a user can greatly help people with cognitive and physical disabilities by increasing their mobility. In this work, we address the problem of safe, comfortable, and customizable motion planning of such assistive mobile robots.
We recognize that for an assistive robot to be acceptable to human users, its motion should not only be safe, it should also be comfortable. Further, different users should be able to customize the motion according to their comfort. We formalize the notion of motion comfort as a discomfort measure that can be minimized to compute comfortable trajectories, and identify several properties that a trajectory must have for the motion to be comfortable. We develop a motion planning framework for planning safe, comfortable, and customizable trajectories in small-scale space. This framework removes the limitations of existing methods, none of which can compute trajectories with all the properties necessary for comfort.
We formulate a discomfort cost functional as a weighted sum of total travel time, time integral of squared tangential jerk, and time integral of squared normal jerk. We then define the problem of safe and comfortable motion planning as that of minimizing this discomfort such that the trajectories satisfy boundary conditions on configuration and its higher derivatives, avoid obstacles, and satisfy dynamic constraints. This description is transformed into a precise mathematical problem statement using a general non-linear constrained optimization approach. The main idea is to formulate a well-posed infinite-dimensional optimization problem and discretize it into a finite-dimensional problem in an appropriate function space for a numerical solution.
Our approach consists of the following steps. First, since the cost functional is a weighted sum of dimensionally different terms, we determine the weights by dimensional analysis. Next, we choose a scaled arc-length parameterization of the trajectory that results in relatively simple expressions for the cost functional and other dynamic quantities. Then, we analyze the cost functional to determine the appropriate space in which it should be discretized to be mathematically meaningful. We also perform analysis of boundary conditions to determine the boundary conditions that should be imposed for the problem to be well-posed. Next, we choose a representation of obstacles as piecewise smooth star-shaped domains and incorporate obstacle-avoidance constraints. To numerically solve the infinite-dimensional optimization problem, we use a conforming finite-element discretization to convert it into a finite-dimensional problem. Finally, we develop a method for computing good initial guesses for the above nonlinear optimization problem.
We also outline a method by which a user may customize the motion and present some guidelines for conducting human user studies to validate and/or refine the discomfort measure presented in this work.
Results show that our framework is capable of reliably planning trajectories that have all the properties necessary for comfort. We believe that our work is an important step in developing autonomous assistive robots that are acceptable to human users.