A Framework for Characterization, Planning, and Evaluation of Safe, Comfortable and Customizable Motion of Assistive Mobile Robots (Dissertation Proposal)

Assistive mobile robots that can navigate autonomously can greatly benefit people with mobility impairments. Several important problems need to be addressed for developing such an autonomous robot. This research focuses on one such problem, namely, motion planning in small-scale space. Small-scale space is space within the robot’s sensory horizon. Motion planning consists of finding a time-parameterized robot pose function, called a trajectory, given the initial and final state such that the path of the robot does not intersect any obstacles. In addition, the trajectory should satisfy kinematic and dynamic constraints resulting from engineering limitations and comfort requirements. This is a challenging problem and has received significant attention. There are two main paradigms for motion planning. In decoupled motion planning, first a collision-free geometric path is planned and then a timing function to determine the motion on the path is computed. This decoupling of dynamics from path planning may result in a path that is not dynamically realizable by the robot. In direct trajectory planning, a trajectory that satisfies the kinematic and dynamic constraints is directly computed. For direct trajectory planning, two approaches that have been found to be of practical use are sampling based methods and variational methods. Sampling based methods rely on a discretization of the state space or the control space or both. While discretization allows efficient construction of trajectories starting from an initial state, the resolution of the discretization determines the accuracy with which a trajectory may reach a goal state. Variational methods can find trajectories that exactly connect specified initial and final states and are optimal with respect to some performance measure. These methods have been applied to motion planning for mobile robots under various limiting assumptions and have largely ignored the presence of obstacles. Several considerations preclude a straightforward application of existing direct trajectory planning methods to assistive mobile robots. These considerations arise from the fact that an assistive robot is expected to transport a human user from one place to another. These considerations include the requirements that the trajectory be computed in real-time, that the safety of a user be assured, and that the goal state boundary conditions be exactly satisfied. Further, the motion should not only be safe, it should also be comfortable and customizable by multiple users. This research formally characterizes comfortable motion and develops a framework for safe and comfortable motion planning. We formulate a measure of discomfort as a weighted sum of total travel-time and time integrals of derivatives of robot pose. We use dimensional analysis to determine the weights. Each weight is factored into two parts – a characteristic weight that is a function of the length and velocity scales of the task, and a dimensionless multiplicative factor that can be customized by a user. For motion planning, we propose a hybrid approach. First, an efficient path-planning algorithm is used to find a geometric path in space. Then, this path is used to generate a trajectory that serves as an initial guess for a variational optimization problem. The variational optimization problem consists of minimizing a measure of discomfort to find optimal trajectories. We perform a comprehensive analysis of boundary conditions and propose a robust and efficient solution method. Results show fast convergence to a minimum for a variety of boundary conditions. The characteristic weights determined using dimensional analysis result in similar average values of the discomfort measure for different boundary conditions. We have implemented a version of the proposed hybrid approach on a robotic wheelchair. A fast updating local perceptual map, constructed using laser and vision sensors, forms the representation of the local surround. An existing path-planing algorithm uses this representation to find collision-free paths. These paths are used to instantiate a set of boundary value problems for the variational trajectory planner. Preliminary results on a few tasks in indoor and outdoor environments show that the resulting wheelchair motion is safe. The paths look natural and the motion appears comfortable – this will be confirmed by human evaluations in future work. In our current implementation, while the path-planning algorithm finds collision free paths, the trajectory computed by the variational minimization method can potentially intersect obstacles. This is because we have not formulated the variational problem to account for obstacles. Future work consists of formulating the variational minimization problem to include obstacles as constraints such sthat a collision would require violation of a constraint. Finally, human subjects will ride the wheelchair and evaluate the planning framework. This study is expected to confirm that the wheelchair motion is comfortable, can be customized according to user preferences, and that customization in one task results in acceptable performance in other tasks. Part of the work presented in this proposal has been presented in the following articles: • S. Gulati, C. Jhurani, B. Kuipers and R. Longoria. A framework for planning comfortable and customizable motion of an assistive mobile robot. In IEEE/RSJ International Conference on Intelligent Robots and Systems, 2009. To appear. • A. Murarka, S. Gulati, P. Beeson, and B. Kuipers. Towards a safe, low-cost, intelligent wheelchair. Workshop on Planning, Perception and Navigation for Intelligent Vehicles (PPNIV), 2009. To appear. • S. Gulati and B. Kuipers. High performance control for graceful motion of an intelligent wheelchair. In IEEE International Conference on Robotics and Automation, pages 3932-3938, 2008.