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Shape Space Planning for Balancing Mobile Robots

Balancing mobile robots are underactuated systems with second-order, non-integrable constraints on their dynamics that restrict the family of feasible configuration trajectories. The configuration space of any dynamic system can be divided into position and shape space. The position variables represent the position of the system in the world, whereas the shape variables are those that affect the inertia matrix of the system and dominate the system dynamics. In balancing mobile robots, the strong coupling between the position and shape dynamics makes it impossible to ignore the shape dynamics while tracking desired motions in position space. Therefore, it is necessary to plan appropriate shape space motions to achieve the desired position space motions. This work focuses on shape-accelerated balancing mobile robots like the ballbot, wherein non-zero shape configurations result in accelerations in position space.

In this work, a shape trajectory planner was developed for shape-accelerated balancing mobile robots like the ballbot, which uses just the dynamic constraint equations to plan shape trajectories, which when tracked will result in approximate tracking of desired position trajectories. The planner exploits the relationship between shape changes and acceleration in position space to plan the appropriate shape trajectories. The planner can handle systems with high-dimensional shape space and can also handle cases where a subset of the shape variables is artificially constrained. In the case of ballbot, the shape planner can plan trajectories for the body and arm angles in order to achieve desired ball motions on the floor. The planner is significantly faster than the direct collocation methods in finding feasible trajectories that best approximate the desired position space motions. Moreover, since this approach uses only the dynamic constraint equations, a subset of the equations of the motion, it is more robust to modeling uncertainties in actuator mechanisms and nonlinear friction effects.

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Related Publications

Shape Space Planner for Shape-Accelerated Balancing Mobile Robots
Umashankar Nagarajan and Ralph Hollis
International Journal of Robotics Research (IJRR), Volume 32, Issue 11, pp. 1323 – 1341, September 2013

Planning in High-dimensional Shape Space for a Single-wheeled Balancing Mobile Robot with Arms
Umashankar Nagarajan, Byungjun Kim and Ralph Hollis
IEEE International Conference on Robotics & Automation (ICRA), pp. 130 - 135, May 2012
IEEEXplore | PDF

Dynamic Constraint-based Optimal Shape Trajectory Planner for Shape-Accelerated Underactuated Balancing Systems
Umashankar Nagarajan
Robotics: Science and Systems (RSS), pp. 243 - 250, June 2010

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