Asymptotically Optimal Kinodynamic Motion Planning for a Class of Modular Self-Reconfigurable Robots

Self-reconfigurable robots are composed of many individual modules that can autonomously move to transform the shape and structure of the robot. The task of selfreconfiguration, transforming a set of modules from one arrangement to another specified arrangement, is a key problem for these robots and has been heavily studied. However, consideration of this problem has typically been limited to kinematics and so in this work we introduce analysis of dynamics for the problem. We characterize optimal reconfiguration movements in terms of basic laws of physics relating force, mass, acceleration, distance traveled, and movement time. A key property resulting from this is that through the simultaneous application of constant-bounded forces by a system of modules, certain modules in the system can achieve velocities exceeding any constant bounds. This delays some modules in order to accelerate others. To exhibit the significance of simultaneously considering both kinematic and dynamics bounds, we consider the following “x-axis to y-axis” reconfiguration problem. Given a horizontal row of n modules, reconfigure that collection into a vertical column of n modules. The goal is to determine the sequence of movements of the modules that minimizes the movement time needed to achieve the desired reconfiguration of the modules. In this work we prove tight Θ( √ n) upper and lower bounds on the movement time for the above reconfiguration problem. Prior work on reconfiguration problems which focused only on kinematic constraints kept a constant velocity bound on individual modules and so required time linear in n to complete problems of this type.