Motion planning for self-reconfiguring robotic systems
Larkworthy, Thomas James
Robots that can actively change morphology offer many advantages over fixed shape, or monolithic, robots: flexibility, increased maneuverability and modularity. So called self-reconfiguring systems (SRS) are endowed with a shape changing ability enabled by an active connection mechanism. This mechanism allows a mechanical link to be engaged or disengaged between two neighboring robotic subunits. Through utilization of embedded joints to change the geometry plus the connection mechanism to change the topology of the kinematics, a collection of robotic subunits can drastically alter the overall kinematics. Thus, an SRS is a large robot comprised of many small cooperating robots that is able to change its morphology on demand. By design, such a system has many and variable degrees of freedom (DOF). To gain the benefits of self-reconfiguration, the process of morphological change needs to be controlled in response to the environment. This is a motion planning problem in a high dimensional configuration space. This problem is complex because each subunit only has a few internal DOFs, and each subunit's range of motion depends on the state of its connected neighbors. Together with the high dimensionality, the problem may initially appear to be intractable, because as the number of subunits grow, the state space expands combinatorially. However, there is hope. If individual robotic subunits are identical, then there will exist some form of regularity in the resulting state space of the conglomerate. If this regularity can be exploited, then there may exist tractable motion planning algorithms for self-reconfiguring system. Existing approaches in the literature have been successful in developing algorithms for specific SRSs. However, it is not possible to transfer one motion planning algorithm onto another system. SRSs share a similar form of regularity, so one might hope that a tool from mathematical literature would identify the common properties that are exploitable for motion planning. So, while there exists a number of algorithms for certain subsets of possible SRS instantiations, there is no general motion planning methodology applicable to all SRSs. In this thesis, firstly, the best existing general motion planning techniques were evaluated to the SRS motion planning problem. Greedy search, simulated annealing, rapidly exploring random trees and probabilistic roadmap planning were found not to scale well, requiring exponential computation time, as the number of subunits in the SRS increased. The planners performance was limited by the availability of a good general purpose heuristic. There does not currently exist a heuristic which can accurately guide a path through the search space toward a far away goal configuration. Secondly, it is shown that a computationally efficient reconfiguration algorithms do exist by development of an efficient motion planning algorithm for an exemplary SRS, the Claytronics formulation of the Hexagonal Metamorphic Robot (HMR). The developed algorithm was able to solve a randomly generated shape-to-shape planning task for the SRS in near linear time as the number of units in the configuration grew. Configurations containing 20,000 units were solvable in under ten seconds on modest computational hardware. The key to the success of the approach was discovering a subspace of the motion planning space that corresponded with configurations with high mobility. Plans could be discovered in this sub-space much more readily because the risk of the search entering a blind alley was greatly reduced. Thirdly, in order to extract general conclusions, the efficient subspace, and other efficient subspaces utilized in other works, are analyzed using graph theoretic methods. The high mobility is observable as an increase in the state space's Cheeger constant, which can be estimated with a local sampling procedure. Furthermore, state spaces associated with an efficient motion planning algorithm are well ordered by the graph minor relation. These qualitative observations are discoverable by machine without human intervention, and could be useful components in development of a general purpose SRS motion planner compiler.
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