Reconfiguration-Complete Motion Primitives with Constructive Planning for Deformable Planar Modular Robots

We study centralized reconfiguration problems for geometric amoebot structures. A set of $n$ amoebots occupy nodes on the triangular grid and can reconfigure via expansion and contraction operations. We focus on the joint movement extension, where amoebots may expand and contract in parallel, enabling coordinated motion of larger substructures. Prior work introduced this extension and analyzed reconfiguration under additional assumptions such as metamodules. In contrast, we investigate the intrinsic dynamics of reconfiguration without such assumptions by restricting attention to centralized algorithms, leaving distributed solutions for future work. We study the reconfiguration problem between two classes of amoebot structures $A$ and $B$: For every structure $S\in A$, the goal is to compute a schedule that reconfigures $S$ into some structure $S'\in B$. Our focus is on sublinear-time algorithms. We affirmatively answer the open problem by Padalkin et al. (Auton. Robots, 2025) whether a within-the-model sublinear-time universal reconfiguration algorithm is possible, by proving that any structure can be reconfigured into a canonical line-segment structure in $O(\sqrt{n}\log n)$ rounds. Additionally, we give a constant-time algorithm for reconfiguring any spiral structure into a line segment. These results are enabled by new constant-time primitives that facilitate efficient parallel movement. Our findings demonstrate that the joint movement model supports sublinear reconfiguration without auxiliary assumptions. A central open question is whether universal reconfiguration within this model can be achieved in polylogarithmic or even constant time.

Research in modular robotics has produced capable approaches allowing a robot's morphology to change online, with recent efforts also developing approaches to decide which morphology to assume and automatically propagate that decision into the robot's motion planning and control. These approaches are powerful and increase adaptability in the field. However, an alternative objective is not to build robots whose structures can change, but robots whose fundamental capabilities can change, where capability is a joint function across several domains, including kino-dynamics, perception, compute, and high-level coordinating behaviors. A robot designed to be reconfigured across these domains has a greater capacity to alter its capability than one that can be reconfigured in a single domain. We refer to this cross-domain reconfigurability as integration span, and recognize a complementary measure of the resistance to reconfiguration, which we refer to as integration inertia. Current modular robots have reduced integration inertia in the structural domain while it remains high in the other domains that contribute to integration span. We assert that the systems that can provide the most utility through reconfiguration in practice are those maximizing span and minimizing inertia and call this general problem recompositional robotics: adaptation over a heterogeneous set of modules including hardware, software, compute, and behavior that abstracts each component by the interfaces it requires and provides such that they can be reasoned over holistically. We define the problem, ground it in two deployed systems and active research efforts, and pose open questions about the future of recompositional robotics.

We propose a workspace-fibered decomposition framework for motion planning in nR planar redundant manipulators operating in cluttered environments. Rather than planning directly in the full n-dimensional configuration space, the method incrementally constructs obstacle-constrained reachable workspaces of lower-dimensional non-redundant sub-chains and recursively lifts them through redundant orientation fibers. This yields a sequence of reduced planning manifolds that preserve branch-consistent reachability structure while avoiding explicit construction of the full configuration-space obstacle geometry. We first establish that, for planar position-only manipulators, the obstacle-constrained reachable workspace induced by the minimal non-redundant sub-chain provides an exact characterization of feasibility with respect to the connected component of the start configuration, enabling early infeasibility detection prior to introducing redundant degrees of freedom (DOF). We then introduce an incremental fiber-lifting procedure that propagates reachable workspace structure through successive redundant links while enforcing local inverse-kinematic branch consistency using Jacobian determinant continuity constraints. The resulting representation admits efficient reduced-space planning directly on recursively-constructed workspace-fiber manifolds. Experimental results on redundant nR planar manipulators demonstrate that the proposed construction preserves collision-free connectivity structure across successive lifting stages while substantially reducing collision checking complexity relative to direct configuration space reasoning.