We present object handling and transporting by a multi-robot team with a deformable sheet as a carrier. Due to the deformability of the sheet and the high dimension of the whole system, it is challenging to clearly describe all the possible positions of the object on the sheet for a given formation of the multi-robot system. A complete forward kinematics (FK) method is proposed for object handling by an $N$-mobile robot team with a deformable sheet. Based on the virtual variable cables model (VVCM), a constrained quadratic problem (CQP) is formulated by combining the geometric constraints and minimum potential energy conditions of the system. Analytical solutions to the CQP are presented and then further verified with the force closure condition. We present an FK algorithm based on the FK method to obtain all possible solutions with the given initial sheet shape and the robot team formation. We demonstrate the effectiveness, completeness, and efficiency of the FK algorithm with experimental results and case study examples.

Multi-mobile robot systems show great advantages over one single robot in many applications. However, the robots are required to form desired task-specified formations, making feasible motions decrease significantly. Thus, it is challenging to determine whether the robots can pass through an obstructed environment under formation constraints, especially in an obstacle-rich environment. Furthermore, is there an optimal path for the robots? To deal with the two problems, a novel graphbased motion planner is proposed in this paper. A mapping between workspace and configuration space of multi-mobile robot systems is first built, where valid configurations can be acquired to satisfy both formation constraints and collision avoidance. Then, an undirected graph is generated by verifying connectivity between valid configurations. The breadth-first search method is employed to answer the question of whether there is a feasible path on the graph. Finally, an optimal path will be planned on the updated graph, considering the cost of path length and formation preference. Simulation results show that the planner can be applied to get optimal motions of robots under formation constraints in obstacle-rich environments. Additionally, different constraints are considered.

Using a deformable sheet to handle objects is convenient and found in many practical applications. For object manipulation through a deformable sheet that is held by multiple mobile robots, it is a challenging task to model the object-sheet interactions. We present a computational model and algorithm to capture the object position on the deformable sheet with changing robotic team formations. A virtual variable cables model (VVCM) is proposed to simplify the modeling of the robot-sheet-object system. With the VVCM, we further present a motion planner for the robotic team to transport the object in a three-dimensional (3D) cluttered environment. Simulation and experimental results with different robot team sizes show the effectiveness and versatility of the proposed VVCM. We also compare and demonstrate the planning results to avoid the obstacle in 3D space with the other benchmark planner.