Multi-Nonholonomic Robot Object Transportation with Obstacle Crossing Using a Deformable Sheet

In this paper, we address multi-robot formation planning where nonholonomic robots collaboratively transport objects using a deformable sheet in unstructured, cluttered environments. The formation can expand or contract to adjust the height of the object on the sheet. However, interactions between the robots and sheet introduce complex constraints for formation planning. Complexity increases further when the only feasible solution requires crossing an obstacle, i.e. where robots navigate in different homotopy classes around an obstacle such that the object hovers above it. Most existing nonholonomic formation planners do not admit obstacle crossing, limiting performance. In this paper, we present a two-stage iterative trajectory optimization framework which explicitly considers obstacle crossing. First, we capture the set of all feasible homotopy classes for each robot using a topological probabilistic roadmap. We then iteratively apply numerical optimization techniques to find a safe and feasible solution for the formation. We demonstrate the efficacy of our framework in simulation and on real robot hardware.