Coordinated Control of a Group of Warehouse Cobots for Collaborative Cargo Transport over Various Surface Types

Motion planning for a group of mobile robots collaboratively transporting a load over non-uniform support surfaces is a challenging task. The core difficulty lies in simultaneously satisfying conflicting requirements: safe obstacle avoidance, maintaining group formation, minimizing travel time or path length, and adhering to dynamic constraints imposed by varying ground properties. This paper proposes a hybrid method that overcomes the fundamental limitations of existing approaches, such as the low computational speed of sampling-based methods (RRT*), the non-strict constraint satisfaction in reinforcement learning (RL), and the rigid smoothness requirements of classical optimal control methods. The key idea is to combine optimal control with machine learning, where a neural network model approximates the objective function — a more versatile approach compared to approximating system dynamics or environment models. Two training strategies are investigated: supervised learning for accurately reproducing an objective function and reinforcement learning (DDPG algorithm) for flexibly defining it via a reward function. Constraints, including acceleration limits dependent on the surface type, are defined analytically using a smoothed discrete space and bilinear interpolation. The optimization problem is solved using the high-performance solver FATROP, integrated with the CasADi automatic differentiation framework. Simulation results demonstrate that the proposed method outperforms a previous RRT*-based implementation, reducing trajectory computation time 58-fold and decreasing path traversal time by 20 %. The experiments also showed that reinforcement learning allows for flexibly redefining the optimization goal, finding a shorter path (8.9 m vs. 9.4 m) at the cost of a slight increase in travel time. The FATROP solver also proved to be 22 % faster than the traditional IPOPT. These results confirm the potential of the hybrid approach for multi-robot motion planning tasks, enabling the integration of complex nonlinear dependencies without a significant loss in performance.