A Distributed Optimization Approach for Collaborative Object Lifting Using Multiple Aerial Robots

In the past decade, multi-robot collaborative object transport has garnered significant attention, with the majority of research targeting transport strategies. This study recasts the collaborative object lifting challenge into an optimization problem framework. Within this setup, each robot leverages a local evaluation function to determine its lifting location. Collectively, these robots strive to optimize a unified evaluation function. An intertwined equation constraint is embedded within the optimization schema, ensuring that the system's mass center remains stable throughout the lifting process. Furthermore, we impose local feasibility constraints, thereby delimiting the optimal lifting location to a specified region. This research introduces several algorithms, differentiated based on the constraints applied to robot velocity. By harnessing these algorithms, robots can autonomously pinpoint the most apt lifting location that aligns with predetermined criteria. This methodology necessitates a robot to engage in exchanges of auxiliary variables solely with its immediate peers. Noteworthily, parameters such as location, velocity, and mass are accessed in a localized manner, reinforcing data privacy and reducing communication burdens. The paper concludes with a robust mathematical validation that underscores asymptotic convergence to the exact optimal lifting location, underpinned by numerical simulations which attest to the potency of the proposed algorithms.