We consider the planning and control of multiple aerial robots manipulating and transporting a payload in three dimensions via cables. Individual robot control laws and motion plans enable the control of the payload (position and orientation) along a desired trajectory. We address the fact that robot configurations may admit multiple payload equilibrium solutions by developing constraints for the robot configuration that guarantee the existence of a unique payload pose. Further, we formulate individual robot control laws that enforce these constraints and enable the design of non-trivial payload motion plans. Finally, we propose two quality measures for motion plan design that minimize individual robot motion and maximize payload stability along the trajectory. The methods proposed in the work are evaluated through simulation and experimentation with a team of three quadrotors.

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Abstract-In this paper we study the problem of manipulating and transporting multiple objects on the plane using a cable attached at each end to a mobile robot. This problem is motivated by the use of boats with booms in skimming operations for cleaning oil spills or removing debris on the surface of the water. The goal in this paper is to automate the task of separating the objects of interest from a collection of objects by manipulating them with cables that are actuated only at the ends, and then transporting them to specified destinations. Because the cable is flexible, the shape of the cable must be explicitly modeled in the problem. Further, the robots must cooperatively plan motions to achieve the required cable shape and gross position/orientation to separate the objects of interest and then transport them as specified. The theoretical foundation for the problem is derived from topological invariants, homology and homotopy. We first derive the necessary topological conditions for achieving the desired separation of objects. We then propose a distributed search-based planning technique for finding optimal robot trajectories for separation and transportation. We demonstrate the applicability of this method using a dynamic simulation platform with explicit models of the cable dynamics, the contact between the cable and one or more objects, and the surface drag on the cable and on the objects. We also describe our preliminary efforts to develop an experimental platform consisting of a system of two cooperating autonomous boats.

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This paper addresses the forward and inverse kinematics of payloads carried by aerial robots. We address the cases with one, two, and three aerial robots and derive the kinematics and conditions for stable static equilibrium. For the case with one or two robots, we can establish the maximum number of equilibrium positions. The three-robot case is seen to be much harder primarily because of the non-negative tension constraints. We restrict the set of possible solutions to the forward and inverse problems by considering the equations of static equilibrium and kinematic constraints. Analytic and numeric methods to determine equilibrium configurations and stability are presented.

Abstract-In this paper we study the problem of manipulating and transporting multiple objects on the plane using a cable attached at each end to a mobile robot. This problem is motivated by the use of boats with booms in skimming operations for cleaning oil spills or removing debris on the surface of the water. The goal in this paper is to automate the task of separating the objects of interest from a collection of objects by manipulating them with cables that are actuated only at the ends, and then transporting them to specified destinations. Because the cable is flexible, the shape of the cable must be explicitly modeled in the problem. Further, the robots must cooperatively plan motions to achieve the required cable shape and gross position/orientation to separate the objects of interest and then transport them as specified. The theoretical foundation for the problem is derived from topological invariants, homology and homotopy. We first derive the necessary topological conditions for achieving the desired separation of objects. We then propose a distributed search-based planning technique for finding optimal robot trajectories for separation and transportation. We demonstrate the applicability of this method using a dynamic simulation platform with explicit models of the cable dynamics, the contact between the cable and one or more objects, and the surface drag on the cable and on the objects. We also describe our preliminary efforts to develop an experimental platform consisting of a system of two cooperating autonomous boats.