Iterative optimal feedback control design under relaxed rigidity constraints for multi-robot cooperative manipulation

Abstract

Abstract-Cooperative manipulation of multiple robots presents an interesting control application scenario of coupled dynamical systems with a common goal. Here, we treat the problem of moving a formation of physically interconnected robots to a desired goal while maintaining the formation. This control problen is for example relevant in cooperative transport of an object from an initial to a final configuration by mobile robotic manipulators. To achieve the control goal we formulate an LQR-like optimal control problem that, in addition to goal regulation and minimization of input energy, includes the formation rigidity constraint in a relaxed form expressed as a biquadratic penalty term. The control problem is solved by two different iterative algorithms, a gradient descent using adjoint states and a quasi-Newton method, that determine a static linear state-feedback matrix. The proposed control design and the iterative algorithms are validated and compared in numerical simulations showing the efficacy of both approaches.

Deformation-based shape control with a multirobot system

“…Precise knowledge of object deformation is not a fundamental consideration for some multirobot manipulation approaches which deal with objects that are either essentially rigid [1], [3], [5]- [9] or, on the other hand, highly deformable. In the latter case, it may be sufficient to simply respect upper and lower inter-robot distance bounds [10], [11].…”

“…Compared to a single robot, a multirobot team can manipulate larger and heavier objects and provide more refined and precise behaviors. The team's actions when manipulating a rigid or deformable body must be carefully coordinated, to avoid damaging it and encountering unpredictable motions [1]- [3]. In particular, the robots typically need to ensure that the object remains close to a desired state.…”

Dynamic Movement Primitives for cooperative manipulation and synchronized motions

“…without exerting excessive forces. If the robots are able to maintain a rigid formation, , the internal forces are significantly reduced [1]. In order to achieve successful task execution, a flexible, robust, and distributed control mechanism is required.…”

Formation-based approach for multi-robot cooperative manipulation based on optimal control design

“…. ∈ R E which is required to satisfy f (x) = p. Identical to (10) and (14), the state variable x is concenated by x i and also contains the manipulator positions ξ i . Here, p = .…”

“…Our proposed controller is evaluated in experiments and its benefit for cooperative tasks is shown. For a theoretical treatment using numerical investigations of iterative control design under relaxed rigidity we refer to [10].…”