Robust Cooperative Manipulation Without Force/Torque Measurements: Control Design and Experiments

Abstract

This paper presents two novel control methodologies for the cooperative manipulation of an object by N robotic agents. Firstly, we design an adaptive control protocol which employs quaternion feedback for the object orientation to avoid potential representation singularities. Secondly, we propose a control protocol that guarantees predefined transient and steadystate performance for the object trajectory. Both methodologies are decentralized, since the agents calculate their own signals without communicating with each other, as well as robust to external disturbances and model uncertainties. Moreover, we consider that the grasping points are rigid, and avoid the need for force/torque measurements. Load distribution is also included via a grasp matrix pseudo-inverse to account for potential differences in the agents' power capabilities. Finally, simulation and experimental results with two robotic arms verify the theoretical findings.

Asymptotic Stability of Uncertain Lagrangian Systems with Prescribed Transient Response

“…where γ d > 0 is a positive constant gain. Remark 1: The control design procedure follows closely the prescribed performance backstepping-like methodology of the previous works [11]- [13], [16], introduced in [31]. The desired signals and control laws in these works consist only of proportional terms with respect to the transformed errors ε p , ε v , which are guaranteed to be ultimately bounded.…”

“…Funnel control is a high-gain control scheme that usually does not use any information on the system model, and has had numerous applications during the last years. Examples include chemical reactors [9], robotic manipulation [10], [11], vehicle platooning [12], temporal logic planning [13], and multi-agent systems [14]- [16]. Intuitively, funnel control design is based on an adaptive gain, which increases to infinity as the system state approaches the funnel boundary, "pushing" in that way the state to remain in the funnel, by also compensating for the (possibly unknown) dynamics.…”

Fully Distributed Cooperation for Networked Uncertain Mobile Manipulators

“…Theorem 1: As for the cooperative task allocation to the mobile manipulators, the proposed distributed estimation law (22) with the trajectory parameter updating law (23) guarantee the estimation error convergence of desired allocated task trajectory, i.e. δ i =x d,i − T ti − x td → 0 andδ i → 0.…”

“…To verify the efficacy of the distributed cooperative task allocation (22), we define the first Lyapunov function candidate as…”

Adaptive Leader-Follower Coordination of Lagrangian Multi-Agent Systems under Transient Constraints

“…The terms M i , C i and g i are continuous in their arguments, the terms f i are Lebesgue measurable and locally bounded, and d i are uniformly bounded. Moreover, we consider that the dynamic terms M i , C i , and g i include unknown constant dynamic parameters of the agents (e.g., masses, moments of inertia), denoted by the vectors θ i ∈ R , ∈ N, ∀i ∈ N , and satisfy the following well-known properties [31]:…”