Timed abstractions for distributed cooperative manipulation

Abstract

This paper addresses the problem of deriving well-defined timed abstractions for the decentralized cooperative manipulation of a single object by N robotic agents. In particular, we propose a distributed model-free control protocol for the trajectory tracking of the cooperatively manipulated object without necessitating feedback of the contact forces/torques or inter-agent communication. Certain prespecified performance functions determine the transient and steady state of the coupled object-agents system. The latter, along with a region partition of the workspace that depends on the physical volume of the object and the agents, allows us to define timed transitions for the coupled system among the derived workspace regions. Therefore, we abstract its motion as a finite transition system and, by employing standard automata-based methodologies, we define high level complex tasks for the object that can be encoded by This is one of the several papers published in Autonomous Robots comprising the Special Issue on Online Decision Making in Multi-Robot Coordination.

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

“…Moreover, the joint torques in both control schemes respect the saturation values we set. For comparison purposes, we also simulate the same system by using the Prescribed Performance Control methodology of [46], without taking into account any input constraints, since the input constraint analysis of Appendix A is not performed in [46]. In order to achieve good performance in terms of overshoot, rise, and settling time, we set the control gains as g s = 1, g v = 200.…”

“…The first control scheme is an extension of our preliminary work [45], where we designed a similar adaptive quaternionbased controller, guaranteeing, however, only local stability, and no experimental validation was provided. Furthermore, we have employed the PPC scheme in our previous work [46] to design timed transition systems for a cooperatively manipulated object. In this work, however, we perform a more extended and detailed analysis by deriving specific bounds for the inputs of the robotic arms (i.e., joint velocities and torques), as well as real-time experiments.…”

“…The aforementioned analysis of the Prescribed Performance Control methodology reveals the derivation of bounds for the velocity v i and control input u i of each agent. In contrast to our previous work [46], we derive in Appendix A explicit boundsv i andū i for v i and u i (see (55), (56)), respectively, which depend on the control gains, the bounds of the dynamic terms, the desired trajectory, and the performance functions. Therefore, given desired bounds for the agents' velocityv i,b and inputū i,b (derived from bounds on the joint velocities and torquesq i , τ i , respectively) and that the upper bounds of the dynamic terms are known, we can tune appropriately the control gain g s , g v as well as the parameters ρ s k ,0 , ρ v k ,0 , ρ s k ,∞ , ρ v k ,∞ , l s k , l v k in order to achievev i ≤v i,b ,ū i ≤ū i,b , ∀i ∈ N .…”

“…Simulation results for the controller of Section IV-B, and of[46]; Top: The position errors e sx (t), e sy (t), e sz (t) (with blue and green, respectively) along with the respective performance functions (with red); Bottom: The orientation errors e s φ (t), e s θ (t), e s ψ (t) (with blue and green, respectively) along with the respective performance functions (with red), ∀t ∈ [0, 40]. Zoomed versions of the transient and steady state response have been included for all plots.…”

Asymptotic Stability of Uncertain Lagrangian Systems with Prescribed Transient Response

“…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.…”