Dynamics, Control and Planning for Cooperative Manipulation of Payloads Suspended by Cables from Multiple Quadrotor Robots

Abstract

Abstract-We address the problem of cooperative transportation of a cable-suspended payload by multiple quadrotors. In previous work, quasi-static models have been used to study this problem. However, these approaches are severely limited because they ignore the payload dynamics, and do not explicitly model the underactuation in the control problem. Thus, there are no guarantees on the payload trajectory or the cable tensions, which must be non negative. In this paper, we develop a complete dynamic model for the case when payload is a point load and for the case when the payload is a rigid body. We show in both cases the resulting system is differentially flat when the cable tensions are strictly positive. We also consider the case where the tensions are non negative (including the case with zero tensions) and establish that these systems are differentially flat hybrid systems by considering the switching dynamics induced by the unilateral tension constraints. We use the differential flatness property to find dynamically feasible trajectories for the payload+quadrotors system. We show using numerical and experimental methods that these trajectories are superior to those obtained by quasi-static models.

Dynamically Feasible Motion Planning through Partial Differential Flatness.

“…In contrast to differentially-flat hybrid systems, as defined in [21], for partially differentially-flat hybrid sys- tems, the guards may not be determined only from the flat outputs and their higher-order derivatives. Instead, r-states would need to be known, which can only be obtained through integration.…”

“…In recent years, quadrotors systems were shown to be differentially flat, leading to significant progress in trajectory generation and control of quadrotor systems. For instance, in [2], a flatness-based flight planning / replanning strategy is proposed for a quadrotor; while in [7], differential flatness of position dynamics of quadrotor is exploited to design a controller via feedforward linearization; and recently in [21], the underactuated dynamical system comprising of multiple quadrotors cooperatively carrying a cable-suspended load was shown to be differentially flat.…”

“…From equation (21) and assuming B is invertible, we getq,q, τ s as function of our flat outputs and its higher order derivatives. Thus we obtain the input torque τ s , the s-states [R, ω,q] andq as a function of our flat outputs and its higher order derivatives and if we know the initial conditions of our system, we can obtain the r-state [q] by integrating the expression forq.…”

Toward autonomous avian-inspired grasping for micro aerial vehicles

“…The capabilities of Micro Aerial Vehicles (MAVs) are rapidly expanding to include surveillance [3], construction [4], manipulation of slung loads [5], collaborative transportation [6,7], and mapping of unknown environments using aerodynamic effects [8]. However, aerial vehicles' flight durations are limited by the energy density of batteries and the speed of aerial manipulation is restricted to quasi-static interactions with the environment.…”

Control of motion and internal stresses for a chain of two underactuated aerial robots

“…Nevertheless, the physical interaction problem is becoming the center of several researches in aerial robotics, see, e.g., [3] and references therein. For example many works are done in order to exploit aerial robots for manipulation and transportation of loads [4], [5].…”