PASSIVITY-BASED CONTROL OF MULTIPLE QUAD-COPTERS WITH A CABLE-SUSPENDED PAYLOAD

Abstract

This thesis proposes several motion controllers to allow multiple quad-copters cooperatively carry a cable-suspended payload. The problem is motivated by a desire for developing a resilient scalable delivery vehicle that can be easily customized to its payload. The control problem poses a number of challenges that complicate its design. These include the quad-copter under-actuation, non-rigidity of the cables that connect the payload to the copters, external disturbances, potential for inter-drone collisions, and communication time-delay among the quad-copters. Simple robust controllers with guaranteed stability are highly desirable in such safety critical applications. In this thesis, the energetic passivity property of the multi-body system combining the quad-copters, cables and payload is employed to design novel motion controllers for the system. These controllers make no assumption about the tension status of the cables since this property holds whether the cables are in tension or not. The design and stability analysis of the controllers rely on storage functions inspired by the physical energy of the system. Quad-copters are able to produce thrust force only along their propellers' axis. This under-actuation prevents direct application of passivity-based controllers to the system under study. A cascade control structure with an outer-loop position control and an inner-loop attitude control is employed to deal with the under-actuation. The first proposed controller assumes that the cables are attached to the quadcopters center of masses (COMs). This helps decouple the angular dynamics of the quad-copters from the rest of the dynamics. As a result, the inner-loop attitude controllers can be designed independently. First, angular controllers with exponentially stable tracking errors are considered. While this produces nice theoretical results, it requires measurements of linear acceleration and jerk, limiting its practical use. Then, a modified cascade control structure is proposed that takes into account the under-actuation and only needs measurements that are typically available in such systems. Semi-global stability of the closed-loop system is shown, where the region of attraction can be made arbitrary large by proper choice of control gains. An energy observer/compensator is proposed to estimate perturbation-induced energy and dissipate it through time-varying dampers. This helps suppress disturbance-induced oscillations in the system response. The proposed controller is further revised to allow the cables be attached to the quad-copters and the payload at arbitrary points. This controller is augmented with an inter-drone collision avoidance term to prevent potential collisions among the drones. Another variation of the controller is developed by introducing inter-drone coupling terms meant to improve the controller ability to preserve the formation shape of the quad-copters. These coupling terms could potentially introduce time delay into some of the feedback signal paths. An analysis is carried out to establish conditions that the controller gains must satisfy in order to ensure closed-loop stability in the presence of these time delays. The final contribution of this thesis focuses on the design of the reference positions for the quad-copters for the use in the controllers introduced earlier. In the proposed approach, the user specifies the desired position and orientation for the payload. Given this desired pose, an optimization problem is formulated to find a set of reference positions for the quad-copters that would minimize the total power consumed under quasi-static conditions. The proposed controllers have been successfully evaluated in an indoor laboratory setting using measurements from a motion capture system and on-board IMUs. Results of the experiments are provided throughout the thesis.