77 research outputs found
Differential-Flatness and Control of Quadrotor(s) with a Payload Suspended through Flexible Cable(s)
We present the coordinate-free dynamics of three different quadrotor systems
: (a) single quadrotor with a point-mass payload suspended through a flexible
cable; (b) multiple quadrotors with a shared point-mass payload suspended
through flexible cables; and (c) multiple quadrotors with a shared rigid-body
payload suspended through flexible cables. We model the flexible cable(s) as a
finite series of links with spherical joints with mass concentrated at the end
of each link. The resulting systems are thus high-dimensional with high
degree-of-underactuation. For each of these systems, we show that the dynamics
are differentially-flat, enabling planning of dynamically feasible
trajectories. For the single quadrotor with a point-mass payload suspended
through a flexible cable with five links (16 degrees-of-freedom and 12
degrees-of-underactuation), we use the coordinate-free dynamics to develop a
geometric variation-based linearized equations of motion about a desired
trajectory. We show that a finite-horizon linear quadratic regulator can be
used to track a desired trajectory with a relatively large region of
attraction
AutoTrans: A Complete Planning and Control Framework for Autonomous UAV Payload Transportation
The robotics community is increasingly interested in autonomous aerial
transportation. Unmanned aerial vehicles with suspended payloads have
advantages over other systems, including mechanical simplicity and agility, but
pose great challenges in planning and control. To realize fully autonomous
aerial transportation, this paper presents a systematic solution to address
these difficulties. First, we present a real-time planning method that
generates smooth trajectories considering the time-varying shape and non-linear
dynamics of the system, ensuring whole-body safety and dynamic feasibility.
Additionally, an adaptive NMPC with a hierarchical disturbance compensation
strategy is designed to overcome unknown external perturbations and inaccurate
model parameters. Extensive experiments show that our method is capable of
generating high-quality trajectories online, even in highly constrained
environments, and tracking aggressive flight trajectories accurately, even
under significant uncertainty. We plan to release our code to benefit the
community.Comment: Accepted by IEEE Robotics and Automation Letter
A framework to design interaction control of aerial slung load systems: transfer from existing flight control of under-actuated aerial vehicles
This paper establishes a framework within which interaction control is designed for the aerial slung load system composed of an underactuated aerial vehicle, a cable and a load. Instead of developing a new control law for the system, we propose the interaction control scheme by the controllers for under-actuated aerial systems. By selecting the deferentially flat output as the configuration, the equations of motion of the two systems are described in an identical form. The flight control task of the under-actuated aerial vehicle is thus converted into the control of the aerial slung load system. With the help of an admittance filter, the compliant trajectory is generated for the load subject to external interaction force. Moreover, the convergence of the whole system is proved by using the boundedness of the tracking error of vehicle attitude tracking as well as the estimation error of external force. Based on the developed theoretical results, an example is provided to illustrate the design algorithm of interaction controller for the aerial slung load via an existing flight controller directly. The correctness and applicability of the obtained results are demonstrated via the illustrative numerical example
๋น์ ํ ์ต์ ํ๋ฅผ ์ด์ฉํ ๋ฉํฐ๋กํฐ ํ์ ์ด์ก์ ๊ฒฝ๋ก ๊ณํ ๋ฐ ์ ์ด ๊ธฐ๋ฒ
ํ์๋
ผ๋ฌธ(๋ฐ์ฌ) -- ์์ธ๋ํ๊ต๋ํ์ : ๊ณต๊ณผ๋ํ ๊ธฐ๊ณํญ๊ณต๊ณตํ๋ถ, 2021.8. ๊นํ์ง.๊ฒฝ๋ก ๊ณํ๊ณผ ์ ์ด๋ ์์ ํ๊ณ ์์ ์ ์ผ๋ก ๋ฉํฐ๋กํฐ๋ฅผ ์ด์ฉํ๊ธฐ ์ํด์ ํ์์ ์ธ ์์์ด๋ค. ์ถฉ๋์ ํํผํ๋ฉฐ ํจ์จ์ ์ธ ๊ฒฝ๋ก๋ฅผ ์์ฑํ๊ณ ์ด๋ฅผ ์ค์ ๋ก ์ถ์ข
ํ๊ธฐ ์ํด์๋ ๋์ญํ ๋ชจ๋ธ์ด ๊ณ ๋ ค๋์ด์ผ ํ๋ค. ์ผ๋ฐ ๋ฉํฐ๋กํฐ์ ๋์ญํ ๋ชจ๋ธ์ ๋์ ์ฐจ์์ ๊ฐ์ง ๋น์ ํ์์ผ๋ก ํํ๋๋๋ฐ, ํ์ ์ด์ก ๋ฌผ์ฒด๋ฅผ ์ถ๊ฐํ ๊ฒฝ์ฐ ๊ณ์ฐ์ด ๋์ฑ ๋ณต์กํด์ง๋ค. ๋ณธ ๋
ผ๋ฌธ์ ๋ฉํฐ๋กํฐ๋ฅผ ์ด์ฉํ ํ์ ์ด์ก์ ์์ด ๊ฒฝ๋ก ๊ณํ๊ณผ ์ ์ด์ ๋ํ ํจ์จ์ ์ธ ๊ธฐ๋ฒ์ ์ ์ํ๋ค.
์ฒซ ๋ฒ์งธ๋ก ๋จ์ผ ๋ฉํฐ๋กํฐ๋ฅผ ์ด์ฉํ ํ์ ์ด์ก์ ๋ค๋ฃฌ๋ค. ๋ฌผ์ฒด๊ฐ ๋ณ๋์ ์์ธ์์ดํฐ ์์ด ์ด์ก๋ ๊ฒฝ์ฐ ๋ฌผ์ฒด๋ ๊ธฐ์ฒด์ ์์ง์์ ์ํด์๋ง ์ ์ด๊ฐ ๊ฐ๋ฅํ๋ค. ํ์ง๋ง, ๋์ญํ์์ ๋์ ๋น์ ํ์ฑ์ผ๋ก ์ด์ฉ์ ์ด๋ ค์์ด ์กด์ฌํ๋ค. ์ด๋ฅผ ๊ฒฝ๊ฐ์ํค๊ธฐ ์ํด์ ํ์ ๋์ญํ์์ ๋น์ ํ์ฑ์ ์ค์ด๊ณ ์์ธ ์ ์ด์ ์กด์ฌํ๋ ์๊ฐ ์ง์ฐ์ ๊ณ ๋ คํ์ฌ ๋์ญํ์์ ๊ฐ์ํํ๋ค. ๊ฒฝ๋ก ๊ณํ์ ์์ด์๋ ์ถฉ๋ ํํผ๋ฅผ ์ํด ๊ธฐ์ฒด, ์ผ์ด๋ธ, ๊ทธ๋ฆฌ๊ณ ์ด์ก ๋ฌผ์ฒด๋ฅผ ๋ค๋ฅธ ํฌ๊ธฐ์ ๋ชจ์์ ๊ฐ์ง ํ์์ฒด๋ค๋ก ๊ฐ์ธ๋ฉฐ, ํจ๊ณผ์ ์ด๋ฉด์๋ ๋ ๋ณด์์ ์ธ ๋ฐฉ์์ผ๋ก ์ถฉ๋ ํํผ ๊ตฌ์์กฐ๊ฑด์ ๋ถ๊ณผํ๋ค. Augmented Lagrangian ๋ฐฉ๋ฒ์ ์ด์ฉํ์ฌ ๋น์ ํ ๊ตฌ์์กฐ๊ฑด์ด ๋ถ๊ณผ๋ ๋น์ ํ ๋ฌธ์ ๋ฅผ ์ค์๊ฐ ์ต์ ํํ์ฌ ๊ฒฝ๋ก๋ฅผ ์์ฑํ๋ค. ์์ฑ๋ ๊ฒฝ๋ก๋ฅผ ์ถ์ข
ํ๊ธฐ ์ํด์ Sequential linear quadratic ์๋ฒ๋ฅผ ์ด์ฉํ ๋ชจ๋ธ ์์ธก ์ ์ด๊ธฐ๋ก ์ต์ ์ ์ด ์
๋ ฅ์ ๊ณ์ฐํ๋ค. ์ ์๋ ๊ธฐ๋ฒ์ ์ฌ๋ฌ ์๋ฎฌ๋ ์ด์
๊ณผ ์คํ์ ํตํด ๊ฒ์ฆํ๋ค.
๋ค์์ผ๋ก, ๋ค์ค ๋ฉํฐ๋กํฐ๋ฅผ ์ด์ฉํ ํ์
ํ์ ์ด์ก ์์คํ
์ ๋ค๋ฃฌ๋ค. ํด๋น ์์คํ
์ ์ํ ๋ณ์๋ ๋์ญํ์์์ ์ฐ๊ฒฐ๋(coupled) ํญ์ ๊ฐ์๋ ๊ธฐ์ฒด์ ์์ ๋น๋กํ์ฌ ์ฆ๊ฐํ๊ธฐ ๋๋ฌธ์, ํจ๊ณผ์ ์ธ ๊ธฐ๋ฒ ์์ด๋ ์ต์ ํ์ ๋ง์ ์๊ฐ์ด ์์๋๋ค. ๋์ ๋น์ ํ์ฑ์ ๊ฐ์ง ๋์ญํ์์ ๋ณต์ก์ฑ์ ๋ฎ์ถ๊ธฐ ์ํ์ฌ ๋ฏธ๋ถ ํํ์ฑ์ ์ฌ์ฉํ๋ค. ๊ฒฝ๋ก ๋ํ piece-wise Bernstein ๋คํญ์์ ์ด์ฉํ์ฌ ๋งค๊ฐ๋ณ์ํํ์ฌ ์ต์ ํ ๋ณ์์ ๊ฐ์๋ฅผ ์ค์ธ๋ค. ์ต์ ํ ๋ฌธ์ ๋ฅผ ๋ถํดํ๊ณ ์ถฉ๋ ํํผ ๊ตฌ์์กฐ๊ฑด๋ค์ ๋ํด ๋ณผ๋กํ(convexification)๋ฅผ ์ํํ์ฌ ์ด์ก ๋ฌผ์ฒด์ ๊ฒฝ๋ก์ ์ฅ๋ ฅ์ ๊ฒฝ๋ก์ ๋ํ ๋ณผ๋กํ(convex) ํ์๋ฌธ์ ๋ค์ด ๋ง๋ค์ด์ง๋ค. ์ฒซ ๋ฒ์งธ ํ์๋ฌธ์ ์ธ ๋ฌผ์ฒด ๊ฒฝ๋ก ์์ฑ์์๋, ์ฅ์ ๋ฌผ ํํผ์ ๋ฉํฐ๋กํฐ์ ๊ณต๊ฐ์ ํ๋ณดํ๊ธฐ ์ํ์ฌ ์์ ๋นํ ํต๋ก(safe flight corridor, SFC)์ ์ฌ์ ๊ฐ๊ฒฉ ๊ตฌ์์กฐ๊ฑด์ ๊ณ ๋ คํ์ฌ ์ต์ ํํ๋ค. ๋ค์์ผ๋ก, ์ฅ๋ ฅ ๋ฒกํฐ๋ค์ ๊ฒฝ๋ก๋ ์ฅ์ ๋ฌผ ํํผ์ ์ํธ ์ถฉ๋์ ๋ฐฉ์งํ๊ธฐ ์ํ์ฌ ์์ ๋นํ ์นํฐ(safe flight sector, SFS)์ ์๋ ์์ ๋นํ ์นํฐ(relative safe flight sector, RSFS) ๊ตฌ์์กฐ๊ฑด์ ๋ถ๊ณผํ์ฌ ์ต์ ํํ๋ค. ์๋ฎฌ๋ ์ด์
๊ณผ ์คํ์ผ๋ก ๋ณต์กํ ํ๊ฒฝ์์ ํจ์จ์ ์ธ ๊ฒฝ๋ก ๊ณํ ๊ธฐ๋ฒ์ ์์ฐํ๋ฉฐ ๊ฒ์ฆํ๋ค.Trajectory generation and control are fundamental requirements for safe and stable operation of multi-rotors. The dynamic model should be considered to generate efficient and collision-free trajectories with feasibility. While the dynamic model of a bare multi-rotor is expressed non-linearly with high dimensions which results in computational loads, the suspended load increases the complexity further. This dissertation presents efficient algorithms for trajectory generation and control of multi-rotors with a suspended load.
A single multi-rotor with a suspended load is addressed first. Since the load is suspended through a cable without any actuator, movement of the load must be controlled via maneuvers of the multi-rotor. However, the highly non-linear dynamics of the system results in difficulties. To relive them, the rotational dynamics is simplified to reduce the non-linearity and consider the delay in attitude control. For trajectory generation, the vehicle, cable, and load are considered as ellipsoids with different sizes and shapes, and collision-free constraints are expressed in an efficient and less-conservative way. The augmented Lagrangian method is applied to solve a nonlinear optimization problem with nonlinear constraints in real-time. Model predictive control with the sequential linear quadratic solver is used to track the generated trajectories. The proposed algorithm is validated with several simulations and experiment.
A system with multiple multi-rotors for cooperative transportation of a suspended load is addressed next. As the system has more state variables and coupling terms in the dynamic equation than the system with a single multi-rotor, optimization takes a long time without an efficient method. The differential flatness of the system is used to reduce the complexity of the highly non-linear dynamic equation. The trajectories are also parameterized using piece-wise Bernstein polynomials to decrease the number of optimization variables. By decomposing an optimization problem and performing convexification, convex sub-problems are formulated for the load and the tension trajectories optimization, respectively. In each sub-problem, a light-weight sampling method is used to find a feasible and low-cost trajectory as initialization. In the first sub-problem, the load trajectory is optimized with safe flight corridor (SFC) and clearance constraints for collision avoidance and security of space for the multi-rotors. Then, the tension histories are optimized with safe flight sector (SFS) and relative safe flight sector (RSFS) constraints for obstacle and inter-agent collision avoidance. Simulations and experiments are conducted to demonstrate efficient trajectory generation in a cluttered environment and validate the proposed algorithms.Chapter 1 Introduction 1
1.1 Literature Survey 5
1.2 Contributions 9
1.3 Outline 10
Chapter 2 Single Multi-rotor with a Suspended Load 11
2.1 Dynamics 11
2.2 Trajectory Generation 23
2.3 Optimal Control 31
Chapter 3 Multiple Multi-rotors with a Suspended Load 36
3.1 Problem Setting 36
3.2 Load Trajectory Generation 45
3.3 Tension History Generation 54
Chapter 4 Experimental Validation 68
4.1 Single Multi-rotor with a Suspended Load 68
4.2 Multiple Multi-rotors with a Suspended Load 79
Chapter 5 Conclusion 100
Appendix
A Detailed Derivation of Dierential Flatness 102
B Preliminaries of Bernstein Polynomials 108
B.1 Denition of a Bernstein Polynomial 108
B.2 Convex hull property of a Bernstein Polynomial 110
B.3 Representation of a General Polynomial with Bernstein Basis Polynomials 111
B.4 Representation of the Derivative of a Bernstein Polynomial with Bernstein Basis Polynomials 112
References 113
Abstract (in Korean) 119๋ฐ
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