Research Papers

The Hexapodopter: A Hybrid Flying Hexapod—Holonomic Flying Analysis

[+] Author and Article Information
Daniel Soto-Guerrero

Cinvestav Tamaulipas Cd. Victoria,
Tamaulipas 87130, México
e-mail: dsoto@tamps.cinvestav.mx

José Gabriel Ramírez-Torres

Cinvestav Tamaulipas Cd. Victoria,
Tamaulipas 87130, México
e-mail: grtorres@tamps.cinvestav.mx

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received May 17, 2017; final manuscript received June 18, 2018; published online July 18, 2018. Assoc. Editor: K. H. Low.

J. Mechanisms Robotics 10(5), 051008 (Jul 18, 2018) (8 pages) Paper No: JMR-17-1153; doi: 10.1115/1.4040631 History: Received May 17, 2017; Revised June 18, 2018

This document introduces the holonomic flying capabilities of the Hexapodopter, a six-legged walking machine capable of vertical take-off and landing. For ground locomotion, each limb has two degrees-of-freedom (2DoF); while the thrust required for flying is provided by six motors mounted close to every knee, so the thrust vector can be reoriented depending on the configuration of each limb. The capacity of reorienting the thrust forces makes the Hexapodopter a true holonomic vehicle, capable of individually controlling its six degrees-of-freedom (6DoF) on the air without reorienting any of the thrust motors nor the body. The main design criteria and validation will be discussed on this paper, as well as a control law for the vehicle.

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Bingran, Z. , and Wenhan, Q. , 1998, “ A Force-Closure Test for Soft Multi-Fingered Grasps,” Sci. China Technol. Sci., 41(1), pp. 62–69.
Ryll, M. , Bülthoff, H. H. , and Giordano, P. R. , 2015, “ A Novel Overactuated Quadrotor Unmanned Aerial Vehicle: Modeling, Control, and Experimental Validation,” IEEE Trans. Control Syst. Technol., 23(2), pp. 540–556. [CrossRef]
Segui-Gasco, P. , Al-Rihani, Y. , Shin, H.-S. , and Savvaris, A. , 2013, “ A Novel Actuation Concept for a Multi Rotor UAV,” International Conference on Unmanned Aircraft Systems (ICUAS), Atlanta, GA, May 28–31, pp. 373–382.
Shimizu, T. , Suzuki, S. , Kawamura, T. , Ueno, H. , and Murakami, H. , 2015, “ Proposal of 6DoF Multi-Copter and Verification of Its Controllability,” 54th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE), Hangzhou, China, July 28–30, pp. 810–815.
Ryll, M. , Bicego, D. , and Franchi, A. , 2016, “ Modeling and Control of Fast-Hex: A Fully—Actuated by Synchronized–Tilting Hexarotor,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, South Korea, Oct. 9–14, pp. 1689–1694.
Rajappa, S. , Ryll, M. , Bülthoff, H. H. , and Franchi, A. , 2015, “ Modeling, Control and Design Optimization for a Fully-Actuated Hexarotor Aerial Vehicle With Tilted Propellers,” IEEE International Conference on Robotics and Automation (ICRA), Seattle, WA, May 26–30, pp. 4006–4013.
Brescianini, D. , and D'Andrea, R. , 2016, “ Design, Modeling and Control of an Omni-Directional Aerial Vehicle,” IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, May 16–21, pp. 3261–3266.
Jiang, G. , and Voyles, R. , 2013, “ Hexrotor Uav Platform Enabling Dextrous Interaction With Structures-Flight Test,” IEEE International Symposium on Safety, Security and Rescue Robotics (SSRR), Linkoping, Sweden, Oct. 21–26, pp. 1–10.
Corke, P. , 2007, “ A Simple and Systematic Approach to Assigning Denavit-Hartenberg Parameters,” IEEE Trans. Rob., 23(3), pp. 590–594. [CrossRef]
Alaimo, A. , Artale, V. , Milazzo, C. , Ricciardello, A. , and Trefiletti, L. , 2013, “ Mathematical Modeling and Control of a Hexacopter,” International Conference on Unmanned Aircraft Systems (ICUAS), Atlanta, GA, May 28–31, pp. 1043–1050.
Tomic, T. , 2014, “ Evaluation of Acceleration-Based Disturbance Observation for Multicopter Control,” European Control Conference (ECC), Strasbourg, France, June 24–27, pp. 2937–2944.
Mehmood, H. , Nakamura, T. , and Johnson, E. N. , 2016, “ A maneuverability Analysis of a Novel Hexarotor UAV Concept,” International Conference on Unmanned Aircraft Systems (ICUAS), Arlington, VA, June 7–10, pp. 437–446.


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Fig. 1

Four different arrangements with fixed and dynamic active reorientation of the thrust force for each motor: (a) a standard hexacopter represents a fixed arrangment with all motors axes parallel to each other, (b) tilting propeller quadcopter, each thrust force can be reoriented independently modifying θi, (c) thrust vectoring quadcopter, a mechanism with 2DoF (βi and θi) can reorient each thrust force, and (d) an hexacopter with three nonconsecutive motors tilted outward and the rest outward

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Fig. 2

A render of the hexapodopter

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Fig. 3

The hexapodopter mechanical description: (a) the kinematic chain for one of the legs of the Hexapodopter, shown mounted on the main body frame B. All reference frames are labeled and the rotational linkages are denoted with cylinders. (b) Robot base. The six legs disposed around the center of gravity can swing thanks to the six servos mounted on the Si coordinates, note θs. The brushless motors and their propellers are mounted close to the knees.

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Fig. 4

The form closure test and its tendency with respect to ωmax and the mass of the vehicle: (a) maximum acceleration in the x- and y-axes, versus the form closure metric d and Γ(d) and (b) the behavior of the two functions when the ωmax is fixed and the mass m varies (left), the opposite escenario is shown on the right plot

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Fig. 5

Simulation in open loop: (a) the lemniscate trajectory and (b) the resulting angular speeds of the six motors

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Fig. 6

Controller architecture

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Fig. 7

Simulation in closed loop: (a) the trajectory of the vehicle on closed loop, (b) the simulated angular speeds of the six motors mounted on the hexapodopter in the closed loop scheme, and (c) Euler angles for the closed loop. Roll and pitch stay close to zero, while the yaw angle reaches the desired value.



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