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Research Papers

Aggressive Flight With Quadrotors for Perching on Inclined Surfaces

[+] Author and Article Information
Justin Thomas

GRASP Lab,
Department of Mechanical Engineering
and Applied Mechanics,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: jut@seas.upenn.edu

Morgan Pope

Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94305
e-mail: mpope@stanford.edu

Giuseppe Loianno

GRASP Lab,
Department of Mechanical Engineering
and Applied Mechanics,
University of Pennsylvania,
Philadelphia, PA 19104
e-mail: loiannog@seas.upenn.edu

Elliot W. Hawkes

Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94305
e-mail: ewhawkes@stanford.edu

Matthew A. Estrada

Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94305
e-mail: estrada1@stanford.edu

Hao Jiang

Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94305
e-mail: jianghao@stanford.edu

Mark R. Cutkosky

Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94305
e-mail: cutkosky@stanford.edu

Vijay Kumar

GRASP Lab
Department of Mechanical Engineering
and Applied Mechanics,
University of Pennsylvania
Philadelphia, PA 19104
e-mail: kumar@seas.upenn.edu

1Corresponding author.

Manuscript received September 21, 2015; final manuscript received December 3, 2015; published online May 4, 2016. Assoc. Editor: James Schmiedeler.

J. Mechanisms Robotics 8(5), 051007 (May 04, 2016) (10 pages) Paper No: JMR-15-1275; doi: 10.1115/1.4032250 History: Received September 21, 2015; Revised December 03, 2015

Micro-aerial vehicles (MAVs) face limited flight times, which adversely impacts their efficacy for scenarios such as first response and disaster recovery, where it might be useful to deploy persistent radio relays and quadrotors for monitoring or sampling. Thus, it is important to enable micro-aerial vehicles to land and perch on different surfaces to save energy by cutting power to motors. We are motivated to use a downward-facing gripper for perching, as opposed to a side-mounted gripper, since it could also be used to carry payloads. In this paper, we predict and verify the performance of a custom gripper designed for perching on smooth surfaces. We also present control and planning algorithms, enabling an underactuated quadrotor with a downward-facing gripper to perch on inclined surfaces while satisfying constraints on actuation and sensing. Experimental results demonstrate the proposed techniques through successful perching on a glass surface at various inclinations, including vertical.

Copyright © 2016 by ASME
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References

Figures

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Fig. 1

A quadrotor perched on a vertical glass surface

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Fig. 2

A view of the underside of the gripper. Initially, the pads are held in place by slight tension between the outer tendons (indicated by outwards-pointing arrows) and the inner tendons (indicated by the inwards-pointing arrows). Then, upon the collapse of the truss mechanism, each pad is placed in shear by pulling the pad toward the center of the gripper using the tension string (downward, partially occluded arrow).

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Fig. 3

A cross section view of the gripper (reproduced from Ref. [23]). The bistable truss mechanism is used to engage the directional adhesive pads upon contact with the surface. (a) Initially, a preloaded spring is tensioned low enough that the truss does not collapse. (b) Upon impact, the truss collapses (the magnets holding the one side together separate) and the tension in the spring is transmitted via tendons to the gripping pads to create shear. Since the mechanism is still in compression, the shear force results in an appropriate loading cycle for high speed engagement. (c) When the robot creates tension in the tendon, whether from the rebound or from static hanging, the truss mechanism resets, and the tension remains transmitted to the pads since the entire mechanism is being pulled away.

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Fig. 4

Qualitative illustration of a failure mode due to an inappropriate matching of tangential velocity and adhesive tile orientation at impact. In (a), the trailing tile impacts first, maintaining tension between the two tiles and preserving a consistent final tile spacing and an appropriate final loading angle of the tendon. In (b), the leading tile impacts first, causing the connecting tendon to go slack and allowing the tiles to settle on the wall closer to each other than intended. This results in inconsistent and nonoptimal loading on rebound, increasing the chance of failure.

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Fig. 5

The perching envelope of the quadrotor based on impact velocities relative to a vertical surface. Successful unpowered (i.e., launched) perches are shown as dots, and unpowered failures are shown as squares. Diamonds indicate successes for trials while the quadrotor was flying under its own power. Predicted boundaries are shown as dashed-dotted lines. The parabolic boundary is determined by calculating the kinetic energy after rebound relative to the maximum energy storage in the rebound spring. The left boundary is estimated based on the recorded low-speed failures, and the top boundary is based on the improper engagement failure observed for upward (positive) impact velocities. One can observe that a reasonable target normal velocity is 1.4 m/s with a tangential velocity of 0.4 m/s in the downward direction.

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Fig. 6

A quadrotor has four rotating propellers. Each rotor generates a force, Fi, and a moment, Mi. Adjacent rotors spin the opposite direction so that the moment resulting from drag is opposing and can be controlled by varying the speed of the pairs of rotors.

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Fig. 7

The control inputs of a quadrotor can be considered to be a net force, f, and moments about each of the principal axes, Mi

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Fig. 8

We define the bc vector based on ψ and b3 in order to determine b2 while avoiding the singularity when e3·b3=0

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Fig. 10

The last 40 ms of a sample perching trajectory. The arrows denote the acceleration direction (i.e., the direction of b3) and magnitude. Notice that the direction of the vector does not change significantly toward the end of the trajectory where the acceleration is bounded during planning.

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Fig. 11

A plot of the nominal acceleration for the trajectory in Fig. 9. Notice that during the last portion of the trajectory, the acceleration is bounded by the black lines, which dictates that the angular velocity will be nearly zero and that the robot will achieve the correct orientation before impact.

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Fig. 9

A sample trajectory with vectors denoting the acceleration direction and magnitude. The quadrotor starts on the bottom right and perches on the left at an incline of 70 deg. The upper left corner is presented in a higher temporal resolution in Fig. 10.

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Fig. 12

The architecture of the system. The ground station handles the trajectory planning and passes the trajectories to the position controller, which receives feedback from the motion capture system. The position controller sends a desired force, fdes, a ψ error, and the necessary feedforward inputs to the robot. Internally, the attitude controller runs at 1 kHz to update the commanded force and moments based on the position controller and the feedback from the IMU.

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Fig. 13

The angular velocities for three different perching trials on a vertical surface as estimated by the motion capture system. The vertical dashed-dotted black line denotes the time of contact with the surface. As desired, the angular velocity is controlled to zero before impact.

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Fig. 14

A strobe of images from a perch sequence. The robot starts on the right hand side outside of the field of view, accelerates toward the target, and rotates in time to achieve a successful perch within the landing envelope of the gripper.

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Fig. 15

Using the proposed planning method, the angle of the surface can be changed without the need for iterative experimental trials. The root of each arrow indicates the position of the robot, and the arrow indicates the direction of the thrust (i.e., the orientation of the robot).

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Fig. 16

The downward-facing gripper can also be used to carry payloads such as this cell phone

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