6D interaction control with aerial robots: The flying end-effector paradigm
Summary (3 min read)
- Direct physical interaction of a robot with its environment is a vast and continuously growing field of research with several relevant applications.
- A drawback of this solution is that typical aerial platforms are underactuated and therefore it is impossible to independently control the 6D (position plus orientation) dynamics of the end-effector.
- In Rajappa et al. (2017), the authors, by exploiting both a wrench estimation and a ring of eight contact sensors, proposed a control able to separate human interaction forces from additional disturbances as wind and parameter uncertainties.
- The authors consider as aerial robot a fully actuated aerial vehicle equipped with an arbitrarily mounted end-effector tool.
- Selecting an alternating sign of α for every other propeller in (4) allows for the full actuation of the aerial vehicle.
- In this section the authors describe the single components of the controller.
- The control framework is based on an outer loop admittance control and an inner loop full-pose controller .
- The state of the aerial robot is estimated by a Unscented Kalman Filter (UKF) that fuses the Inertial Measurement Unit (IMU) acceleration and angular velocity measurements with the position and orientation from a pose sensor (in their case a motion capture system, which could be easily replaced with an onboard camera using a Perspectiven-Point (PnP) algorithm).
- The interaction torques and forces are estimated by a wrench observer.
- The authors will therefore only summarize the controller here.
- The block diagram of Figure 3 shows the control scheme architecture.
- Euler angles are prone to singularity issues.
Contact Wrench Estimation
- To this aim, a force/torque sensor could be mounted on the robot’s tooltip, which is usually capable to provide a reliable measure, but this solution increases both the cost and the weight of the robot.
- Thus, in this paper, the hybrid approach already proposed in Tomic et al. (2017), has been followed.
- More in detail, the acceleration based observer proposed by Yüksel et al. (2014a) is adopted in order to estimate the external interaction forces on the robot CoM, fR, while the external torques, τ RR are obtained by exploiting a momentum-based observer (De Luca and Mattone (2005)).
- The choice of the matrix KI is a trade-off between the convergence rate and the filtering properties of the observer: greater values of the gains allow faster convergence while smaller values allow to filter the high-frequency noise.
- The resulting force and torque profiles are presented in Figure 4.
Interaction wrench compensation
- To achieve optimal results of the admittance filter a highly stiff low-level tracking is desired.
- Accepted for The International Journal of Robotics Research 2019 (17) and, thus, the same stability properties hold.
- Otherwise, under the trivial assumption that the interaction wrench is bounded, the wrench estimation error can be viewed as a bounded term as well.
- Moreover, if the interaction wrench is constant, the wrench estimation error is convergent to zero, and, thus, after it vanishes also the tracking error will converge to zero as well.
- The Tilt-Hex robot is a LAAS-CNRS in house developed fully actuated aerial robot.
- All used structural components are either off-the-shelf available or 3D printable by a standard fused deposition modeling printer.
- The total mass, including a 2.2 Ah LiPo-battery and the rigid end-effector accumulates to 1.8 kg.
- To retrieve the Tilt-Hex’s pose estimation and its derivatives the aerial robot contains a standard IMU with accelerometers and gyroscopes, providing the sensor information at 500 Hz.
- The on-board and external sensor information are fused by an UKF state estimator, providing full state estimation at 500Hz.
- The full control framework described above has been implemented in a Matlab Simulink environment to boost a fast development.
- For safety the aerial robot is currently connected via a serial connection (RS232) with the desktop machine, which transmits the desired propeller spinning velocities to the TiltHex and the actual propeller spinning velocity, IMU data, all at 500 Hz, and further status updates, e.g., safety checks, battery status with a lower frequency to the base PC.
- The MoCap measurements (100Hz) are fused via a UKF state estimator with the IMU measurements (500Hz) thus obtaining a full state estimate at 500Hz.
- To present the capabilities and limits of the control framework a broad spectrum of different experiments has been conducted - the interested reader is as well referred to the attached multimedia data.
- Firstly, the authors will present a bench of experiments demonstrating the physical property shaping capabilities of the outer loop admittance filter.
- Secondly, the authors show a hard contact and sliding of the off-centered tool-tip while making use of the afore presented physical property shaping to fulfill a desired task.
- Thirdly the authors present a challenging flying peg-in-hole task.
- Accepted for The International Journal of Robotics Research 2019.
Physical properties shaping
- The authors will now experimentally test and demonstrate the physical property shaping capabilities of the outer loop admittance filter with respect to the end-effector tool-tip.
- By exerting a step-like force profile on the aerial robot the authors will show that they can achieve a large variety of desired massspring-damper behaviors.
- To get a better insight of the effect of a changed damping parameter the authors now compared the ideal msd-system velocity ṗE,i with the real reference velocity output ṗE,r in Figure 7b.
- This behavior is explained by the first order low-pass dynamics of the wrench observer.
Sliding on Surface
- The authors conducted a hard contact between the tool-tip of the rigid end-effector and a tilted wooden surface .
- First the desired trajectory approaches without contact from an initial position to a position 0.14m above the surface (approaching phase).
- To reduce stick slip effects between the tool-tip and the surface during the sliding-phase the desired orientation of the tool-tip is tilted forward by (θR,d = 7.5◦).
- The fourth plot (8d) presents the difference between the components of the preplanned desired position trajectory and the admittance filter output (pR,d − pR,r).
- During the approaching phase the aerial robot’s desired pitch orientation changes from θ = 0◦ to θ = 7.5◦ and remains constant hereafter.
- The experimental setup of the peg-in-hole task employs a 15◦ tilted standing funnel.
- In detail, the desired end-effector trajectory first follows a translation along xW and stops 0.16m above the funnel .
- The experimental results are reported in Figure 12.
- The torque causes the admittance filter to adapt the reference pitch orientation θR,r with respect to the desired angle θR,d until the tip can be fully inserted into the funnel.
Multi contact sliding
- The last conducted experiment is inspired by common industrial tasks like inspection with contact, surface polishing or welding where, while translating, a particular force application on a surface is needed.
- Then, the second phase starts with applying a constant force against the ledge, in direction yW (.
- The end-effector is now in contact with three sides and cannot translate anymore.
- The reference pR,r, desired pR,d and actual positions pR are depicted in Figure 14a, showing first, an error free matching of pR,pR,r and pR,d in the absence of a contact force and second, a divergence between pR,d ,pR,r during contact, while the end-effector pR still perfectly tracks pR,r.
- In contrast to the first three experiments, aerodynamic effects between the aerial robot and the solid surface are observed, resulting in a mismatches between the estimated and measured forces and torques, see Figure 14c.
- The authors tackled the issue of precise 6D aerial physical interaction with the environment.
- The authors utilized a novel fully actuated aerial platform, namely the Tilt-Hex allowing to independently control the linear and the angular acceleration.
- Hereby, the platform can instantaneously counteract any wrench during the contact with the environment.
- An outer loop admittance control scheme steers the system to a desired impedance behavior only during the presence of an interaction wrench by computing a suitable reference trajectory.
- An advanced set of experiments was performed to show the full capabilities of the platform.
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Cites methods from "6D interaction control with aerial ..."
...In  and , such technique has been employed to control the interaction force in the case of a fully-actuated platform equipped with a rigid tool, and of an under-actuated platform equipped with a robotic arm, respectively....
Cites background or methods from "6D interaction control with aerial ..."
...In this case, the prototype has been completely designed and manufactured in our laboratory, and has already been presented in some of our previous contributions [2, 31]....
...Vehicles of this kind have been demonstrated to be particularly suitable for the accomplishment of aerial physical interactions tasks [2, 3], i....
...This translates also into the possibility of decoupling the control of the body force and moment in a larger extent, which becomes particularly useful in many realistic scenarios, ranging from 6D trajectory tracking, see , to aerial physical interaction tasks, see [2, 3], and disturbance rejection in general....
Cites background from "6D interaction control with aerial ..."
...design taxonomy definitions from , platform morphologies can be fully actuated (having a full rank six-DOF allocation matrix) , , or additionally omnidirectional (independent...
...THE demand for industrial contact inspection with aerial robots has been growing rapidly in recent years, coinciding with the development of fully actuated micro aerial vehicles (MAVs) for aerial interaction –....
...varying degrees , , despite known limitations due to underactuation ....
...They can be fully actuated by nonparallel fixedly tilted rotors , , or with actively tilting rotor groups , ....
"6D interaction control with aerial ..." refers background in this paper
...Thus, the orientation kinematics of the robot and the end effector are then expressed by ṘR = RR[ω RR]× (1) ṘE = RE [ω EE ]×, (2) respectively, where [•]× ∈ SO(3) represents the skew symmetric matrix (Siciliano et al. (2009)) associated to vector • ∈ R3....
...(28) The (27) represents the dynamics of a 6-DoF mechanical impedance (Siciliano et al. (2009)) of inertia ME , damping DE and stiffness KE : those matrices are all positive-definite and suitably chosen in a way to impose an over-damped behavior to the system....
...respectively, where 1⁄2 × 2 SO(3) represents the skew symmetric matrix (Siciliano et al., 2009) associated with vector 2 R(3)....
...Equation (27) represents the dynamics of a 6-DoF mechanical impedance (Siciliano et al., 2009) of inertia ME, damping DE, and stiffness KE: those matrices are all positive definite and suitably chosen in a way to impose an overdamped behavior to the system....
...2018) (Lee et al. 2010), we assume that RR,r(t) ∈ C̄ 3 and ω R,r = [RR,rṘR,r]∨, where [·]∨ represents the inverse map from SO(3) to R3....
...Following (Franchi et al. 2018) (Lee et al. 2010), we assume that RR,r(t) ∈ C̄ 3 and ω R,r = [RTR,rṘR,r]∨, where [·]∨ represents the inverse map from SO(3) to R3....
"6D interaction control with aerial ..." refers background or methods in this paper
...…the error dynamics is exponentially convergent to the origin for any positive definite matrix L. Contact torques estimation In order to estimate the interaction torques, exerted by the external environment on the tool-tip, a momentum-based observer (De Luca and Mattone (2005)) has been designed....
...Contact torques estimation In order to estimate the interaction torques, exerted by the external environment on the tool-tip, a momentum-based observer (De Luca and Mattone (2005)) has been designed....
...More in detail, the acceleration based observer proposed by Yüksel et al. (2014a) is adopted in order to estimate the external interaction forces on the robot CoM, fR, while the external torques, τ RR are obtained by exploiting a momentum-based observer (De Luca and Mattone (2005))....
...(2014a) is adopted in order to estimate the external interaction forces on the robot CoM, fR, while the external torques, τ R are obtained by exploiting a momentum-based observer (De Luca and Mattone (2005))....
"6D interaction control with aerial ..." refers background in this paper
...The second possibility is to attach an n-DoF robotic arm to the aerial platform (Muscio et al. (2016, 2017); Baizid et al. (2016); Kim et al. (2013); Tognon et al. (2017)), a solution which aims at overcoming the underactuation of the end-effector dynamics by exploiting the increased number of…...
...The second possibility is to attach an n-DoF robotic arm to the aerial platform (Baizid et al., 2016; Kim et al., 2013; Muscio et al., 2017, 2016; Tognon et al., 2017), a solution which aims at overcoming the underactuation of the endeffector dynamics by exploiting the increased number of actuators provided by the arm....
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Q1. What contributions have the authors mentioned in the paper "6d interaction control with aerial robots: the flying end-effector paradigm" ?
This paper presents a novel paradigm for physical interactive tasks in aerial robotics allowing to increase reliability and decrease weight and costs compared to state of the art approaches.