Design and Control of an Aerial Manipulator for Contact-based Inspection
DDesign and Control of an Aerial Manipulator for Contact–basedInspection
Varun Nayak , Christos Papachristos , and Kostas Alexis Abstract — Manipulator dynamics, external forces and mo-ments raise issues in stability and efficient control during aerialmanipulation. Additionally, multirotor Micro Aerial Vehiclesimpose stringent limits on payload, actuation and system states.In view of these challenges, this work addressed the designand control of a 3-DoF serial aerial manipulator for con-tact inspection. A lightweight design with sufficient dexterousworkspace for NDT (Non-Destructive Testing) inspection ispresented. This operation requires the regulation of normalforce on the inspected point. Contact dynamics have beendiscussed along with a simulation of the closed-loop dynamicsduring contact. The simulated controller preserves inherentsystem nonlinearities and uses a passivity approach to ensurethe convergence of error to zero. A transition scheme from free-flight to contact was developed along with the hardware andsoftware frameworks for implementation. This paper concludeswith important drawbacks and prospects.
I. INTRODUCTIONUnmanned Aerial Vehicles (UAV) are being widely usedtoday for applications such as mapping, inspection, explo-ration and photography [1], [2], [3], [4], [5]. An importantobservation regarding most applications of aerial robots isthat they do not involve any kind of contact with the envi-ronment. This phenomenon can be attributed to several chal-lenges. Traditional robotic manipulators whose base links arefixed to the ground (earth) are able to efficiently dissipateexternal and inertial forces encountered during manipulation.The reaction forces necessary for balancing external as wellas inertial forces acting on the manipulator are availableimmediately owing to the fixed contact relationship of thebase link with the infinitely dissipative ground. However,this is not the case for aerial manipulators as multirotorvehicle dynamics are relatively sensitive and “slow” becauseof inherent aerodynamic forces as well as inertia. Therefore,the task of maintaining the desired vehicle attitude againstthese external contact forces becomes a challenge. Sincemultirotors are unstable in general, compensator design andstability for closed-loop contact dynamics must be addressed.Along with performing control during contact, the transitionbetween the free-flight regime and the contact regime canpresent some complications. Physical properties of the UAVplatform such as payload, limits on thrust and inertia lead tointricate design challenges. Varun Nayak is an undergraduate student pursuing mechanical engineer-ing at Birla Institute of Technology and Science (BITS), Pilani, Goa, India [email protected] Christos Papachristos, and Kostas Alexis are with the Au-tonomous Robots Lab, Department of Computer Science and Engi-neering, University of Nevada, Reno [email protected],[email protected]
Fig. 1. The fully assembled aerial manipulator system developed in thiswork. The image shows the 3-DoF RRR serial manipulator mounted on topof a DJI Matrice 100 quadrotor.
Researchers have employed a variety of approaches indesign and control methodologies in aerial manipulationapplications [6], [7], [8], [9], [10], [11], [12], [13], [14], [15],[16], [17], [18]. Previous research touches on topics such askinematics for workspace and dexterity, full-body control,lightweight design, accurate end-effector position control,interaction control, etc. The work in [9] developed a novelparallel manipulator with a large workspace and current-based torque control to employ impedance control schemes.The work in [6] designed a lightweight 5-DoF aerial manip-ulator for pick and place applications. It has a smart self-folding mechanism to minimize space occupation and staticCoG imbalance. A special differential mechanism to cancelattitude disturbances was also designed. The research pre-sented in [11] used delta-kinematics for designing a fast andprecise aerial manipulator for contact-based inspection. Thesophisticated delta structure possesses compliance allowingfor slight tracking errors. The researchers in [17] demon-strated the design and operation of a unique superstructuremanipulator that has the ability to perch on a vertical surfacethrough impact. It is lightweight and possesses unilateralcompliance for perch and release operations.The authors in [8] developed a 7-DoF aerial manipulatorfor heavy payloads. Hence, it used a backstepping-basedcontroller for the multi-rotor, which considers full coupleddynamics and the rapidly shifting CoG. An admittance-based manipulator controller is outlined in the paper. Thecontribution in [10] presented a multi-objective full-bodycontroller for the system described in. The fast dynamics ofthe parallel manipulator ensured efficient kinematic tracking. a r X i v : . [ c s . R O ] A p r urthermore, the work in [16] addressed the problem ofinteraction in order to track desired contact force usinghybrid control for the manipulator, using an impedance-basedcontroller for position and a PI controller for regulating nor-mal force. The authors in [7] presented the design and controlof a parallel aerial manipulator for industrial inspection. Theapproach considered the environment as a compliant contactand used the Hunt-Crossley interaction model.This work modeled the NDT (Non-Destructive Testing)inspection task as a force regulation problem [7] and de-signed a lightweight 3-DoF RRR manipulator with sufficientdexterity. A planar model of the dynamics during contact wasdeveloped, along with a passivity-based PD controller whilepreserving the nonlinearity of the model. Keeping in mindactuation limits and stability requirements, a simulation ofthe closed-loop dynamics is presented with a smooth free-flight to contact transition scheme. This paper also describesthe hardware and software framework for implementation.II. MANIPULATOR DESIGNAlthough most aerial manipulators have been mountedbelow the plane of the rotor and t were designed for pick andplace tasks. This makes sense spatially as well as for stability.However, since our objective was to achieve continuouscontact in the horizontal plane, the manipulator was mountedas a super-structure. Placing the manipulator on top makesthe external force a stabilizing moment and also reduces therequired manipulator workspace. Fig. 2. A 2-D free body diagram of the aerial manipulator in contact withthe manipulated surface. The figure shows all considered forces, momentsand the coordinate system used in the analysis. θ is the pitch angle, F H isthe horizontal contact force, F V is the vertical contact force, T and T arethe thrust values as shown in the figure and L , l v and l H are the geometricparameters as shown. Additionally, a static analysis of the system in contactshowed that system nonlinearities are more pronounced whenthe contact force exceeds 6 N. Hence, it was decided topreserve this inherent nonlinearity for the analysis.
A. Kinematics
The manipulator is an RRR type with the base joint foryaw decoupling of the arm from the multirotor heading. Thisallows for better error correction during manipulator positiontracking. This makes the rest of the arm a planar 2-DoF RR
Fig. 3. Static simulation results during contact: The plot shows thevariation of the individual thrust components with respect to the contactforce required. A nominal friction force µ = 0 . is taken in the downwarddirection (conservative) has been considered. The nonlinearity for largevalues is evident.Fig. 4. Side-view of RRR manipulator assembly showing the coordinatesystems, joint angles and other definitive geometric parameters type, which provides sufficient dexterity without being tooheavy.The forward kinematics of the manipulator were developedusing the Denavit-Hartenberg (DH) convention. The DHparameters of the manipulator are shown in TABLE I. Theinverse kinematics were developed analytically. The firstjoint angle is obtained using spherical coordinate decoupling.Following this, solving for the inverse kinematics of a 2-DoFRR manipulator is trivial. Transform from link i − to i r i d i α i θ i i = 1 l π/ θ i = 2 l θ i = 3 l θ TABLE IDH P
ARAMETERS OF THE
RRR S
ERIAL M ANIPULATOR . In the workspace analysis, the joint torque requirementsduring manipulation were considered since these needed tobe minimized to reduce motor size. The relationship τ = J T F was used. Here F is the end-effector force, τ is thejoint torque vector and J is the manipulator Jacobian.A typical load-configuration combination for this systemis F H = 6 N with in-plane frictional forces equal toabout . N at the configuration θ = 0 ◦ , θ = 35 ◦ and ig. 5. The figure shows the manipulator in a typical pose during contact.The true workspace is the displayed workspace revolve-swept about the basejoint axis. The application space is the set of points that the end-effector canreach with the desired orientation while satisfying all spatial constraints. θ = − ◦ . The required torques for this configurationfrom equation (4.14) are computed as M = 1 . N.m , M = 3 . N.m and M = 1 . N.m . The motors wereselected by simulating similar such cases.
B. Compliant Mechanism
Integration of a compliant mechanism at the end-effectorwas conceived in order to satisfy the following objectives: • To absorb impact when the quadrotor first comes incontact to slow down the resulting contact dynamics. • To allow for slight curvatures on the surface and smallerrors in the end-effector pose. • To enable compliant force-sensing at the end-effector.
Fig. 6. Exploded view of the compliant mechanism. The springs arepreloaded and force feedback is obtained from a resistive force sensor. Thethree springs in parallel allow for the contact plane adjusting to surfacecurvatures and eccentric forces.
The entire manipulator along with the motors weighedonly 327 grams, which was about half of the maximumpayload of the quadrotor used for implementation.III. CONTACT DYNAMICS AND CONTROLThe manipulator designed in this work weighed only327 grams against the platform weight of 2400 g. In additionto this, the maximum shift in CoG for the entire configurationspace of the aerial manipulator system was only 2 cm from the vertical axis passing through the centroid of the multi-rotor. Therefore, no special consideration was given to theeffect of the inertial effects of the manipulator with respectto the aerial vehicle in the closed-loop dynamics simulations.However, contact introduces an additional external force onthe system. The constraints on the thrust values, thrust ratesand state variables during flight necessitates a fundamentalclosed-loop dynamics analysis. An important assumption wasthat the nature of the equation of motion in the verticaldirection was considered as static. As contact dynamics arefast compared to that during free-flight, the analysis of thecontroller performance for this direction is crucial. Hence,this assumption was acceptable. The analysis is performedin a 2-D plane and friction has been ignored, compensatedby a safety factor.Applying Newton’s 2 nd Law, we can write the equationsof motion in state-space form. I yy is the moment of inertiaabout the axis parallel to the y-axis and passing through theCoM of the entire system. For simplicity, the explicit timedependency symbol is dropped hereafter. ˙ x ¨ x ˙ θ ¨ θ = ˙ x − F H M ˙ θ F H l H I yy + sin θM sin θM − L I yy L I yy (cid:20) T T (cid:21) (1)This equation is in the vector-valued nonlinear affine(affine in u ) form. ˙ x = f ( x ) + g ( x ) u Here, x is the state vector and u is the control input. x = x ˙ xθ ˙ θ , u = (cid:20) T T (cid:21) . The expression for force from the dynamics can be writtenas follows: F H = M g tan θ − M ¨ x (2)Since the objective was to regulate the contact force, a gen-eral approach would have demanded force feedback controlfrom the end-effector. It is indicative from the equation thatthe regulation of the pitch angle and the x-position impliesthe regulation of the normal force. Since force-feedbackcontrol (impedance or compliant control) was beyond thescope of this work, this model was used. Thus, the aim wasto control the x-position and the pitch angle. The outputstate to be controlled is expressed by the function y = h ( x ) .A passivization approach through a nonlinear PD controllerwas used to model the control law for this system. As thesystem is affine in u , the control law was derived using theinput-output linearization technique.Insisting that the error convergence should follow second-order dynamics, we can write: h − ¨ h desired + k ( ˙ h − ˙ h desired ) + k ( h − h desired ) = 0 (3)In the above equations, k and k are positive definitematrices containing the gains required for stable dynamics.Using Lie derivatives, the control law was derived. u = L g , f h − ( − L f , f h + v ) (4)The expression for v comes from the second order errordynamics. v = k p ( h desired − h ) + k d ( ˙ h desired − ˙ h ) (5)The energy function can be plotted against time to checkfor convergence to zero. The energy of the now closed-loopsystem E ( t ) in consideration is given by the sum of thepotential and kinetic energies. E ( t ) = ( 12 M ˙ x ( t ) + 12 I yy ˙ θ ( t ) ) + ( 12 k p ( x desired − x ( t )) + 12 k p ( θ desired − θ ( t )) ) (6) With appropriate controller gains and initial conditions,the energy equation was shown to converge to zero. Fromthe expression ¨ y = v it can be said that the system is stablefor any positive damping coefficient.The initial conditions have a significant influence on theresponse since the system is nonlinear. These include thex-position x , x-velocity ˙ x , pitch angle θ and pitch rate ˙ θ . Through appropriate gain selection, the simulation wascarried out with conservative limits for the thrust rates. Thepitch rate was limited to rad/s [15]. Fig. 7. (LEFT) Simulation results of closed-loop contact dynamics foracceptable initial conditions x = − . m , ˙ x = 0 m/s , θ = 0 . rad , ˙ θ = 1 rad/s regulating the state x desired = 0 m and F H,desired =8 . N . (RIGHT) Simulation results of closed-loop contact dynamics for theinitial conditions x = − . m , ˙ x = 0 m/s , θ = 0 . rad , ˙ θ =1 rad/s regulating the state x desired = 0 m and F H,desired = 8 . N . Since the contact control mode is force-triggered, theinitial value for force is about . N. Figure (7) (left)shows that steady state is achieved within 0.5 seconds forthe force and the pitch angle. The settling time for the x-position is large but that is not relevant as the constantly running inverse kinematics engine of the manipulator willcompensate for such errors. Additionally, the thrust valuesduring the transient phase are well below their maximumvalue of 21 N. Hence, this simulation result for this particularset of initial conditions is satisfactory.There are certain cases that might occur during transitionthat may cause the controller to fail i.e. the required controlinputs may exceed physical limits. These include cases inwhich the initial error from the reference values are largeenough to cause undesired behaviour in the controller outputs T and T . • Initial X-Position x : This parameter has the leasteffect on the controller response as the errors associatedwill not be too large. • Initial X-Velocity ˙ x : Ideally, this is zero as the velocitytends to be small when continuous contact is estab-lished. However, certain large positive values tend toreduce the required thrust considerably. • Initial Pitch Angle θ : If the initial pitch angle reducesto smaller values (below 0.05 rad), the required thrustfor satisfactory reference increases rapidly as the contactdynamics are fast compared to the pitching responsein figure (7) (right). A value too large would lead todynamic instability as well as large force values. Sincethere exists a finite positive value of ˙ θ , a starting valueless than the reference is desired. A value of 0.1 rad ischosen since it results in an initial force close to thetriggering value and a small overshoot. • Initial Pitch Rate ˙ θ : The worst and the most highlyunlikely case is when this is a negative value. This canhappen if large impacts create moments in the oppositedirection.According to the above discussion the control wouldtransition smoothly from free-flight regime to contact regimewhen the following conditions are achieved:1) Detection of contact and a threshold force : The end-effector must come into contact with the surface andmust possess a threshold force value. To ensure smoothtransition and elimination of chatter, a schmitt triggerapproach is followed for this condition.2)
Achieving the desired pose : The pose that agrees withthe above discussion as well as the manipulator basejoint pose requirements for successful manipulation i.e.that the point on the surface to be applied falls withinthe workspace and can be manipulated with the desiredend-effector orientation.IV. IMPLEMENTATIONThe aerial platform used in this work is a DJI MatriceM100 quadrotor. It has a weight (with battery) of about2400 grams with a maximum take-off weight of 3600g. Thelightweight nature of the manipulator is the result of cleverdesign optimization as well as high strength-to-weight ratiomaterials like composites. The servomotor used for link 1 isthe MKS DS1220 which is capable of providing 30.4 kg.cmof torque. Link 2, which requires the largest amount oforque, used an MKS HV777 capable of a holding torqueof 38 kg.cm. For link 3, a faster and lighter servo was used– Hitec HS77-BB.
Fig. 8. Hardware signal flow diagram showing the various hardwarecomponents, information flows and integration scheme for experimentaltesting using VICON. For operating in conditions with VICON absent,a visual-inertial localization scheme for the quadrotor along with visualservoing method for the manipulator can be used.
The onboard processing unit was an Intel NUC i7. Itruns a 3.5 GHz processor with 16 GB of RAM. An ArduinoNano microcontroller was used to interface between theservomotors for PWM control as well as to compute the forceon the force sensor. It served as a device to receive serialcommands from the Intel NUC containing desired manipu-lator configuration information and to send the value of forceback to the NUC. The onboard computer ran ROS (RoboticOperating System) over a Linux OS. Nodes for high-levelquadrotor control using MPC (Model Predictive Control),MCU interfacing, control transition and manipulator inversekinematics were integrated for the inspection operation.V. CONCLUSIONS AND OUTLOOKIn conclusion, this work demonstrated the design, con-troller simulation results and implementation scheme forNDT contact inspection using a three degree-of-freedomaerial manipulator.One of the most important drawbacks of this work isthe assumption of force regulation through pitch and 2-Dposition regulation alone. Thus, a more reliable state observerfor force is needed. Such state observers are included in tech-niques such as torque-based control and compliant control ofmanipulator interaction. Additionally, the model, althoughintended to capture the low-level nonlinear dynamics, didnot consider the effect of the manipulator inertia on thesystem. From a design perspective, the serial manipulatorin this work provides a large workspace and sufficientdexterity. However, a parallel mechanism tends to be faster inkinematic reference tracking along the manipulated surfacedue to additional actuators. Another point of improvement isthe overall design. The off-center weights may be reduced bymounting all motors along the vertical axis of the quadrotor and use drive mechanisms such as pulley-belts or chain-sprockets. R
EFERENCES[1] A. Bircher, M. Kamel, K. Alexis, H. Oleynikova, and R. Siegwart,“Receding horizon path planning for 3d exploration and surfaceinspection,”
Autonomous Robots , pp. 1–16, 2016.[2] A. Bircher, M. Kamel, K. Alexis, H. Oleynikova and R. Siegwart,“Receding horizon ”next-best-view” planner for 3d exploration,” in
IEEE International Conference on Robotics and Automation (ICRA) ,May 2016.[3] A. Bircher, M. Kamel, K. Alexis, M. Burri, P. Oettershagen, S. Omari,T. Mantel and R. Siegwart, “Three-dimensional coverage path planningvia viewpoint resampling and tour optimization for aerial robots,”
Autonomous Robots , pp. 1–25, 2015.[4] K. Alexis, G. Darivianakis, M. Burri, and R. Siegwart, “Aerialrobotic contact-based inspection: planning and control,”
AutonomousRobots , pp. 1–25, 2015. [Online]. Available: http://dx.doi.org/10.1007/s10514-015-9485-5[5] A. Bircher, K. Alexis, M. Burri, P. Oettershagen, S. Omari,T. Mantel and R. Siegwart, “Structural inspection path planningvia iterative viewpoint resampling with application to aerialrobotics,” in
IEEE International Conference on Robotics andAutomation (ICRA) , May 2015, pp. 6423–6430. [Online]. Available:https://github.com/ethz-asl/StructuralInspectionPlanner[6] C. D. Bellicoso, L. R. Buonocore, V. Lippiello, and B. Siciliano,“Design, modeling and control of a 5-dof light-weight robot arm foraerial manipulation,” in
Control and Automation (MED), 2015 23thMediterranean Conference on . IEEE, 2015, pp. 853–858.[7] M. Fumagalli, R. Naldi, A. Macchelli, R. Carloni, S. Stramigioli,and L. Marconi, “Modeling and control of a flying robot for contactinspection,” in
Intelligent Robots and Systems (IROS), 2012 IEEE/RSJInternational Conference on . IEEE, 2012, pp. 3532–3537.[8] G. Heredia, A. Jimenez-Cano, I. Sanchez, D. Llorente, V. Vega,J. Braga, J. Acosta, and A. Ollero, “Control of a multirotor outdooraerial manipulator,” in
Intelligent Robots and Systems (IROS 2014),2014 IEEE/RSJ International Conference on . IEEE, 2014, pp. 3417–3422.[9] M. Kamel, K. Alexis, and R. Siegwart, “Design and modeling of dex-terous aerial manipulator,” in
Intelligent Robots and Systems (IROS),2016 IEEE/RSJ International Conference on . IEEE, 2016, pp. 4870–4876.[10] M. Kamel, S. Comari, and R. Siegwart, “Full-body multi-objectivecontroller for aerial manipulation,” in
Control and Automation (MED),2016 24th Mediterranean Conference on . IEEE, 2016, pp. 659–664.[11] A. Q. Keemink, M. Fumagalli, S. Stramigioli, and R. Carloni, “Me-chanical design of a manipulation system for unmanned aerial vehi-cles,” in
Robotics and Automation (ICRA), 2012 IEEE InternationalConference on . IEEE, 2012, pp. 3147–3152.[12] R. M. Murray,
A mathematical introduction to robotic manipulation .CRC press, 2017.[13] R. Ortega, Z. P. Jiang, and D. J. Hill, “Passivity-based control ofnonlinear systems: A tutorial,” in
American Control Conference, 1997.Proceedings of the 1997 , vol. 5. IEEE, 1997, pp. 2633–2637.[14] P. E. Pounds and A. M. Dollar, “Uav rotorcraft in compliant contact:Stability analysis and simulation,” in
Intelligent Robots and Systems(IROS), 2011 IEEE/RSJ International Conference on . IEEE, 2011,pp. 2660–2667.[15] I. Sa, M. Kamel, R. Khanna, M. Popovic, J. Nieto, and R. Siegwart,“Dynamic system identification, and control for a cost effective open-source vtol mav,” arXiv preprint arXiv:1701.08623 , 2017.[16] J. L. Scholten, M. Fumagalli, S. Stramigioli, and R. Carloni, “Interac-tion control of an uav endowed with a manipulator,” in
Robotics andAutomation (ICRA), 2013 IEEE International Conference on . IEEE,2013, pp. 4910–4915.[17] H. W. Wopereis, T. van der Molen, T. Post, S. Stramigioli, andM. Fumagalli, “Mechanism for perching on smooth surfaces usingaerial impacts,” in
Safety, Security, and Rescue Robotics (SSRR), 2016IEEE International Symposium on . IEEE, 2016, pp. 154–159.[18] C. Papachristos, K. Alexis, and A. Tzes, “Efficient force exertion foraerial robotic manipulation: Exploiting the thrust-vectoring authorityof a tri-tiltrotor uav,” in