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Control Engineering Practice 10 (2002) 697711Control of a heavy-duty robotic excavator using time delay controlwith integral sliding surfaceSung-Uk Lee*, Pyung Hun ChangDepartment of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Science Town, 373-1 Koosung-dong, Yusung-ku,Taejon 305-701, South KoreaReceived 22 March 2001; accepted 14 December 2001AbstractThe control of a robotic excavator is difcult from the standpoint of the following problems: parameter variations in mechanicalstructures, various nonlinearities in hydraulic actuators and disturbance due to the contact with the ground. In addition, the morethe size of robotic excavators increase, the more the length and mass of excavators links; the more the parameters of a heavy-dutyexcavator vary. A time-delay control with switching action (TDCSA) using an integral sliding surface isproposed in thispaper forthe control of a 21-ton robotic excavator. Through analysis and experiments, we show that using an integral sliding surface for theswitching action of TDCSA is better than using a PD-type sliding surface. The proposed controller is applied to straight-linemotions of a 21-ton robotic excavator with a speed level at which skillful operators work. Experiments, which were designed forsurfaces with various inclinations and over broad ranges of joint motions, show that the proposed controller exhibits goodperformance. r 2002 Elsevier Science Ltd. All rights reserved.Keywords: Time-delay control; Robust control; Switching action; Robotic excavator; Trajectory control1. IntroductionA hydraulic excavator isa multi-functional construc-tion machine. Workers in the construction industry useit for tasks such as excavating, dumping, nishing,lifting work, etc. However, operatorswho controlhydraulic excavatorsmust be trained for many yearsto do such work quickly and skillfully. A hydraulicexcavator hasthree links: boom, arm and bucket; andthe operator hastwo arms. Thus, it isnot easy forbeginnersto execute elaborate work that manipulatesthree links at the same time. Moreover, because theoperatorshave to run work in variousdangerousanddirty environments, the number of skillful operators isever decreasing. For that reason, studying the automa-tion of hydraulic excavators is necessary for improvingproductivity, efciency, and safety.The automation of hydraulic excavatorshasbeenstudied by several researchers (Singh, 1997). Among theseveral tasks to be automated, Bradley and Seward(1998) developed the Lancaster University computerizedintelligent excavator (LUCIE) and used it to automatethe digging work. Stentz, Bares, Singh, and Rowe (1998)developed a complete system for loading trucks fullyautonomously on a 25-ton robotic excavator. Changand Lee (2002) automated straight-line motions on a 13-ton robotic excavator under working speed conditions.Here, the straight-line motion represents the importanttask of scraping or attening the ground and serves as afundamental element used as a basis for developingmore complicated tasks. As illustrated in Fig. 1, the end-effector of the manipulator needsto be controlled totrack a linear path on the task surface. An operatorshould manipulate three links simultaneously to executeit. Though an operator isskillful, performing thestraight-line motions for a long time results in thefatigue of an operator and decreases productivity.The control of robotic excavator isdifcult from thestandpoint of the following problems: parameter varia-tionsin mechanical structures, variousnonlinearitiesinhydraulic actuators, and disturbance due to the contactwith the ground. In mechanical structures, the inertial*Corresponding author. Tel.: +82-42-869-3266; fax: +82-42-869-5226.E-mail address: s sulee123cais.kaist.ac.kr (S.-U. Lee).0967-0661/02/$-see front matter r 2002 Elsevier Science Ltd. All rights reserved.PII: S 0967-0661(02)00027-8force and gravitational force varieslargely with jointmotions. Hydraulic actuators, massively coupled andcomplexly connected, have variousnonlinear compo-nents. For such reasons, various difculties exist incontrolling a robotic excavator.To solve these problems, several research works havebeen performed, which may be categorized aseithersimulation studies or experimental studies. In terms ofsimulation studies, for instance, Chiba and Takeda(1982) applied an optimal control scheme to the controlof the manipulator of an excavator. Morita and Sakawa(1986) used PID control with feedforward control basedon inverse dynamics. Medanic, Yuan, and Medanic(1997) proposed a polar controller-based variablestructure control. Song and Koivo (1995) used afeedforward multiplayer neural network and a PIDcontroller over a wide range of parameter variations. Asfor experimental studies, Bradley and Seward (1998)used a high-level controller that was based on rulesobtained by observation of skilled operators, and a PIDlow-level motion controller that moved the end-effectorin response to a demand from the high-level controller.Lee (1993) used P control together with a fuzzy controltechnique that used response error and its derivative onthe phase plane. Sepehri, Lawrence, Sassani, andFrenette (1994) analyzed the phenomenon of couplingin the hydraulic actuator, and proposed a feedforwardscheme that compensates coupling and load variation byusing a simple valve model and measured pressure.Yokota, Sasao, and Ichiryu (1996) used disturbanceobserver and PI control, and applied it to a miniexcavator. Chang and Lee (2002) used time-delaycontrol (TDC) and compensators based on the dy-namicsof the excavator and applied it to straight-linemotionsof a 13-ton excavator with a bucket speed of0:5m=s; a speed level at which skillful operators work.However, almost all the research works above tend tobe limited to experimentson a mini excavator underrelatively lower speed conditions. Among the experi-mental research works above, only that of Chang andLee (2002), which wasperformed on the control of aheavy-duty 13-ton robotic excavator, wasperformedunder working speed conditions. The more the size ofexcavators increase, the more the length and mass ofexcavatorslinksincrease, and the more the parametersof a heavy-duty excavator vary. Therefore, the controlof a heavy-duty excavator becomesmore difcult thanthe control of a mini excavator. The control of a heavy-duty excavator (a 21-ton robotic excavator (Fig. 2) usedin thispaper) requiresa robust controller.In thispaper, we apply time-delay control withswitching action (TDCSA) using an integral slidingsurface (ISS) to the control of a 21-ton robotic excavatorand validate the proposed control algorithm throughexperimentson a straight-line motion tracking control.In addition, we show the advantage of the TDCSA usingan ISS. TDCSA, which wasproposed by Chang andPark (1998), consists of a TDC and a switching action.The switching action based on sliding mode control(SMC) compensates for the error of the time-delayestimation (TDE) and makes the TDC more robust.Chang and Park (1998) used a PD-type sliding surface(PDSS) for the switching action and applied the TDCSAusing a PDSS to a pneumatic system for compensatingthe stick-slip, but we use an ISS for the switching actionto improve the control performance in thispaper(Slotine & Li, 1991; Utkin & Shi, 1996). Asa similarcontroller, a new integral variable structure regulationcontroller, designed using an integral sliding surface anddisturbance observer, was proposed by Lee and Youn(1999). Lee and Youn, however, have demonstrated theusefulness of their proposed algorithm by simulationsabout regulation controlsof a two-link manipulator. Incontrast, we will perform experiments on the control ofa robotic excavator.Fig. 1. Illustration of straight-line motion.Fig. 2. Appearance of Robex210LC-3 excavator.S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711698The rest of this paper is organized as follows. Section2 will briey analyze the characteristics of the roboticexcavator system, Section 3 presents the design ofcontroller. In Section 4, the effectiveness of the proposedcontroller will be veried through experimentson a 21-ton robotic excavator. Finally, conclusions will bedrawn in Section 5.2. Overview of robotic excavator systemThis section describes briey the characteristics of therobotic excavator. More detailsabout the model of arobotic excavator can be found in Chang and Lee(2002). In thispaper, the swing motor together with thetraveling motor is not considered for straight-linemotion; only the boom, arm and bucket are considered.The mathematical model that isneeded for designing acontroller isdescribed in Appendix A. Since a roboticexcavator consists of a manipulator and actuators, thecharacteristic of these two parts will be described briey.2.1. ManipulatorIn the dynamic equation (Eq. (A.1), the inertialforcesand gravitational forcesaswell asthe centrifugaland Coriolisforcesvary nonlinearly with the change ofanglesof the links, and have coupling elementsbetweenlinks. Among these terms, the centrifugal and Coriolisforceshave a smaller effect on the control performance,since the velocity of each link is not that great. Incomparison, the inertial forces and gravitational forcesvary largely, since the total weight of boom, arm andbucket used in this research is 2:67 ton and the range ofjoint anglesare broad. The size and variation in each ofthe inertial and the gravitational forcesin a straight-linemotion with incline of 01 are shown in Fig. 3. We canobserve that the inertial forces and gravitational forcesvary largely.2.2. Hydraulic actuatorsThe hydraulic actuator of the robotic excavator usedin thispaper hasat least three kindsof nonlinearitiesasfollows: valve characteristics, dead zone and time lag.2.2.1. Valve characteristicsHydraulic valvesare devicesthat transfer the owfrom the pump to cylinder. From the general valve owequation Q cdADPp; the ow that istransferredfrom the pump to cylinder isdetermined by owcoefcient, the area of the valve and pressure difference.The area of a spool valve has a nonlinear shape asshown in Fig. 4. Therefore, valves have nonlinearcharacteristics according to the nonlinear area of thevalve andDPp:2.2.2. Dead zoneThe geometry of the spool valve used in a Ro-bex210LC-3 excavator is an overlapped shape as shownin Fig. 4 and causes the dead zone nonlinearity. Theoverlapped region isdesigned for the convenience of anoperator. Therefore, when the spool is displaced in theoverlapped region, the valve becomes closed: this causes0 2 4 6 8_3000_2000_10000100020003000timesecforceNewton(a) Inertial forceboomarm0 2 4 6 8_505101520x 104timesecforceNewton(b) Gravitational forceboomarmFig. 3. Inertial forcesand gravitational forcesof boom and arm.S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711 699the dead zone nonlinearity. The overlapped region isabout 30 percent of the whole spool displacement.2.2.3. Time lagA phenomenon similar to a dead zone occurs becauseof the time taken for the pump output pressure to reachthe pressure level that is sufcient to move the link. Notethat thisphenomenon issomewhat different from thepure time delay often found in transmission lines. Fig. 5illustrates this phenomenon with the experimentalresults. In the presence of maximum control input, theboom doesnot move until the time is0 :13 s; when thepump pressure begins to exceed the pressure of theboom cylinder plus the offset pressure, as shown inFig. 5. Thisphenomenon occursonly when the boomlink beginsto move and it doesnot exist any more oncethe pump output pressure reaches the pressure levelsufcient to move the link. Moreover, this phenomenoncan be compensated by the compensator which will beproposed in Section 3.2.3. Controller designA robotic excavator hasthe following nonlinearities:variationsin the inertial and gravitational forcesin themanipulator; and nonlinear valve characteristics, deadzone and time lag in the hydraulic actuator. Toovercome these aforementioned nonlinearities, Changand Lee (2002) suggested the TDC and compensatorsand used these to control a 13-ton robotic excavator, butwe need a more robust controller to control a 21-tonrobotic excavator effectively. The greatest differencebetween the 21-ton robotic excavator used in this paperand the 13-ton robotic excavator used in Chang and Lee(2002) exists in the length and mass of excavators links.The linksof the former are one and half timesthe lengthand weight of those of the latter. Therefore, theparameter variationsof a 21-ton excavator are moreserious than those of a 13-ton excavator. A more robustcontroller than TDC isrequired to control the straight-line motion of a 21-ton robotic excavator.For controlling a 21-ton robotic excavator, we haveconsidered TDCSA, which is more robust than TDC.Spool displacementVavleAreaoverlap regionFig. 4. Rough shapes for areas of spool valve.00.10.20.30.40.50.60.70.80.9 1050100150200(a) Pressures of pump and head side of boom cylindertimesecpressurebarpumphead side of boom cylinder00.10.20.30.40.50.60.70.80.9 1949698100102104106(b) Boom responsetimesecangledegFig. 5. Illustration of the nonlinearity due to time lag.S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711700Then, instead of a PDSS used by Chang and Park(1998), we use an ISS in this paper for improving thecontrol performance (Slotine & Li, 1991; Utkin & Shi,1996).Among the aforementioned nonlinearities, however,the dead zone and the time lag cause the large trackingerrors. Hence, proper compensation is demanded. Forthat reason, we design the two controllers: rst theTDCSA using an ISS as the baseline control and second,compensators to overcome the dead zone and thetime lag.3.1. Design of the TDCSA3.1.1. TDCSA using an ISSIn order to apply the controller to a roboticexcavator, Eq. (A.5) isrearranged into the following:%M.lt%Htut: 1Note that%M isa constant matrix representing theknown angle of MK; whereas%Ht consists of termsrepresenting uncertainties and time-varying factors,which are expressed as%HtHtMKtC0%M.lt: 2Now we dene the desired dynamics of the closed-loopsystem with the following error dynamic:.etKvetKpet0; 3where etldtC0lt denotesthe position error vectorwith ldt denoting the vector of desired piston displace-ments, Kvthe derivative gain matrix, and Kptheproportional gain matrix. The TDC law that meetstherequirement isobtained asutdct%M.ldtKvetKpetC138 #Ht; 4where#Ht denotesan estimate of%Ht:The estimated#Ht can be obtained by using bothEq. (1) and the fact that%Ht isusually a continuousfunction. More specically, when L issmall enough,then#HtE%Ht C0 Lut C0 LC0%M.lt C0 L: 5Combining Eq. (5) with Eq. (4), the TDC law isobtained asfollows:utdct%M.ldtKvetKpetC138 utdct C0 LC0%M.lt C0 L: 6More details about the stability condition and the designof TDC can be found in Youcef-Toumi and Ito (1990)and Hsia and Gao (1990).L should be sufciently small for TDC to meet thedesired error dynamics of Eq. (3). The valve used for L;however, is set to be that of the sampling time, whenTDC isimplemented in a real-time controller. Thevariation of system nonlinearities and disturbances,occurred during the time delay L; caused TDE errorasfollows:%HtC0#Ht%HtC0%Ht C0 LDHt: 7More specically, the friction dynamics cause large TDEerror. Because of the TDE error, TDC does not have thedesired error dynamics of Eq. (3), but the followingerror dynamics:.etKvetKpet%MC01DHt; 8where the right term %MC01DHt denotesthe effect ofthe TDE error.The TDCSA is proposed by adding the switchingaction based on the sliding mode control to TDC, asfollows:utdcsat%M.ldtKvetKpetC138 utdcsat C0 LC0%M.lt C0 LKwsgns; 9where s represents the sliding surface and Kwisaswitching gain matrix. The TDCSA has the followingerror dynamic:.etKvetKpet%MC01DHtC0%MC01Kwsgns: 10In Eq. (10), we see that the switching action can reducethe TDE error.In order to match the desired error dynamics (Eq. (4)with the sliding surface (s), we use the integral slidingsurface as follows:stetKvetKpZt0et dtC0 e0C0Kve0; 11where the sliding surface (s) hasthe initial value of zeroand itsderivative isequal to desired error dynamics(Eq. (3). The necessity and advantage of using anintegral sliding surface will be shown in Section 3.1.4.3.1.2. Stability analysis of TDCSA using an integralsliding surfaceFor the stability analysis of the overall system, we usethe second method of Lyapunov. If the Lyapunovfunction isselected as V 12sTs; itstime derivative isasfollows:V sTs sT.e Kve KpeC138sT.ldC0%MC01u %MC01%H Kve KpeC138sTf.ldC0%MC01%M.ldKve Kpe#H KwsgnsC138%MC01%H Kve KpegsTC0%MC01#H %MC01%H C0%MC01KwsgnsC138sT%MC01DH C0%MC01KwsgnsC138: 12Therefore, the following condition isneeded so that thetime derivative of the Lyapunov function should benegative denite:Kwii jDHij for i 1;y;3: 13S.-U. Lee, P. Hun Chang / Control Engineering Practice 10 (2002) 697711 701In other words, the magnitude of the switching gainKw must be larger than that of the term due to the TDestimation error.3.1.3. Saturation functionTDCSA uses a switching action for compensating theTDE error, but the switching action in TDCSA causes achattering problem. Therefore, we use a saturationfunction to reduce the chattering problem (Slotine & Li,1991). A saturation function can be used as follows:satst;fstf if jstjof;sgnst otherwise;8jDHij; the minimum tracking guarantee isjessijo%MC01iDHitKpi%MC01iKwili=fi: 22For a constant right-hand side of Eq. (21), however, thesteady-state solution of Eq. (21) is eit-0 andRt0eit dt-0: Therefore, TDCSA using an ISS candrive the tracking