Autonomous Exploration in Unknown Urban Environments for Unmanned Aerial Vehicles
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1 Autonomous Exploraton n Unknown Urban Envronments for Unmanned Aeral Vehcles Davd H. hm * and Hoam Chung Unversty of Calforna, Berkeley, CA, 9470 H. Jn Km eoul Natonal Unversty, eoul, Korea and hankar astry Unversty of Calforna, Berkeley, CA, 9470 In ths paper, we present an autonomous exploraton method for unmanned aeral vehcles n unknown urban envronment. We address two major aspects of exploraton- map buldng and obstacle avodance- by combnng model predctve control (MPC) wth a local obstacle map bulder. An onboard laser scanner s used to buld the onlne map of obstacles around the vehcle durng the flght. A real-tme MPC algorthm wth a cost functon that penalzes the dstance to the nearest obstacle replans the path. The adjusted trajectory s sent to the poston trackng layer n the Berkeley UAV avoncs. The proposed approach s mplemented on Berkeley rotorcraft UAVs and successfully tested n urban flght experment setup. I. Introducton NMANNED aeral vehcles (UAVs) have become an ndspensable platform for many applcatons where U manned operaton s consdered unnecessary or too rsky. As UAVs fnd ther way nto more demandng applcatons such as ground support or urban warfare, they are expected to fly autonomously wthout colldng nto obstacles. o far, those stuatons have been avoded by operatng UAVs at hgher alttudes where chances of runnng nto obstacles are very slm, or, f really necessary, by controllng UAVs wth human operators n the loop. However, as UAVs are requred to operate n cluttered or dynamcally changng envronments wth more authorty, the need for autonomous exploraton capablty s greatly ncreasng. Explorng autonomously n an unknown envronment requres two crucal component technologes: map buldng and onlne trajectory replannng. Map buldng and obstacle avodance have been ntensvely covered by robotcs socety snce late 70s. As a result of these efforts, varous algorthms and mplementatons are currently avalable for gudng moble robots safely n unknown or partally known two-dmensonal world. Although some algorthms can be extended to the modelng of three-dmensonal spaces, these are stll computatonally expensve, and have lmtatons n outdoor applcatons. In 1990s, researchers ntroduced probablty theores nto map buldng technques, 1 enhancng robustness and performance of those algorthms even wth cheaper and naccurate sensors. Naturally, ntensve computatons are requred for these enhancements, and the stuaton becomes worse n three-dmensonal problems. UAVs also pose more challenges than the ground robots do n the development and mplementaton. UAVs typcally fly at a much faster speed than the ground robots, and therefore demand faster and more accurate decson makng. The payload allocated to the avoncs and onboard sensors s no less lmtng than ground robots. Fnally, durng the * Prncpal Research Engneer, Department of Electrcal Engneerng and Computer cence, Correspondng Author (hcshm@eecs.berkeley.edu) Ph.D. Canddate, Department of Mechancal Engneerng (hachung@eecs.berkeley.edu). Assstant Professor, chool of Mechancal and Aerospace Engneerng (hjnkm@snu.ac.kr). Professor, Department of Electrcal Engneerng and Computer cence (sastry@eecs.berkeley.edu). 1
2 development stage, tral-and-error approaches are strctly prohbted because any falure to avod obstacles nescapably leads to a costly and very dangerous accdent. Model predctve control has been found hghly attractve for addressng control problems n dynamc envronments. The onlne optmzaton 3 wth prevew enables a control system more responsve to the changes n the system dynamcs and the surroundngs. Further, t has been suggested a varety of performance goals, n addton to the feedback stablzaton, can be ncorporated nto the cost functon. hm, Km, and astry 4 proposed MPC-based flght control algorthms by ntroducng a set of cost functons for decentralzed collson avodance and aeral pursut-evason. 5 Partcularly, t s shown that MPC s capable of obstacle avodance usng a cost functon that penalzes the dstance to the nearest obstacle. The obstacles n the flght path can be made known to the path planner by a pre-programmed map or a dynamcally bult obstacle map. Whereas the former approach does not suffer from any sensor-nduced errors, the map tself may be naccurate or outdated. Therefore, we favor onboard sensors, especally, the laser scanner due to ts accuracy and long detecton range. In ths paper, we propose an autonomous exploraton algorthm sutable for, but not lmted to, urban navgaton by combnng the MPC-based obstacle avodance wth local obstacle map buldng usng onboard laser scannng. tartng from the gven trajectory, the MPC layer solves for a collson-free trajectory by the real-tme gradentsearch based algorthm. The proposed algorthm s valdated n smulatons, and n experments usng a smulated urban envronment as shown n Fgure 1. II. Formulaton In ths secton, we provde some background n the system dynamcs, MPC formulaton, and the coordnate transformaton for laser scannng. A. ystem Dynamcs and Path Generaton usng MPC A model for a gven system dynamcs can be wrtten as a dscrete-tme dynamc equaton such that: x( k+ 1) = f( x( k)) + g( x( k)) u ( k) (1) We are nterested n solvng a dscrete-tme optmal control problem for the system n Eq. (1) to fnd the optmal * u ( k) T such that k = nput sequence { } subject to the dynamc equaton (1). 1 * T T { ( k) } = arg q( ( k), ( k) ) + qf ( ( T + 1) ) u x u x () k = 1 k = 1 * Nonlnear model predctve control (NMPC) problem solves for the optmal control law { u ( k) } T k = 1 * x and mplement the optmal nput { u } nonlnear dynamc equaton n Eq. (1), startng from (1) Fgure 1. Berkeley UAV flyng autonomously n a smulated urban envronment ( ) k for the k τ = 1 1 τ T and then repeat these steps from the state x( τ + 1) at k = τ + 1. ur model-predctve path plannng strategy combnes the potental feld concept wth the onlne optmzaton wth prevew. The cost functon n Eq. () s formulated to reflect the aspect of a potental functon for path plannng n the envronment wth statonary or movng obstacles. Ths allows the trajectory generaton and vehcle stablzaton to be combned nto a sngle problem, and the look-ahead feature of the MPC framework makes ths for
3 approach less vulnerable to local ma. 4 In ths scenaro, we assume that each vehcle s aware of nearby obstacles by means of onboard sensors or a pre-programmed map. q x( k), u ( k) : The followng potental functon term s added to the cost functon ( ) q obst K ( x ( k)) =, (3) a x k x k + b y k y k + c z k z k + ε N = 1 ( ( ) ( )) ( ( ) ( )) ( ( ) ( )) where ( x, y, z ) denotes the poston of the vehcle, and ( x, y, z ) denotes the poston of the -th nearest obstacle (or the poston of other vehcles) n local Cartesan coordnate frame. Eq. (3) ntroduces a potental feld near N obstacle ponts nto the MPC framework. ( a, b, c ) s a set of scalng factors n x, y, z drectons, respectvely. Note ε s a postve constant to prevent Eq. (3) from beng sngular when ( x, y, z ) = ( x, y, z ). It has been shown n Ref. 4, along wth the detaled descrpton on algorthms, that the proposed MPC framework allows the trajectory generaton and the vehcle stablzaton problems to be combned nto a sngle problem. In ecton III, we wll present an obstacle avodance algorthm usng the MPC framework shown above for urban exploraton problems. B. Coordnate Transformaton for aser can Data The laser scanner we adopted n our research conssts of a laser source, a rotatng mrror for planar scannng, and a laser receptor. The mrror reflects the laser beam n a plane. At each scannng, the sensor reports a stream of measurements that supples the followng nformaton: {(, β ), 1,..., } Y = d n = N, (4) n n meas where d n, β n, and N meas represent the dstance from an obstacle, the angle n the scannng plane, and the total number of measurements per scan, respectvely. Each measurement can be wrtten nto a vector form such that where and j are orthonormal unt vectors lyng n the scannng plane. The subscrpts D and represent scanned data and laser scanner, respectvely. In order to fnd the spatal coordnates of each detected pont, we need a few coordnate transformatons among three coordnate systems: body coordnate systems attached to the laser scanner and to the host vehcle, respectvely, and the spatal coordnate system, to whch the vehcle locaton and atttude are referred. In order to fly around obstacles n the surroundng envronment, the laser scanner should be able to scan the area large enough to cover the space that the entre vehcle body may pass through wth some clearance. For example, f the laser ( cos β sn β ) D / n dn n + nj =, (5) scanner s nstalled to scan the area horzontally, an actuaton n the ptch axs s added so that the scanner can cover the area hgher than the rotor plane and lower than the landng gear. Each laser measurement vector n laser scanner-attached body coordnates s frst transformed nto the vehcleattached body coordnates and then the spatal coordnate system as followng: Z B B Z scanner obstacle Fgure. Coordnate transformatons for laser scan data B V / B Z D / = R D/ / D/ = R R ( α) / B B/ D/, (6) 3
4 where the subscrpts and B represent spatal- and body-coordnate system, respectvely. R B/ α ( ) s the transformaton matrx from the laser body coordnate to vehcle body coordnate B where α s the tlt angle wth respect to the vehcle body. If the laser scanner s mounted wthout addtonal tltng moton, R B/ α ( ) reduces to a constant matrx. R / Bdenotes the transformaton matrx from vehcle body coordnates to spatal coordnates. Fnally, the spatal coordnate of the obstacle s found by: = + + D D/ / B B = R R ( α) + R + B / B B/ D/ / B / B B (7) Usng Eq. (7), one can fnd the spatal coordnate of a detected obstacle pont by combnng the raw measurement vector wth the poston and atttude of the vehcle, whch s avalable from the IN and the GP onboard. Note that the accuracy of the detecton n the spatal coordnate system not only depends on the laser scanner tself, but also the accuracy of the vehcle poston and atttude. Fgure 3 shows fxed and actuated types of laser scanner mountngs on Berkeley UAVs. The scanner shown n the left s a fxed mountng and the one on the rght s nstalled on a tlt actuator wth a tlt angle encoder. It s noted the laser scanner on a fxed mountng can provde vertcal scannng wth a lmted range due to the small body moton caused by the man rotor gyraton. Fgure 3. aser scannng devces mounted on Berkeley UAVs (left: fxed, rght: actuated mountng) III. Autonomous Exploraton usng MPC wth ocal Maps In ths secton, we present a MPC-based trajectory generaton for autonomous exploraton n an unknown envronment wth obstacles. Partcularly, we are nterested n addressng safe navgaton of UAV n urban envronments wth no pror nformaton avalable on the obstacles. We begn wth the followng statement: Problem tatement Fnd a trajectory that allows the vehcle to navgate from the gven startng pont A to the destnaton pont B wth safe dstance from obstacles n the envronment. We address the problem wth an ntegral approach of MPC-based trajectory planner wth local obstacle map generaton usng onboard sensors. A. Trajectory Replannng wth MPC In ths secton, we consder a navgaton problem from pont A to pont B, connected by a reference trajectory. Wthout loss of generalty, the trajectory s assumed as a straght lne. The MPC approach n ecton II-A can be formulated as a trackng control problem wth a cost functon term for Eq. () such that 4
5 trk 1 T q ( x( k)) = ( yref ( k) x( k) ) Q( yref ( k) x ( k) ), (8) where ( ( )) trk obst q x k = q ( x( k)) + q ( x ( k)) n Eq. (). In Ref. 4, Eq. (1) s chosen to be the full vehcle dynamc model so that the optmzed varable u ( k) s the stablzng control nput that also mzes other penaltes for trackng, obstacle avodance, or aeral pursutevason games. Although the MPC can be formulated ether for drect stablzaton or reference trajectory generaton, we opt for the latter due to the safety durng flght experments usng our UAVs. By separatng the trajectory layer from the stablzaton layer, any falure of the optmzaton routne to converge to a soluton does not drectly affect the stablty of the overall vehcle. However, the dfference between the reference poston and the physcal poston due to the trackng error should be consdered n the obstacle map buldng process n ecton III-B. Therefore, n ths paper, we choose a smplfed dynamc model to generate a reference trajectory n order to lower the numercal load of the optmzaton process for experment. T x( k+ 1) = x( k) + Tu ( k), (9) T where x [ x y z ], u vx vy v z and T s the samplng tme of the dscretzed model. In ths setup, s the optmzaton results n the reference velocty n the spatal coordnates. The optmzaton output s fed back nto Eq. (9) to obtan the reference trajectory, whch s then sent to the trackng layer n Berkeley UAV avoncs. 6 As descrbed n ecton II, an MPC-based trajectory generator can be formulated for obstacle avodance as well. In Ref. 4, t was shown that the cost term (Eq. (3)) wth N=1 s suffcent although Eq. (3) wth N > 1 s expected to result n a smoother cost functon surface and thus allow a better convergence n the gradent-search based optmzaton. In favor of effcency of algorthms and computaton, we choose the nearest-pont method,.e., N=1 so that only the nearest pont s consdered n the optmzaton(fgure 4). The cost term n Eq. (3) for urban navgaton s set to s ( ) 1 q obst ( x ( k)) = K ( x ( k) x ( k)) + ( y ( k) y ( k)) + ( z ( k) z ( k)) + ε, (10) obs where the cost functon s chosen to decay unformly n every drecton from the obstacle pont at ( x, y, z ). K obs s a tunng parameter to balance the tendency to stay on the orgnal gven path and to break away from the gven path to go around obstacles. B. ocal bstacle Map Buldng For the MPC-based trajectory generaton wth obstacle avodance, we need to fnd mum length from the reference poston to a pont on an obstacle such that, the relatve vector wth ( ) = arg, (11) ref ref obs where s Eucldan norm n three-dmensonal space and obs s the set of all ponts on the obstacles n the surroundng three-dmensonal space. Theoretcally, Eq. (11) demands a perfect knowledge on all obstacles n the surroundng envronment, whch would requre an deal sensor capable of omn-drectonal scannng wth nfnte detecton range. Further, f the MPC s for reference trajectory generaton, the deal sensor should be movng along the trajectory of the reference ponts durng the state propagaton over a fnte horzon at every optmzaton stage. bvously, such a scenaro s mpractcal. Therefore, n order to provde to the MPC-based trajectory Fgure 4. Nearest-pont method / B 5
6 generator wth these restrctons, t s necessary to mantan a local obstacle map consstng of recent measurements from onboard sensors. At each sample tme, the sensor provdes N meas measurements of scan ponts on obstacles nearby. Due to the mperfect coverage of the surroundngs wth possble measurement error, each measurement set s frst fltered, transformed nto local Cartesan coordnates, and cached n the local obstacle map. A frst-n frst-out (FIF) buffer s chosen for the data structure for such a map, whose update rate depends on the types of obstacles nearby. If the surroundng s known to be statc, the cachng tme s desred to be as long as the memory and processng overhead permts. n the other hand, a more dynamc envronment would requre shorter cachng to reduce the chance to detect an obstacle that may not exst any more. In order to solve Eq. (11), the measurement set n the FIF should be sorted n an ascendng order of for all ref Raw scan data from aser canner Fnd Nearest obstacle pt to MPC Flter out naccurate measurements ort and flter out small obstacles Vehcle poston and atttude from Host vehcle Convert to local cartesan coordnates Fnd N1 ponts closest to host vehcle Fgure 5. ocal partal map buldng method for nearest-pont approach usng MPC n the local obstacle map. Pror to be regstered n the database, any anomales such as saltand-pepper nose are dscarded. In case that the sensor detects small debrs, such as grass blades or leaves blown by the vehcle, those small-sze objects, not beng a serous threat for safety, should be gnored by the trajectory planner. We apply an algorthm that computes a boundng box of the mum volume that contans a seres of subsequent ponts n FIF where the dstance between adjacent ponts n the sorted sequence s less than a predefned length. Then, f the volume of the box s larger than a threshold so that t s consdered as a safety threat, the coordnates of the nearest pont n the boundng box s found and used for computng Eq. (3). The procedure of the local obstacle map buldng method proposed above s llustrated n Fgure 5. IV. Experment Results In ths secton, we present the smulaton and experment results of autonomous exploraton n an urban envronment. The experment desgn s strongly affected by the safety regulatons: t s performed n a feld wth portable canopes smulatng buldngs, not wth real buldngs. The canopes, measurng 3 meter 3 meter 3 meter each, are arranged as shown n Fgure 6. The dstance between canopes s set to 10 meters n the north-south drecton and 1 meters n the east-west drecton so that the UAV wth 3.5 meter long fuselage can pass between the canopes wth mal safe clearance, about 3 meters from the tp to a canopy when stayng on course. For valdaton, the MPC engne developed n Ref. 4 s appled to the proposed urban experment setup. A smulaton Fgure 6. Aeral vew of urban experment (black: gven straght path, red: actual flght path of UAV durng experment) Fgure 7. mulaton of MPC-based path plannng n the proposed urban experment setup 6
7 model s constructed n MATAB TM /mulnk TM, where the local map buldng wth a laser scanner s replaced wth a pre-programmed map to avod buldng a laser sensng model. The MPC algorthm wth the local map buldng algorthm s mplemented n C language for speed and portablty. As shown n Fgure 7, the MPC path planner s capable of generatng a collson-free trajectory around the buldngs from the orgnal trajectory wth ntentonal ntersecton wth buldngs. The green and red lnes pontng to the buldngs are at each sample tme. For experments, the mulnk model s modfed to functon as the onlne trajectory generator. Although mulnk was not desgned for a real-tme controller n the loop, t can be forced to run for soft real-tme control by addng a real-tme enforcng block. Usng the behavor of TCP/IP communcaton, a custom TCP/IP transport block s confgured to enforce soft real-tme operaton of the mulnk model at 10Hz n ths case. Urban exploraton experments were performed usng a Berkeley UAV, whose detaled specfcaton s gven n Table 1. For obstacle detecton, the vehcle s equpped wth an M-00 from ck AG (Fgure 3), a twodmensonal laser range fnder, whch s capable of 80 m scannng range wth 10 mm resoluton and weghs 4.5 kg. The measurement s sent to the flght computer va R-3 and then relayed to the ground staton runnng the MPCbased trajectory generator n mulnk and the ground staton software wth a three-dmensonal renderng wndow. The laser scanner data stream s then processed followng the method proposed n ecton III-B. In Fgure 8, a threedmensonal renderng from the ground staton software s gven. The dsplay shows the locaton of the UAV, the reference pont marker, to a pont n the local obstacle map at that moment, and laser-scanned ponts as blue / B Table 1. pecfcaton of a Berkeley UAV Base platform Yamaha R-50 Industral Helcopter Dmenson 0.7 m(w) 3.5 m () 1.08 m (H) Rotor Dameter m 44 kg (dry weght) Weght 0 kg (payload ncludng avoncs) cycle gasolne engne Engne 1 hp Fuel: 40 utes peraton Tme Avoncs: 00 utes Two PC104-based computers Boeng DQI-NP IN NovAtel GP MllenRT- nboard ystem IEEE 80.11b Wreless Ethernet Ultrasonc altmeters ICK laser range fnder (M-00) Pan-tlt-zoom Camera Waypont navgaton Capabltes Poston trackng Interactve operaton mode Canopy n preprogrammed map aser scan ponts from canopy / B UAV reference poston marker Fgure 8. A snapshot of three-dmensonal renderng durng an urban exploraton experment 7
8 dots. Durng the experments, the laser scanner used n our experment demonstrated ts capablty to detect the canopes wthn the lne of sght wth great accuracy, and other surroundng natural and artfcal objects ncludng buldngs, trees and power lnes. The processed laser scanned data n a form of local obstacle map s used to generate a trajectory usng the algorthm n ecton III-A. The trajectory s then sent va IEEE 80.11b to the avoncs system wth a dedcated process runnng to enforce the command update rate at 10Hz. The trackng control layer enables the host vehcle to follow the gven trajectory wth suffcent dstance. In the repeated experments, the vehcle was able to fly around the obstacles wth suffcent dstance to reach the destnaton as shown n Fgure 6 (red lne). V. Concluson Ths paper presented an autonomous exploraton method for unmanned aeral vehcles n unknown urban envronments. An onboard laser scanner s used to buld an onlne map of obstacles around the vehcle. Ths local map s combned wth a real-tme MPC algorthm that generates a safe vehcle path, whch uses a cost functon that penalzes the dstance to the nearest obstacle. The adjusted trajectory s then sent to a poston trackng layer n the herarchcal UAV avoncs archtecture. In a seres of experments usng a Berkeley UAV, the proposed approach successfully guded the vehcle safely through the urban canyon. VI. Acknowledgment Ths research was supported by DARPA (F C-3614) and AR MURI (DAAD ). References 1. Thrun. Robotc mappng: A survey. In G. akemeyer and B. Nebel, edtors, Explorng Artfcal Intellgence n the New Mllenum. Morgan Kaufmann, 00. M. C. Martn and H. P. Moravec, Robot Evdence Grds, CMU Robotcs Insttute Techncal Report, CMU-RI- TR , Mar G. J. utton and R. R. Btmead, Computatonal Implementaton of NMPC to Nonlnear ubmarne, n F. Allgöwer and A. Zheng, edtors, Nonlnear Model Predctve Control, volume 6, pages , Brkhäuser, D. H. hm, H. J. Km, and. astry, Decentralzed Nonlnear Model Predctve Control of Multple Flyng Robots, IEEE Conference on Decson and Control, Mau, HI, December J. prnkle, J. M. Eklund, H. J. Km and. astry, Encodng Aeral Pursut/Evason Games wth Fxed Wng Arcraft nto a Nonlnear Model Predctve Trackng Controller, pages , 43rd IEEE Conference on Decson and Control, Paradse Island, Bahamas, December, D. H. hm, Herarchcal Control ystem ynthess for Rotorcraft-based Unmanned Aeral Vehcles, Ph. D. thess, Unversty of Calforna, Berkeley,
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