Robus localizaion algorihms for an auonomous campus our guide Richard Thrapp Chrisian Wesbrook Devika Subramanian Rice Universiy Presened a ICRA 200 Ouline The ask and is echnical challenges The localizaion problem Adapive sae esimaion Experimenal resuls Relaed work and conclusions
The ask and is challenges Task: To give ours of he Rice Universiy Campus. Challenges Environmen canno be modified o assis robo. Low budge projec --- no expensive sensors! Robo needs o inerac wih people. Localizaion errors of more han 40 cm canno be oleraed. Cos of failure high! Virgil: The Rice Tour Guide On-board odomery Sonars and bumpers for collision avoidance RWI ATRV Jr equipped wih cheap differenial GPS ($2K) Suppored by a gran from Rice s Engineering School 2
The Engineering Quad Tour Engineering quesion How well can we localize he robo in an urban campus wih los of buildings and rees wih cheap differenial GPS (s error of over meer) and onboard odomery? 3
The localizaion problem Esimae of robo posiion localizer course se poin Navigaion algorihm u odomery (x,y,q) GPS Proporional conroller Robo Localizer esimaes robo posiion from odomery and GPS using an exended Kalman filer. EKF basics: sae evoluion Sae X of robo evolves according o he following equaion X = f ( X, u, w f is a non-linear funcion (f is esimaed off line by a sae idenificaion process). u is he commanded ranslaion and roaion a ime. w = N(0,Q ) is he process noise. ) 4
EKF (cond.): Measuremen GPS reading z measures he sae X of he robo. z = h( X ) v v =N(0,R ) is he measuremen noise. h is a coordinae ransformaion. The EKF calculaion Recursive leas squares esimaion echnique for compuing X from a sequence of measuremens z,,z. Two phase calculaion Predicion: from he esimae of sae a ime -, and he commanded acion a ime -, predic sae a ime. (uses odomery) Correcion: Using measuremen of sae a ime, i correcs he previously derived sae esimae. (uses GPS) 5
6 Exended Kalman filer Predicion Correcion T Q A P A P u X f X = =,0), ( ) ( ) ( ) ( = = = R P P K P K I P X z K X X How well does EKF work? To accommodae large variaion in GPS daa qualiy, we pick a large value of measuremen error variance R k. This causes slow convergence even when daa qualiy is high! Shifs in GPS daa qualiy are no handled well; e.g., when robo emerges ino a clear area wih many visible saellies, i akes a while before localizaion accuracy reflecs he qualiy of he GPS daa.
GPS daa (near buildings) GPS daa (in clear space) 7
Characerisics of GPS daa Abrup shifs in GPS daa qualiy when saellies drop ou of view (e.g., when robo is near concree buildings or ravels under rees). Gradual drifs in GPS daa qualiy caused by amospheric effecs. Adapive sae esimaor Esimae of robo posiion localizer Localizer parameers course se poin Navigaion algorihm u odomery (x,y,q) GPS Proporional conroller Robo 8
Adapive sae esimaor For abrup shifs in GPS daa qualiy: Learn measuremen error R indexed by number of visible saellies. Use gain scheduling and swap in appropriae R for curren number of visible saellies a each ime. For gradual shifs in GPS daa qualiy: use exponenial forgeing, i.e., use a window of N (=00) GPS observaions and updae R based on i. Experimen Hypohesis an adapive EKF based sae esimaor ha handles ime-dependen errors in GPS signals correcly will ouperform a non-adapive EKF based sae esimaor. Experimenal se up repeaed runs of he Engineering Quad Tour wih adapive and non-adapive sae esimaion. 9
Evaluaion merics and resuls Raio of lengh of acual pah aken o he shores pah beween via poins on our. Non-adapive EKF.33 Adapive EKF.08 Mean and sandard deviaion of he difference beween rue heading and heading as esimaed by odomery sampled a 0Hz hrough he our. Non-adapive EKF 2.05 (.64) Adapive EKF.33 (.54) Resuls wih non-adapive EKF 0
Resuls wih adapive EKF Relaed work Use of EKF for fusing odomery and GPS daa in several papers including Goel e. al. IROS 99, Aono e. al. ICRA 98, Sukkarieh e. al. ICRA 98, Bouve e. al. ICRA 2000.
Conclusion and fuure work Our conribuion is in making he sae esimaion process adapive by exploiing properies of he GPS signal. We use gain scheduling and exponenial forgeing o handle GPS signal qualiy changes ha occur a differen ime scales. We are working o exend he range of he our o he enire campus, o build in safe mechanisms for crossing wo busy srees on campus, and adding voice recogniion o inerac wih our groups. We are now saring o compare EKF based sensor fusion mehods o paricle filer mehods. A video of Virgil Video made by William Diegaard of Rice Universiy 2