IROS2019国际学术会议论文集1785

Belief-Driven Control Policy of a Drone with Microphones for Multiple Sound Source Search Kenshiro Yamada1, Makoto Kumon2and Tomonari Furukawa3 AbstractThis paper proposes a belief-driven control policy of a drone with microphones for multiple sound source search. As the sound source localization by drones is uncertain because of the observation signifi cantly distorted by noise such as rotor noise, the belief on the estimated targets may consist of multiple peaks that are spread over the bounded search area. The proposed control policy is formulated with a robust cost func- tion so that the function encodes the search mission properly. A peak management mechanism is additionally introduced to keep tracking all targets by masking suffi ciently observed and well estimated targets whose peaks normally become steep and high. The proposed control policy was evaluated by numerical simulations, and experiments, and those results have validated the effi cacy of the proposed control policy. I. INTRODUCTION Recent years have seen dramatic advancement in multi- rotor helicopters, which are commonly known as drones these days. Multi-rotor helicopters are expected for surveil- lance missions of inaccessible areas for human such as hazardous sites in the near future 1, 2. While visual data from cameras provides the most useful information at an early stage, auditory information is additionally effective in the vicinity of sound targets such as victims in disaster rescue scenarios 1. This gives rise to need for the estimation of multiple sound source search by a drone, which is a topic of this paper. Technologies for acoustic sensing with drones have been developed variously as a part of Robot Audition 3. These in- clude direction-of-arrival (DoA) estimation techniques since drones generate signifi cant noise for themselves 4, 5, 6. In other efforts, Ishiki 7, 8 studied the microphone array confi guration taking the fl ight control dynamics into account. Nakadai 9 proposed a compact microphone array component that was installed away from rotors to attenuate the effect from the rotor noise, and Hoshiba 10 analyzed the sound source localization (SSL) performance of that microphone array system. Wang 11 developed another mi- crophone confi guration for a small drone where microphones were installed in the body surrounded by rotors, and pro- posed a robust DoA estimation algorithm. Hioka 12 utilized a directional microphone pointing to the sound source in 1Kenshiro Yamada is with Graduate School of Science and Technology, Kumamoto University, 2-39-1, Kurokami, Chuoku, Kumamoto, 860-8555, Japan 2Makoto Kumon is with Faculty of Advanced Science and Technology, and International Research Organization of Advanced Science and Technol- ogy, Kumamoto University, 2-39-1, Kurokami, Chuoku, Kumamoto, 860- 8555, Japankumongpo.kumamoto-u.ac.jp 3Tomonari Furukawa is with Deparment of Mechanical Engineering, Virginia Polytechnic Institute and State University, 635 Prices Fork Road - MC 0238 Blacksburg, VA 24061, USA order to record the target signal clearly. For sound source position estimation, Basiri 13 deployed a particle fi lter and estimated the position of a known acoustic signal from the source on the ground, and Washizaki 14 proposed a robust sound source localization technique based on triangulation with statistical false observation reduction. Autonomous fl ight control is another essential element for multiple sound source search due to the need for covering a large area and has been extensively studied, having its origin as a search theory in the fi eld of Operations Research 15. The developed techniques have been used in unmanned aerial vehicles; a survey 2 shows search techniques including area coverage path planning, routing and self-networking of multiple drones, can be realized by optimization. Such fl ight control has been primarily achieved in conjunction with visual feedback e.g. 16, 17, which is less uncertain than acoustic sensing if the target of concern is observable. Search by visual feedback, on the other hand, becomes heavily uncertain due to the unobservability of the target. Bourgault 18, 19 and Furukawa 20 formulated search in the non-Gaussian recursive Bayesian estimation (RBE) framework and further generalized optimal control for search and tracking. Partly because measurement noise is considerable in acoustic sensing by drones and partly because a distant target generally gives uncertain observation owing to the propagation decay, the likelihood of the existence of the target computed from the acoustic observation becomes a noisy, broad distribution over the search space, which is generally bounded. This makes the distribution of the target position estimated via the RBE, which is called belief, also multimodal. Therefore, the control policy driven by the belief must be decided by taking this multimodality into account. This paper presents a belief-driven control policy of a drone with microphones for multiple sound source search. The audible fi eld of the drone fl ying in the air may contain multiple sound sources, which results in a multimodal belief with some peaks of the belief correspondingto the potential locations of the targets. If some of those peaks dominate the distribution, the rest of targets to search are not clearly encoded in the belief distribution. Therefore, the proposed control policy introduces a mechanism to manage the belief to represent the targets appropriately, which is the additional contribution of this paper. II. BELIEF-DRIVENSEARCH ANDTRACKING The RBE 18, 21 maintains belief on a target by updat- ing it in both time and observation. The method is briefl y 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Macau, China, November 4-8, 2019 978-1-7281-4003-2/19/$31.00 2019 IEEE5326 outlined in this section following the previous work 22. The position of a target at time step k is denoted by xkX where X represents the search space. The information about the target that is measured by a sensor at step k is denoted by zk, and the robot can be controlled according to the control command at step k that is denoted by uk. Assume that a sensor model that provides a likelihood estimate for the target position is known, and let l(xk|zk) denote the likelihood that the target is located at xk, given the observation zk. Denote the control commands from step 1 to step k1, and observations from step 1 to step k by u1:k1and z1:k, respectively, and denote the estimated target position by the belief at step k as bel(xk|u1:k1,z1:k), which provides the distribution related to the probability of the target location at step k, given the observations and control commands. The belief is also simply noted as bel(x) if it is not confused. The dynamics of the target are modeled probabilistically with pd(xk+1|xk,uk) corresponding to the probability of the target to move from xkto xk+1under the control action uk. The dynamical model drives the belief bel(xk|u1:k1, z1:k) as follows: bel(xk+1|u1:k,z1:k)= X pd(xk+1|xk,uk)bel(xk|u1:k1,z1:k)dxk, (1) which can be used to predict the position of the target. In order to cope with the target tracking, the belief is represented in the relative coordinate with respect to the drone, and, hence, bel(xk) depends on the control actions although the target dynamics itself is not affected by the control actions. Observations of the target over time are fused recursively, as follows. Assume that at step k+1 the observation zk+1 is given. Then, the following update law incorporates the observation into the predicted estimation given by (1): bel(xk+1|u1:k,z1:k+1) = l(xk+1|zk+1)bel(xk+1|u1:k,z1:k) X l(x|zk+1)bel(x|u1:k,z1:k)dx . (2) By repeating (1) and (2) for each time step, the belief on the target location is kept to track the target. The integral in (1) and (2) can be replaced by a summation when a discrete search space is considered. With the computed belief, a control action is decided by a Model Predictive Control manner. Let denote the horizon to predict the future state as M, and assume that the system can keep observing the observation from steps k+1 to k+M as it observed at the step k, and denote them as zk,k+ifor i = 1, ,M, or Zk,k+1:k+M= z k,k+1, ,zk,k+M . Given a series of control action candidates as uk,k, , uk,k+M1, or uk,k:k+M1= u k,k, ,uk,k:M1 , RBE can predict the future belief based on the virtual observations, and the predicted belief makes it possible to evaluate the control actions by computing the cost function that encodes the task as J(bel(xk|u1:k1,z1:k),Uk,k:k+M1,Zk,k+1:k+M) = M i=1 wifcost (bel(x k+i| u 1:k1,uk,k, ,uk,k1+i , z 1:k,zk,k+1, ,zk,k+i ), (3) Fig. 1.Drone with microphone array where fcostand wishow a non-negative function corresponds to the given task, and a weight over time. The control actions that optimize the cost function J of (3) are selected as the optimal control policy for the step at k. As this optimiza- tion process becomes computationally heavy, control action candidates can be limited to a set of primitives as in 22, and the optimization can be implemented as a combinatorial optimization. III. SOUNDSOURCELOCALIZATION BYDRONE WITH MICROPHONES In this section, the drone with a microphone array for sound source localization that developed in the authors previous works 1, 9, 10 is briefl y introduced. 1) Drone with microphones: Fig. 1 shows a photo of the hex-rotor helicopter with a compact spherical microphone array. A white sphere of the bottom right corner of the photo is the microphone array that has 16 microphones to record an acoustic signal, and it is an extension of the authors previous work in 9, 10. As the array is installed at the end of the arm sticking outside from the body, the rotor noise can be separated based on the relative geometric confi guration 10. Audio stream obtained by the microphone array is pro- cessed by an embedded signal processing module, then, DoA information, the drone attitude and its position are sent to the ground control station (GCS) by radio communication modules. GCS analyzes the sound source position, and it computes and send the fl ight plan back to the drone. 2) Sound source position estimation: Firstly, acoustic signal obtained by the microphone array is processed to estimate DoA by multiple signal classifi cation (MUSIC) 23 that is a method to decompose mixed signal received by multiple receivers based on the subspace approach. MUSIC encodes directional information as MUSIC spectrum which shows steep peaks corresponding to DoA, or the azimuth and elevation angles to the sound sources. In order to estimate the position of the sound source on the ground by DoA, a simple fl at plane model of the terrain as in the previous work 1 is introduced. The estimated source position gives a likelihood l(x|z) of (2). The likelihood in this paper is given by a normal distribution whose mean corresponds to z, and its covariance matrix is designed as it has large uncertainty along the radial direction. This comes from the fact that the elevation estimation is more uncertain than the azimuth because of the confi guration of microphones. The uncertainty grows as 5327 Measurement MUSIC Peak detection Position estimation MUSIC spectrum Audio stream GPS/IMU DoA Likelihood RBE CorrectionRBE Prediction Source detection Mask update MPC RBE Correction with virtual measurement RBE Prediction with given control policy Evalute the given policy Receding Horizon Policy decision Action (flight control) Policy pool RBE control cmd Next step Fig. 2.Sketch of the proposed system the source becomes more distant. When there are multiple detected sources, sum of likelihoods is invoked as the joint observation likelihood, which generally generates a multi- modal distribution. IV. PROPOSEDMETHOD In this section, the belief-driven control policy for multiple sound source search utilizing the observation model shown in Sec. III is proposed. A sketch of the proposed algorithm is presented in Fig. 2. DoA computed from the MUSIC spectrum is projected on a model terrain, and the likelihood is computed by the projected source position. RBE that estimates the belief of the source is extended to achieve a target selection. This selection mechanism modifi es the belief to update the peak of interest to track by a mask distribution that has lower priority around the area where the system has suffi ciently searched. Then, the optimal fl ight command policy that minimizes the given cost function is chosen from the policy pool. The system assesses a steep belief peak as a sound source if the peak satisfi es the following criteria; maxbel(xs)(4) xBr(xs) bel(x)log(bel(x)E(5) where xs,and E are the position of the peak, thresholds, and where Br(x) represents r-neighborhood of x. The pa- rameter r is selected to small enough to detect the target within a reasonable time. The cost function for the search in the bounded search space and the mask distribution are the main contribution of this paper, and they are described in the following subsec- tions. A. Cost function The search space is denoted by X and it is generally bounded for practical cases. For simplicity, a single sound source case is considered in this subsection. When the likelihood locates close the boundary of the search space, a part of the distribution may spread beyond -5-3.505 0 0.015 Entropy = 6.8117 bit(s) Belief Initial belief Observation -20-3.5 020 0 0.015 Entropy = 7.3936 bit(s) Initial belief Belief Observation Observation z = 3.5 -5 -4.005 0 0.015 Entropy = 6.7251 bit(s) Belief Initial belief Observation -20-4020 0 0.015 Entropy = 7.3936 bit(s) Observation Belief Initial belief Observation z = 4.0 -4.505 0 0.015 Entropy = 6.6354 bit(s) Observation Belief Initial belief -20-4.5020 0 0.015 Entropy = 7.3936 bit(s) Belief Initial belief Observation Observation z = 4.5 (a) X = 5,5(b) X = 20,20 Fig. 3.Effect of bounded search space One step of RBE is shown. The prior belief is same for all fi gures, and the observation likelihood has same variance but its center is altered as z = 3.5, 4.0 and 4.5. The search space of (a) is narrower than that of (b), which means the observation of (a) is more uncertain. the boundary, and the part is eliminated in the computation, which distorts the induced belief, and it affects the estimation of the cost function (3). In order to evaluate the control action that emphasizes the peak, it is thought to be appropriate to compute the sharpness of the belief. Information entropy 24 is one of such common metrics, where it is given as fentropy= xX bel(x)log(bel(x).(6) Recalling that the uncertain observation likelihood of the sound source search by a drone may be limited because of the bounded search space, the distribution for the computation becomes sharper than the true distribution (Fig. 3 (a). This fact directs the observation close to the boundary brings smaller entropy than the observation close to the center of the search space, or the one close to the drone when the state is represented with respect to the drone-centered coordinate. Therefore, the optimal action based on information entropy fentropymay send the drone away from the sound source, which contradicts to the intuitive search objective; for ex- ample, the minimum entropy of Fig. 3(a) case was obtained when the observation was obtained at the most distant point (z = 4.5). It is worth noting that the observation from a distant target contains more uncertainty than that from the closer point. Therefore, it can be concluded that the cost function that computes the sharpness itself like (6) is not appropriate in this scenario. As fentropydoes not change signifi cantly when the observation is less uncertain, that is shown in Fig. 3(b), this property is specifi c to the case of uncertain observations. 5328 Source 1 Source 2 Likelihood Belief Observation Mask Previous belief Previous mask Fig. 4.Sketch of the observation process to obtain the belief This fi gure shows how the observation of two sources is fed to compute the belief. Multimodal likelihood is computed according to the observation of two sources, and the mask is merged to the likelihood and the belief of the previous step. In this example, the target that generates the lowest peak of the likelihood is enhanced, which realizes the selection mechanism to decide the search fi eld. Because the belief from uncertain observations tends to spread widely, the peak becomes broad. This paper proposes the following spatial gradient as the measure instead of (6); fgrad= 1 |Xa| xXa (|bel(x)|+)2,(7) where Xais the subset of the search space X where the be- lief is more than a threshold as Xa= x X |bel(x) 1 N , andis a small positive constant. fgradof (7) becomes small if the area where belief is larger than the threshold varies over the space, and fl at sections with little gradient have a dominant effect to make its value large. Therefore, the metric fgradshows the small value for a smoothly inclined peak with a large domain, which is suitable for guiding the drone. As an example, values of fgradof Fig. 3(a) were 1.368 for z = 4.0, and 8.477 for z = 4.5 where the value was normalized by selecting it as 1.0 for z = 3.5. Note that the minimum value was for z = 3.5 while the minimum entropy was for z = 4.5. The cost function fgradis integrated over the control horizon as J of (3) in Sec. II to obtain the optimal control policy at the step k. B. Multiple Source Search Next, the search algorithm for multiple sources is investi- gated. As it is noted, the belief becomes a multimodal distri- bution whose peaks correspond to sources. As it is diffi cult to detect the rest targets when one of those peaks overwhelms others, it is important to manage peaks appropriately in order to keep s