IROS2019国际学术会议论文集1604

Human Intention Inference and On-Line Human Hand Motion Prediction for Human-Robot Collaboration Ren.C Luo and Licong Mai AbstractWith recent development of robotic technology, it is increasingly common that robot coexist with human, in which humans and robots share a common workspace and work in close proximity. To maintain effi ciency and ensure safety under these circumstances, robot should have the ability to predict the future human motion based on the observed on-going motion. In this paper, we present a methodology for on-line inference of human intention and prediction of human hand motion. The proposed framework is built using Probabilistic Dynamic Movement Primitive (PDMP). In the off-line stage, a set of PDMPs is constructed based on the recorded demonstrations and they will then be used for inferring human intention and predicting human hand motion in the on-line stage. A proof of concept evaluation is carried out in a tabletop manipula- tion task. Experimental result shows the proposed framework achieve high performance in human intention inference and in the trajectory similarity between the predicted and the actual hand movement under the normally defi ned environment. We also show the proposed framework can adapt and generalize to the newly defi ned environment. I. INTRODUCTION The industrial manufacturing process had been dramat- ically revolutionized by the deployment of industrial robot over the last 60 years. Benefi t from the reliability and high ef- fi ciency of robot, manufacturers are able to produce products with shorter cycle time and lower cost. To ensure safety, most of the existing industrial robots are caged and separated from human. Although such mechanism is effi cient, it prevents robot from interacting with human and hence excludes robot from many potential applications. With recent development of robotic technology, it is increasingly common that robot coexist with human, in which humans and robots share a common workspace and work collaboratively in a close proximity. Under this circumstance, how to maintain the high effi ciency of robot while preventing human from injuries caused by robot become extremely important. Our work addresses this issue. A common approach to ensure safety in Human-Robot coexisting environment is to consider the human as a dynamic obstacle and the robot constantly monitoring the human movement and iteratively re-planning and executing its motion accordingly to avoid confl ict with human. Although this method had proved to be feasible 1-3, it only considers either the current human movement or the human movement in the immediate future, which may lead to an unnatural and ineffi cient robot Ren C. Luo is with Department of Electrical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, Taiwan 106 .tw Licong Mai is with Department of Electrical Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, Taiwan 106 .tw Fig. 1: Overview of the proposed framework behaviour. Inspired by Human-Human Collaboration (HHC), one possible solution for maintaining effi ciency and safety during Human-Robot Collaboration (HRC) is to integrate the long-term prediction of human movement into the mo- tion planning framework of the robot, for which the robot observes the on-going movement of human and generate an accurate long-term prediction of human movement. By taking the prediction result into consideration, robot can plan its motion accordingly and result in a more effi cient HRC. The main goal of our research is to establish a motion planning framework for autonomous robot operation, which will take into account not only the current, but also the future human motion. As many others 4-7,11,12, our work start with the assumption that the human motions are goal directed. Since the hand position is one of the most infor- mative features in human manipulation movement, this paper will focus on intention inference and hand motion prediction based on the observed on-going hand motion. Note that although we only consider the prediction of hand motion in this paper, however, it is easy to generalize the proposed framework to predict future arm motion. In a fully developed stage, this research will be able to provide robot the ability to anticipate future motion of its human partner and plan its motion accordingly. The primary contribution of our work is a framework for on-line inference of human intention and prediction of future hand motion. The proposed framework is built using Probabilistic Dynamic Movement Primitives (PDMPs) and an overview is given in Fig.1. Our work involves two stages: in the off-line stage, a set of demonstrations is collected and is used to train the PDMPs. While in the on-line stage, the PDMPs are fi rst used to infer human intention and the inference result will then be used for hand motion prediction. 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 IEEE5958 The rest of the paper is organized as follow: after giving a brief literature review in the next section, we introduce the mathematical and algorithmic details of our method in section III. In section IV, we present the experimental results and further discussions. Finally, the conclusions will be included in section V. II. PREVIOUSRESEARCHWORKS Our work contributes to the fi eld of human intention inference and human motion prediction, which is a crucial step toward fl uent Human-Robot Collaboration (HRC). Prior works in this fi eld can be divided into two categories: the deterministic method and the probabilistic method. For the deterministic method, one of the most common methods is minimum jerk model, which assumed the speed profi le of human hand movement fi ts the minimal jerk cri- terion. Under such assumption, algorithms for hand motion prediction had been proposed and integrated into the motion planning framework of the robot in 8-10. Different from 8-10 that simply assumed the underlying cost function of human hand movement is its jerk, 11,12 used an Inverse Reinforcement Learning (IRL) algorithm to recover the cost function from a set of demonstrations and the recovered cost function will then be inserted into a trajectory optimizer to predict future human motion. With recent development of deep learning, Deep Neural Network (DNN) had also became a popular choice for modelling human movement. In 15-17,25-27, various DNNs with different structures were proposed to model and predict human motion. In contrast to probabilistic method, the aforementioned approaches can only provide a deterministic result of motion prediction, that is, without confi dence information about the provided result. As opposite to the deterministic method, probabilistic method tries to capture the variability of human motion by establishing a probabilistic model over the demonstrations. Various probabilistic models such as Hidden Markov Model (HMM) 13, Gaussian Mixture Model (GMM) 4,6,7, Probabilistic Flow Tubes (PFT) 5 and Gaussian Process (GP) 18 had been successfully utilized to encode the demonstrations and hence predict human motion. However, these models are constructed directly over the demonstrations and thus diffi cult to generalize to the new environment which is a major challenge in human motion prediction. In 28,32,33, different task parametrized probabilistic models had been proposed to encode the human demonstrations, which allow the robot to learn skills from the demonstrations and generalize them to the new situation. Although the works proposed in 28,32,33 did successfully applied to robot, however, the way they adapt to the new environment may not be the same as how human react to the new environment. Different from above probabilistic methods, our work establishes the probabilistic model by encoding the demonstrations into the Probabilistic Dynamic Movement Primitive (PDMP), which is the probabilistic version of Dynamic Movement Primitive (DMP). There are two major reasons why we would like to encode the demonstrations into the PDMP. Firstly, it is well demonstrated in many researches that the DMP can readily adapt to the new environment by modifying its weights and/or meta parameters (initial/goal state, temporal scaling factor, etc). Secondly, it is shown that the DMP can be modifi ed to preserve the shape of the learned trajectory while adapting to the new setting (for instance, in 34, the modifi ed DMP generates a human-like motion trajectory while adapting to a time-varying attractor). The idea of applying Movement Primitive (MP) to HRC had also been proposed by several other researches. In 29, the authors used a DMP based algorithm to predict human motion and retrieve the reactive strategy for robot motion planning based on the movement of human partner. While the feasibility of the proposed method had been showed, the representation of collaboration in the space of acceler- ations increases its sensitivity to noise in the observations as it requires computing the accelerations in the weight retrieval stage 31. Similar algorithms also introduced in 30,31 where instead of DMP, the authors used Probabilistic Movement Primitive (ProMP) to model the collaborative be- haviour. Moreover, research 14 had also proposed a ProMP based algorithm to infer human intention and predict future motion during Human Robot Interaction (HRI). Although the ProMP based methods had showed lower noise sensitivity than the work in 29 as they retrieve the weights directly from the observations, the lack of meta parameter makes them less fl exible in the unstructured environment. Different from 14,29-31, our work jointly estimate the states and the weights via PDMP, which avoids computing the accel- erations in the weight retrieval stage and provides better fl exibility in the unstructured environment. Furthermore, the joint estimation allows us to capture the (possibly strong) correlation between the states and the weights. The details of the framework is provided in the next section. III. METHODOLOGY A. DMPs and PDMPs Dynamic Movement Primitive (DMP) encodes a desired movement trajectory in terms of non-linear differential equa- tions 19,20. The original DMP can be viewed as a com- bination of a second order Linear Dynamical System (LDS) and a forcing term. While the dynamical system ensures the trajectory converge to the attractor (goal), the forcing term enforces the trajectory as similar to the desired trajectory as possible. For a 1-D trajectory, the equations are: x = (x(x(gxx) x/)+ fx(s)2(1) s = ss(2) where x, x and x are the position, velocity and acceleration, gxis the goal of the trajectory, is the temporal scaling factor and is set to 1 in this work. The x, xand sare the positive constant coeffi cients, and xand xare chosen as x= 4xso that the eq.(1) is critically damped. The Eq.(2) is the canonical system with s0=1 and it decays toward zero as time evolves. The forcing term fx (s) is defi ned as fx(s) = N i=1xi(s)xi N i=1xi(s) s(gxx0)(3) 5959 where x0is the initial position, and x i = exp(scx i)2/2hxi) (4) is the ithradial basis function kernel, and hx i and cx i are the corresponding width and center. Note that the superscript x indicates the DMP is trained for the movement in x dimen- sion and it can be changed to y and z in the latter section. By properly choosing the weights x i, the DMP can represent arbitrary non-linear function. The weights x i can be learned from the desired trajectory via Locally Weighted Regression (LWR) or Locally Weighted Projection Regression (LWPR). More details about the DMP can be found in 19,20. Following 21, the DMP equations can be discretized by applying Euler discretization with time step t pk= Apk1+Buk1(5) where pk= xk, xk and uk= xxgx+ fx(sk), and A = ? 1t xxt1xt ? , B = ? 0 t ? are the transition matrix and control input matrix of eq.(5). DMP can also be transformed into a probabilistic version, which is denoted as Probabilistic Dynamic Movement Prim- itive (PDMP). Two types of PDMP had been proposed in the prior works: authors of 21 construct the PDMP by adding a white noise term to eq.(5) to model the transition uncertainty, whereas authors of 22 construct the PDMP via Bayesian regression to capture the transition uncertainty with respect to the non-linear forcing term. Different from above works, we construct the PDMP by utilizing the affi ne property of normal distribution. This is achieved by modelling the DMP weights as a multivariate normal distribution x N (x,x) and therefore the forcing term is also a normal distribution f(sk) N (x(sk)x,x(sk)xx(sk)T) where x(sk) = h x 1(sk)sk(gxx0) N i=1xi(sk) x N(sk)sk(gxx0) N i=1xi(sk) i Then, the equation of DMP will be transformed into pk= Apk1+Buk1+k(6) where uk= xxg+x(sk)xand kis the transition un- certainty with k N (0,Bx(sk1)x(Bx(sk1)T) that captures the variability of the demonstrations. B. Prior Weights Distribution One of the greatest challenges of this research comes from the fact that even though in the same task, the duration of human motion will still vary. Therefore, before further processing, the collected motion trajectories must be aligned fi rst. In our work, we fi rst compute the average trajectory for the task via Dynamic Time Warping Barycenter Averaging (DBA). The resulted average trajectory will then serve as a reference trajectory to align all the trajectories in the same task via Dynamic Time Warping (DTW). DTW is an algorithm that used to compute the similar- ity between two time series with different lengths. Given two time series with different lengths, DTW searches for the optimal alignment path by minimizing the cumulative distance between two time series with boundary constraint, monotonicity constraint and step size constraint 23. Based on DTW, 24 had proposed DBA to average multiple time series with different lengths. Given a set of time series x1,.,xN, the general procedure of DBA is 1. Select a time series from x1,.,xNas the initial average time series x0 avg. Note that the length of the average time series is equal to the length of the selected time series. 2. Iteratively repeat the following two steps n times i. Align every time series with the average time series xiavgand compute the corresponding warping path via DTW. ii. Update every points in xi+1 avg(k) by averaging all the points associate to xiavg(k) in (i) until i = n. Since the average duration is the most representative feature of the duration of the task, the average trajectory will be initialized by the trajectory whose duration is closest to the average duration of the collected trajectories within the same task. The DBA algorithm and DTW algorithm will then be used to compute the average trajectory and align the N trajectories within the same task. After the alignment, the aligned trajectories and average trajectory will be used to trained the corresponding DMPs, and their weights ? 1,.,N,avg ? will be used to estimated the prior distribution of the DMP weights with respect to the corresponding task. We model the prior distribution of the DMP weights as a multivariate normal distribution N (,). The mean is set equal to the weights of the average trajectory avg and the covariance matrix is computed as = 1 N1 N i=1 (iavg)(iavg)T C. Reformulation and Parameter Estimation Since the recorded hand motion trajectories are 3-D, we need to reformulate eq.(5) as paug k = Aaugpaug k1+B augg+Bx k1x+B y k1y+B z k1z (7) where paug k = xk,yk,zk, xk, yk, zkTis the augmented state vector, = diag(xx,yy,zz ) is the fi rst coeffi cient matrix, and g = gx,gy,gzTis the 3-D attractor, which is the goal position. The x, yand zare the DMP weights for the movement in x,y,z dimension respectively and we further assume the weights of different dimensions are independent. The transition matrix and control input matrices are Aaug= ? I33t I33 t I33t ? Baug= ? 0 t ? I33,Bx k= ( ? 0 t ? nx)x(sk) where = diag(x,y,z ) is the second coeffi cient matrix and denotes the Kronecker product. We also defi ne nx= 1,0,0T, ny= 0,1,0Tand nz= 0,0,1T. The other two 5960 control input matrices By k and Bz k are similar to Bx k, and are obtained by replacing nxby nyand nz, and replacing x(sk) by y(sk) and z(sk), respectively. Taking the observation model and the uncertainty of the weights into consideration, the new PDMP can be obtained as paug k = Aaugpaug k1+u aug k1+ aug k (8) qk=Caugpaug k +(9) where qkis the Cartesian position, and Caug= I33,033 and N (0,q) are the observation matrix and the obser- vation noise, respectively. The control input and the transition uncertainty are uaug k = Baugg + Bx kx + By ky + Bz kz and aug k N (0,paug k ) with paug k = Bx k1 x (Bxk1)T + By k1 y (B y k1) T +Bz k1 z (Bzk1)T. The only open parameter in eq.(8-9) is the covariance matrix of the observation noise q. This parameter can be estimated by following the standard procedure of LDS parameter estimation via Expectation Maximization (EM) algorithm. D. On-line Intention Inference and Hand Motion Prediction In the off-line stage, we construct a set of PDMPs for the corresponding tasks and these PDMPs will then be used for on-line intention inference and hand motion prediction. a) Intention Inference: The PDMPs are fi rst queried with the observed on-going human hand motion. Suppose there are M interested tasks and their corresponding PDMPs are already obtained in the off-line stage. Then we can use the PDMPs to compute the possibility that the on-going motion is belonged to a specifi ed task. The details