nips nips2008 nips2008-247 knowledge-graph by maker-knowledge-mining

247 nips-2008-Using Bayesian Dynamical Systems for Motion Template Libraries

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Author: Silvia Chiappa, Jens Kober, Jan R. Peters

Abstract: Motor primitives or motion templates have become an important concept for both modeling human motor control as well as generating robot behaviors using imitation learning. Recent impressive results range from humanoid robot movement generation to timing models of human motions. The automatic generation of skill libraries containing multiple motion templates is an important step in robot learning. Such a skill learning system needs to cluster similar movements together and represent each resulting motion template as a generative model which is subsequently used for the execution of the behavior by a robot system. In this paper, we show how human trajectories captured as multi-dimensional time-series can be clustered using Bayesian mixtures of linear Gaussian state-space models based on the similarity of their dynamics. The appropriate number of templates is automatically determined by enforcing a parsimonious parametrization. As the resulting model is intractable, we introduce a novel approximation method based on variational Bayes, which is especially designed to enable the use of efﬁcient inference algorithms. On recorded human Balero movements, this method is not only capable of ﬁnding reasonable motion templates but also yields a generative model which works well in the execution of this complex task on a simulated anthropomorphic SARCOS arm.

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 de Abstract Motor primitives or motion templates have become an important concept for both modeling human motor control as well as generating robot behaviors using imitation learning. [sent-6, score-1.191]

2 Recent impressive results range from humanoid robot movement generation to timing models of human motions. [sent-7, score-0.517]

3 The automatic generation of skill libraries containing multiple motion templates is an important step in robot learning. [sent-8, score-0.993]

4 Such a skill learning system needs to cluster similar movements together and represent each resulting motion template as a generative model which is subsequently used for the execution of the behavior by a robot system. [sent-9, score-1.207]

5 In this paper, we show how human trajectories captured as multi-dimensional time-series can be clustered using Bayesian mixtures of linear Gaussian state-space models based on the similarity of their dynamics. [sent-10, score-0.317]

6 The appropriate number of templates is automatically determined by enforcing a parsimonious parametrization. [sent-11, score-0.288]

7 As the resulting model is intractable, we introduce a novel approximation method based on variational Bayes, which is especially designed to enable the use of efﬁcient inference algorithms. [sent-12, score-0.16]

8 On recorded human Balero movements, this method is not only capable of ﬁnding reasonable motion templates but also yields a generative model which works well in the execution of this complex task on a simulated anthropomorphic SARCOS arm. [sent-13, score-1.11]

9 1 Introduction Humans demonstrate a variety and versatility of movements far beyond the reach of current anthropomorphic robots. [sent-14, score-0.352]

10 It is widely believed that human motor control largely relies on a set of “mental templates” [1] better known as motor primitives or motion templates. [sent-15, score-0.785]

11 This concept has gained increasing attention both in the human motor control literature [1, 2] as well as in robot imitation learning [3, 4]. [sent-16, score-0.465]

12 [3] to use dynamical systems as motor primitives has allowed this approach to scale in the domain of humanoid robot imitation learning and has yielded a variety of interesting applications as well as follow-up publications. [sent-18, score-0.526]

13 However, up to now, the focus of motion template learning has largely been on single template acquisition and self-improvement. [sent-19, score-0.468]

14 Future motor skill learning systems on the other hand need to be able to observe several different behaviors from human presenters and compile libraries of motion templates directly from these examples with as little predetermined structures as possible. [sent-20, score-1.103]

15 An important part of such a motor skill learning system is the clustering of many presented movements into different motion templates. [sent-21, score-0.896]

16 Human trajectories are recorded as multi-dimensional timeseries of joint angles as well as joint velocities using either a marker-based tracking setup (e. [sent-22, score-0.363]

17 [3], we intend to use dynamical systems as generative models of the presented trajectories, i. [sent-30, score-0.123]

18 Our goal is to cluster 1 these multi-dimensional time-series automatically into a small number of motion templates without pre-labeling of the trajectories or assuming an a priori number of templates. [sent-33, score-0.834]

19 Thus, the system has to discover the underlying motion templates, determine the number of templates as well as learn the underlying skill sufﬁciently well for robot application. [sent-34, score-0.917]

20 , a type of K-means) with a method for selecting an appropriate number of clusters and, subsequently, ﬁt a generative model to each cluster. [sent-37, score-0.144]

21 Here we prefer to take a different approach in which the clustering and learning of the underlying time-series dynamics are performed at the same time. [sent-38, score-0.124]

22 This way we aim at ensuring that each obtained cluster can be modeled well by its representative generative model. [sent-39, score-0.174]

23 To date the majority of the work on time-series clustering using generative models has focused on static mixture models. [sent-40, score-0.173]

24 Clustering long or high-dimensional time-series is hard when approached with static models, such that collapsing the trajectories to a few relevant features is often required. [sent-41, score-0.155]

25 This problem would be severe for a high-dimensional motor learning system where the data needs to be represented at high sampling rates in order to ensure the capturing of all relevant details for motor skill learning. [sent-42, score-0.41]

26 In addition, it is difﬁcult to ensure smoothness when the time-series display high variability and, therefore, to obtain accurate generative models with static approaches. [sent-43, score-0.128]

27 A natural alternative is to use mixtures of temporal models which explicitly model the dynamics of the time-series. [sent-44, score-0.155]

28 LGSSMs are probabilistic temporal models which, despite their computational simplicity, can represent many natural dynamical processes [5]. [sent-46, score-0.088]

29 The drawback of these approaches is that training many separate models can lead to a large computational overhead, such that heuristics are often needed to restrict the number of possible cluster conﬁgurations [7]. [sent-49, score-0.109]

30 As a Bayesian treatment of the Mixtures of Linear Gaussian State-Space Models is intractable, we introduce a deterministic approximation based on variational Bayes. [sent-55, score-0.139]

31 As a realistically difﬁcult scenario in this ﬁrst step towards large motor skill libraries, we have selected the game of dexterity Balero (also known as Ball-In-A-Cup or Kendama, see [8]) as an evaluation platform. [sent-57, score-0.372]

32 Several substantially different types of movements exist for performing this task and humans tend to have a large variability in movement execution [9]. [sent-58, score-0.57]

33 From a robotics point of view, Balero can be considered sufﬁciently complex as it involves movements in all major seven degrees of freedom of a human arm as well as an anthropomorphic robot arm. [sent-59, score-0.666]

34 We are able to show that the presented method gives rise to a reasonable number of clusters representing quite distinct movements and that the resulting generative models can be used successfully as motion templates in physically realistic simulations. [sent-60, score-1.019]

35 We will ﬁrst introduce a generative approach for clustering and modeling multi-dimensional time-series with Bayesian Mixtures of LGSSMs and describe how this approach can be made tractable using a variational approximation. [sent-62, score-0.295]

36 2 2 Bayesian Mixtures of Linear Gaussian State-Space Models Our goal is to model both human and robot movements in order to build motion template libraries. [sent-64, score-0.899]

37 In this section, we describe our Bayesian modeling approach and discuss both the underlying assumptions as well as how the structure of the model is selected. [sent-65, score-0.075]

38 As the resulting model is not tractable for analytical solution, we introduce an approximation method based on variational Bayes. [sent-66, score-0.154]

39 The dependency of the priors on ΣH and ΣV is chosen speciﬁcally to render a variational implementation feasible. [sent-100, score-0.145]

40 To model the joint indicator variables, we deﬁne N p(z 1:N |γ) = p(z n |π) p(π|γ), where p(z n = k|π) ≡ πk . [sent-108, score-0.113]

41 In particular, the priors on Ak and B k enk force a sparse parametrization since, during learning, many αk and βj get close to inﬁnity whereby ij k k (the posterior distribution of) Aij and Bj get close to zero (see [11] for an analysis of this pruning effect). [sent-110, score-0.096]

42 Speciﬁcally, this approach ensures that the unnecessary LGSSMs are pruned out from the model during training (for certain k, all 1:N ˆ elements of B k are pruned out such that LGSSM k becomes inactive (p(z n = k|v1:T , Θ1:K , γ) = 0 for all n)). [sent-112, score-0.078]

43 2 Model Intractability and Approximate Solution The Bayesian treatment of the model is non-trivial as the integration over the parameters Θ1:K and π renders the computation of the required posterior distributions intractable. [sent-114, score-0.092]

44 This problem results from the coupling in the posterior distributions between the hidden state variables h1:N and the parameters 1:T Θ1:K as well as between the indicators z 1:N and π, Θ1:K . [sent-115, score-0.109]

45 To deal with this intractability, we use a deterministic approximation method based on variational Bayes. [sent-116, score-0.106]

46 In our variational approach we introduce a new distribution q and make the following approximation4 1:N ˆ p(z 1:N , h1:N , Θ1:K |v1:T , Θ1:K , γ) ≈ q(h1:N |z 1:N )q(z 1:N )q(Θ1:K ). [sent-118, score-0.106]

47 1:T 1:T (2) That is, we approximate the posterior distribution of the hidden variables of the model by one in which the hidden states are decoupled from the parameters given the indicator variables and in which the indicators are decoupled from the parameters. [sent-119, score-0.303]

48 Observation vt is then placed in the most likely respect to q for ﬁxed Θ LGSSM by computing arg maxk q(z n = k). [sent-121, score-0.11]

49 4 Figure 1: This ﬁgure shows one of the Balero motion templates found by our clustering method, i. [sent-124, score-0.678]

50 Here, a sideways movement with a subsequent catch is performed and the uppermost row illustrates this movement with a symbolic sketch. [sent-127, score-0.418]

51 The middle row shows an execution of the movement generated with the LGSSM representing the cluster C2. [sent-128, score-0.417]

52 The lowest row shows a recorded human movement which was attributed to cluster C2 by our method. [sent-129, score-0.485]

53 Note that movements generated from LGSSMs representing other clusters differ signiﬁcantly. [sent-130, score-0.318]

54 (3) Whilst computing this joint density is relatively straightforward, the parameter and indicator variable updates require the non-trivial estimation of the posterior averages hn and hn hn t t t−1 with respect to this distribution. [sent-141, score-0.416]

55 3 Results In this section we show that the model presented in Section 2 can be used effectively both for inferring the motion templates underlying a set of human trajectories and for approximating motion templates with dynamical systems. [sent-143, score-1.556]

56 For doing so, we take the difﬁcult task of Balero, also known as Ball-In-A-Cup or Kendama, and collect human executions of this task using a motion capture 5 C2 0. [sent-144, score-0.663]

57 6 0 Figure 2: In this ﬁgure, we show nine plots where each plot represents one cluster found by our method. [sent-187, score-0.133]

58 Each of the ﬁve shown trajectories in the respective clusters represents a different recorded Balero movement. [sent-188, score-0.242]

59 For better visualization, we do not show joint trajectories here but rather the trajectories of the cup which have an easier physical interpretation and, additionally, reveal the differences between the isolated clusters. [sent-189, score-0.428]

60 We show that the presented model successfully extracts meaningful human motion templates underlying Balero, and that the movements generated by the model are successful in simulation of the Balero task on an anthropomorphic SARCOS arm. [sent-192, score-1.173]

61 1 Data Generation of Balero Motions In the Balero game of dexterity, a human is given a toy consisting of a cup with a ball attached by a string. [sent-194, score-0.378]

62 The goal of the human is to toss the ball into the cup. [sent-195, score-0.201]

63 Humans perform a wide variety of different movements in order to achieve this task [9]. [sent-196, score-0.258]

64 For example, three very distinct movements are: (i) swing the hand slightly upwards to the side and then go back to catch the ball, (ii) hold the cup high and then move very fast to catch the ball, and (iii) jerk the cup upwards and catch the ball in a fast downwards movement. [sent-197, score-1.014]

65 Whilst the difference in these three movements is signiﬁcant and can be easily detected visually, there exist many other movements for which this is not the case. [sent-198, score-0.468]

66 We collected 124 different Balero trajectories where the subject was free to select the employed movement. [sent-199, score-0.121]

67 For doing so, we used a VICONT M data collection system which samples the trajectories at 200Hz to track both the cup as well as all seven major degrees of freedom of the human arm. [sent-200, score-0.427]

68 For the evaluation of our method, we considered the seven joint angles of the human presenter as well as the corresponding seven estimated joint velocities. [sent-201, score-0.324]

69 In the lowest row of Figure 1, we show how the human motion is collected with a VICONT M motion tracking setup. [sent-202, score-0.79]

70 As we will see later, this speciﬁc movement is assigned by our method to cluster C2 whose representative generative LGSSM can be used successfully for imitating this motion (middle row). [sent-203, score-0.642]

71 A sketch of the represented movement is shown in the top row of Figure 1. [sent-204, score-0.19]

72 2 Clustering and Imitation of Motion Templates We trained the variational method with different initial conditions, hidden dimension H = 35 and a number of clusters K which varied from 20 to 50 in order to avoid suboptimal results due to local maxima. [sent-206, score-0.206]

73 These are plotted in Figure 2, where, instead of the 14-dimensional joint angles and velocities, we show the three-dimensional cup trajectories resulting from these joint movements, as it is easier for humans to make sense of cartesian trajectories. [sent-208, score-0.466]

74 Clusters C1, C2 and C3 are movements to the side which subsequently catch the ball. [sent-209, score-0.341]

75 Here, C1 is a short jerk, C3 appears to have a circular movement similar to a jerky movement, while C2 uses a longer but smoother movement to induce kinetic energy in the ball. [sent-210, score-0.304]

76 Motion templates C4 and C5 are dropping movements where the cup moves down fast for more than 1. [sent-211, score-0.666]

77 16 Time[s] (b) Figure 3: (a) Time-series recorded from two executions of the Balero movement assigned by our model to cluster C1. [sent-252, score-0.53]

78 In the ﬁrst and second rows are plotted the positions and velocities respectively (for better visualization each time-series component is plotted with its mean removed). [sent-253, score-0.157]

79 (b) Two executions of the Balero movement generated by our trained model using probability distributions of cluster C1. [sent-254, score-0.464]

80 The template C5 is a smoother movement than C4 with a wider catching movement. [sent-256, score-0.228]

81 For C6 and C7, we observe a signiﬁcantly different movement where the cup is jerked upwards dragging the ball in this direction and then catches the ball on the way down. [sent-257, score-0.564]

82 Clusters C8 and C9 exhibit the most interesting movement where the main motion is forward-backwards and the ball swings into the cup. [sent-258, score-0.549]

83 In C8 this task is achieved by moving upwards at the same time while in C9 there is little loss of height. [sent-259, score-0.096]

84 2:T In Figure 3 (a) we plotted two recorded executions of the Balero task assigned by our model to cluster C1. [sent-262, score-0.441]

85 As we can see, the two executions have similar dynamics but also display some differences due to human variability in performing the same type of movement. [sent-263, score-0.353]

86 In Figure 3 (b) we plotted two executions generated by our model using the learned distributions representing cluster C1. [sent-264, score-0.38]

87 Our model can generate time-series with very similar dynamics to the ones of the recorded time-series. [sent-265, score-0.115]

88 To investigate the accuracy of the obtained motion templates, we used them for executing Balero movements on a simulated anthropomorphic SARCOS arm. [sent-266, score-0.668]

89 [15], a small visual feedback term based on a Jacobian transpose method was activated when the ball was within 3cm in order to ensure task-fulﬁllment. [sent-268, score-0.081]

90 We found that our motion templates are accurate enough to generate successful task executions. [sent-269, score-0.628]

91 This can be seen in Figure 1 for cluster C2 (middle row) and in the video on the author’s website. [sent-270, score-0.109]

92 4 Conclusions In this paper, we addressed the problem of automatic generation of skill libraries for both robot learning and human motion analysis as a unsupervised time-series clustering and learning problem based on human trajectories. [sent-271, score-1.019]

93 We have introduced a novel Bayesian temporal mixture model based on a variational approximation method which is especially designed to enable the use of efﬁcient inference algorithms. [sent-272, score-0.19]

94 We demonstrated that our model gives rise to a meaningful clustering of human executions of the difﬁcult game of dexterity Balero and is able to generate time-series which are very close to the recorded ones. [sent-273, score-0.563]

95 Finally, we have shown that the model can be used to obtain successful executions of the Balero movements on a physically realistic simulation of the SARCOS Master Arm. [sent-274, score-0.469]

96 Modelling motion primitives and their timing in biologically executed movements. [sent-285, score-0.413]

97 On learning, representing and generalizing a task in a humanoid robot. [sent-297, score-0.103]

98 A Bayesian approach to temporal data clustering using hidden Markov models. [sent-314, score-0.149]

99 Increased sleep spindle activity following simple motor procedural learning in humans. [sent-326, score-0.138]

100 Uniﬁed inference for variational Bayesian linear Gaussian statespace models. [sent-357, score-0.106]

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