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1 High-Speed Autonomous Navigation with Motion Prediction for Unknown Moving Obstacles Dizan Vasquez, Frederic Large, Thierry Fraichard and Christian Laugier.

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Présentation au sujet: "1 High-Speed Autonomous Navigation with Motion Prediction for Unknown Moving Obstacles Dizan Vasquez, Frederic Large, Thierry Fraichard and Christian Laugier."— Transcription de la présentation:

1 1 High-Speed Autonomous Navigation with Motion Prediction for Unknown Moving Obstacles Dizan Vasquez, Frederic Large, Thierry Fraichard and Christian Laugier INRIA Rhône-Alpes & Gravir Lab. France IROS 2004

2 2 Objective To design techniques allowing a vehicle to navigate in an environment populated with moving obstacles whose future motion is unknown. Two constraints: Limited response time: f(Dynamicity). Need of reasoning about the future: Prediction. Prediction Validity?

3 3 Autonomous Navigation: Approaches Reactive approaches [Arkins, Simmons, Borenstein, etc.] No look-ahead Improved reactive approaches [Khatib, Montano, Ulrich, etc.] Lack of generality Iterative planning approaches [Hsu, Veloso] Too slow for highly dynamic environment Iterative partial planning [Fraichard, Frazzoli, Petti]

4 4 Autonomous Navigation: Proposed Solution Iterative partial planning approach Fast Motion Planning. The concept of Velocity Obstacle [Fiorini, Shiller] is used in an iterative motion planner which proposes a safe plan for a given time interval. Motion prediction for Moving obstacles. Typical behavior of moving obstacles is learned and then applied for motion prediction.

5 5 Motion Planning: Principle Iterative planner. Plans computed during a given time interval. Incremental calculation of a partial trajectory. Uses a model of the future (prediction). Based on the A* algorithm. Uses the Non Linear Velocity Obstacle concept to speed up the calculation [Large, Shiller] Real Time. Adapts to changes.

6 6 Motion Planning: Velocity Obstacles A NLVO is the set of all the linear velocities of the robot that are constant on a given interval and that induce a collision before.

7 7 Motion Planning: A* implementation Nodes: Dated states. Link: Motion (velocities). Velocities expanded with a two criteria heuristic: 1. Time to Collision cost : 2. Time to Goal cost:

8 8 Motion Planning: Updating the Tree Instead of rebuilding the tree at each step, we update it. Past configuration are pruned excepting for the currently open node. If any collision is detected, another node is chosen in the remaining tree, and explored from the root.

9 9 Motion Prediction: Traditional Approaches Motion Equations and State Estimation Example Fast. Easy to Implement. Estimate and. [Kalman60] Short Time Horizon. Equations are not general (intentional behaviour?). [Zhu90]

10 10 Motion Prediction: Learning-Based Approaches Hypothesis: On a given environment, objects do not move randomly but follow a pattern. Steps: Learning. Prediction. General. Long Time Horizon. Real-Time Capability. Prediction of unobserved behaviors. Unstructured Environments [TadokoroEtAl95] [KruseEtAl96] [BennewitzEtAl02]

11 11 Motion Prediction: Proposed Approach The approach we propose is defined by: A similarity measure. Use of pairwise clustering algorithms. A cluster representation. Calculation of probability of belonging to a cluster.

12 12 Motion Prediction: Learning Stage 1.Dissimilarity Measure Observed Trajectories Dissimilarity Matrix 2. Pairwise Clustering Algorithm 3. Calculation Of Cluster Representation Trajectory Clusters Cluster Mean Values and Std. Dev.

13 13 Motion Prediction: Dissimilarity Measure t q. didi djdj TiTi TjTj

14 14 Motion Prediction: Cluster Representation Cluster Mean-Value: Cluster Standard Deviation:

15 15 Motion Prediction: Prediction Stage The probability of belonging to a cluster is modeled as a Gaussian: Where: Prediction: Maximum likelihood or sampling

16 16 Motion Prediction: Experimental Results Implementation using Complete-Link Hierarchical Clustering and Deterministic Annealing Clustering. Benchmark using Expectation-Maximization Clustering as described in [Bennewitz02]

17 17 Motion Prediction: Experimental Results Evaluation using a performance measure. Tests ran with simulated data.

18 18 Motion Planning: Results Experiments have been performed in a simulated environment.

19 19 Conclusions In this paper a navigation approach is proposed. It consists of two components: A learning-based motion prediction technique able to produce long-term motion estimates. An iterative motion planner based on the concept of Non- Linear Velocity Obstacle which adapts its scope according to available time.

20 20 Perspectives Work in a real system installed in the laboratorys parking. Research on unknown behaviors prediction.

21 21 Thank You!

22 22 PWE: Calcul du Nombre de Clusters

23 23 Résultats Expérimentaux: Génération de lensemble dentraînement (cont…) 1. Les points correspondant aux points de control sont génères en utilisant des distributions gaussiennes avec un écart type fixe. 2. Le mouvement a été simulé en avançant en pas fixes depuis le dernier point de control dans la direction du prochain daccord a une distribution gaussienne. On considère avoir arrivé dans le prochain point de control quand on est plus près quun certain seuil. 3. Le pas 2 es répété jusquà on arrive au dernier point de control.

24 24 Quelques Concepts Importantes Configuration. Mouvement. Estimation de Mouvement. Horizon Temporelle.

25 25 PWE: Deterministic Annealing Lappartenance dans un cluster est calculée de façon itérative: INITIALISER et AU HAZARD; température TT ; WHILE T>T final s0; REPEAT Estimation: Calculer en fonction de ; Maximisation: Calculer a partir de ; ss+1; UNTIL tous (, ) convergent; TηT; ; ; END;

26 26 Experimental Results: Performance Measure Test Trajectory 1. Select Starting Fraction Trajectory Fraction Cluster Set 2. Select Cluster with Max Likelihood Error Value Cluster Mean 3. Calculate Distance Test Trajectory

27 27 Experimental Results: Learning stage results Alg..ParameterNumber Clusters CLmaxDistance=40cm59 CLmaxDistance=30cm101 CLmaxDistance=20cm205 DAK=5959 DAK=10199 DAK= EMσ=20cm36 EMσ=15cm53 EMσ=10cm133

28 28 Experimental Results: Learning stage results Résultats Expérimentaux:

29 29 Experimental Results: Cluster Examples

30 30 Conclusions: Contributions We have proposed an approach based on three calculations: Dissimilarity Measure. Cluster Mean-Value. Probability of Belonging to a Cluster.

31 31 Conclusions: Contributions (cont…) We have implemented our approach using Complete-Link and Deterministic Annealing Clustering We have implemented the approach presented on [Bennewitz 02] According to our performance measure, our technique has a better performance than that based on Estimation-Maximization.

32 32 PWE: Comparaison avec EME PWE: Trouve les groupes et leur représentations en deux pas. Calcule la valeur de K avec lalgorithme Complete-Link. Peut utiliser tous les algorithmes Pairwise Clustering. Représente les clusters avec la trajectoire moyenne. EME: Trouve les groupes et leur représentations simultanément. Calcule la valeur de K avec un algorithme incrémental. Utilise lalgorithme Expectation- Maximization Représente les clusters avec des distributions gaussiennes.

33 33 Estimation basé sur EM (EME) Nous considérons cette technique [Bennewitz 02] comme létat de lart pour notre problème: Apprentissage: Trouve les groupes et ses représentations (séquences de gaussiennes) simultanément. Utilise lalgorithme EM (Expectation-Maximization) Trouve le nombre de clusters en utilisant un algorithme incrémental. Estimation: Basé sur le calcul de la vraisemblance dune trajectoire partielle observé o partial sous chaque un des chemins θ k comme une multiplication de probabilités.

34 34 Estimation basé sur EM (EME): Algorithme EM Calcule les assignations c i k et les chemins θ k 1. Expectation: Calcule la valeur espéré E[c i k ] sous les chemins courants θ k. 2. Maximization: Assume que c i k = E[c i k ] et calcule des nouveaux chemins θ k 3. Fait θ k =θ k et recommence θk1θk1 θk2θk2 θ k

35 35 Estimation basé sur EM (EME): Estimation La vraisemblance dune trajectoire d i sous un chemin θ k est: θk1θk1 θk2θk2 θ k di1di1 di2di2 di5di5

36 36 Résultats Expérimentaux: Mesure de Performance Fonction PerformanceMetric( χ,C,percentage) result0; FOR chaque trajectoire χ i in the test set χ DO calculate χ i percentage ; trouver le cluster C k ayant la majeur vraisemblance pour χ i percentage ; resultresult+δ(χ i,μ k ); END FOR result result/N χ ;

37 37 Estimation basé sur EM (EME): Avantages / Inconvénients Horizons Temporelles Longs Ils ne fait pas de suppositions par rapport a la forme des trajectoires Il estime le nombre de clusters Il nest pas capable de prédire des trajectoires quil na jamais observé.


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