News Blog Paper China
Kernel Trajectory Maps for Multi-Modal Probabilistic Motion Prediction2019-10-07   ${\displaystyle \cong }$
Understanding the dynamics of an environment, such as the movement of humans and vehicles, is crucial for agents to achieve long-term autonomy in urban environments. This requires the development of methods to capture the multi-modal and probabilistic nature of motion patterns. We present Kernel Trajectory Maps (KTM) to capture the trajectories of movement in an environment. KTMs leverage the expressiveness of kernels from non-parametric modelling by projecting input trajectories onto a set of representative trajectories, to condition on a sequence of observed waypoint coordinates, and predict a multi-modal distribution over possible future trajectories. The output is a mixture of continuous stochastic processes, where each realisation is a continuous functional trajectory, which can be queried at arbitrarily fine time steps.
Sub-Goal Trees -- a Framework for Goal-Directed Trajectory Prediction and Optimization2019-06-12   ${\displaystyle \cong }$
Many AI problems, in robotics and other domains, are goal-directed, essentially seeking a trajectory leading to some goal state. In such problems, the way we choose to represent a trajectory underlies algorithms for trajectory prediction and optimization. Interestingly, most all prior work in imitation and reinforcement learning builds on a sequential trajectory representation -- calculating the next state in the trajectory given its predecessors. We propose a different perspective: a goal-conditioned trajectory can be represented by first selecting an intermediate state between start and goal, partitioning the trajectory into two. Then, recursively, predicting intermediate points on each sub-segment, until a complete trajectory is obtained. We call this representation a sub-goal tree, and building on it, we develop new methods for trajectory prediction, learning, and optimization. We show that in a supervised learning setting, sub-goal trees better account for trajectory variability, and can predict trajectories exponentially faster at test time by leveraging a concurrent computation. Then, for optimization, we derive a new dynamic programming equation for sub-goal trees, and use it to develop new planning and reinforcement learning algorithms. These algorithms, which are not based on the standard Bellman equation, naturally account for hierarchical sub-goal structure in a task. Empirical results on motion planning domains show that the sub-goal tree framework significantly improves both accuracy and prediction time.
OCTNet: Trajectory Generation in New Environments from Past Experiences2019-09-25   ${\displaystyle \cong }$
Being able to safely operate for extended periods of time in dynamic environments is a critical capability for autonomous systems. This generally involves the prediction and understanding of motion patterns of dynamic entities, such as vehicles and people, in the surroundings. Many motion prediction methods in the literature can learn a function, mapping position and time to potential trajectories taken by people or other dynamic entities. However, these predictions depend only on previously observed trajectories, and do not explicitly take into consideration the environment. Trends of motion obtained in one environment are typically specific to that environment, and are not used to better predict motion in other environments. In this paper, we address the problem of generating likely motion dynamics conditioned on the environment, represented as an occupancy map. We introduce the Occupancy Conditional Trajectory Network (OCTNet) framework, capable of generalising the previously observed motion in known environments, to generate trajectories in new environments where no observations of motion has not been observed. OCTNet encodes trajectories as a fixed-sized vector of parameters and utilises neural networks to learn conditional distributions over parameters. We empirically demonstrate our method's ability to generate complex multi-modal trajectory patterns in different environments.
TrajGAIL: Generating Urban Trajectories using Generative Adversarial Imitation Learning2020-07-28   ${\displaystyle \cong }$
Recently, there are an abundant amount of urban vehicle trajectory data that is collected in the urban road networks. Many previous researches use different algorithms, especially based on machine learning, to analyze the patterns of the urban vehicle trajectories. Unlike previous researches which used discriminative modelling approach, this research suggests a generative modelling approach to learn the underlying distributions of the urban vehicle trajectory data. A generative model for urban vehicle trajectory can produce synthetic vehicle trajectories similar to the real vehicle trajectories. This model can be used for vehicle trajectory reproduction and private data masking in trajectory privacy issues. This research proposes \textit{TrajGAIL}; a generative adversarial imitation learning framework for urban vehicle trajectory generation. In TrajGAIL, the vehicle trajectory generation is formulated as an imitation learning problem in a partially observable Markov decision process. The model is trained by the generative adversarial framework which use the reward function from the adversarial discriminator. The model is tested with different datasets, and the performance of the model is evaluated in terms of dataset-level measures and trajectory-level measures. The proposed model showed exceptional performance compared to the baseline models.
Variational Autoencoder Trajectory Primitives with Continuous and Discrete Latent Codes2019-12-09   ${\displaystyle \cong }$
Imitation learning is an intuitive approach for teaching motion to robotic systems. Although previous studies have proposed various methods to model demonstrated movement primitives, one of the limitations of existing methods is that it is not trivial to modify their planned trajectory once the model is learned. The trajectory of a robotic manipulator is often high-dimensional, and it is not easy to tune the shape of the planned trajectory in an intuitive manner. We address this problem by learning the latent space of the robot trajectory. If the latent variable of the trajectories can be learned, it can be used to tune the trajectory in an intuitive manner even when the user is an expert. We propose a framework for modeling demonstrated trajectories with a neural network that learns the low-dimensional latent space. Our neural network structure is built on the variational autoencoder (VAE) with discrete and continuous latent variables. We extend the structure of the existing VAE to obtain the decoder that is conditioned on the goal position of the trajectory for generalization to different goal positions. To cope with requirement of the massive training data, we use a trajectory augmentation technique inspired by the data augmentation commonly used in the computer vision community. In the proposed framework, the latent variables that encodes the multiple types of trajectories are learned in an unsupervised manner. The learned decoder can be used as a motion planner in which the user can specify the goal position and the trajectory types by setting the latent variables. The experimental results show that our neural network can be trained using a limited number of demonstrated trajectories and that the interpretable latent representations can be learned.
Interplanetary Transfers via Deep Representations of the Optimal Policy and/or of the Value Function2019-04-18   ${\displaystyle \cong }$
A number of applications to interplanetary trajectories have been recently proposed based on deep networks. These approaches often rely on the availability of a large number of optimal trajectories to learn from. In this paper we introduce a new method to quickly create millions of optimal spacecraft trajectories from a single nominal trajectory. Apart from the generation of the nominal trajectory, no additional optimal control problems need to be solved as all the trajectories, by construction, satisfy Pontryagin's minimum principle and the relevant transversality conditions. We then consider deep feed forward neural networks and benchmark three learning methods on the created dataset: policy imitation, value function learning and value function gradient learning. Our results are shown for the case of the interplanetary trajectory optimization problem of reaching Venus orbit, with the nominal trajectory starting from the Earth. We find that both policy imitation and value function gradient learning are able to learn the optimal state feedback, while in the case of value function learning the optimal policy is not captured, only the final value of the optimal propellant mass is.
It Is Not the Journey but the Destination: Endpoint Conditioned Trajectory Prediction2020-07-18   ${\displaystyle \cong }$
Human trajectory forecasting with multiple socially interacting agents is of critical importance for autonomous navigation in human environments, e.g., for self-driving cars and social robots. In this work, we present Predicted Endpoint Conditioned Network (PECNet) for flexible human trajectory prediction. PECNet infers distant trajectory endpoints to assist in long-range multi-modal trajectory prediction. A novel non-local social pooling layer enables PECNet to infer diverse yet socially compliant trajectories. Additionally, we present a simple "truncation-trick" for improving few-shot multi-modal trajectory prediction performance. We show that PECNet improves state-of-the-art performance on the Stanford Drone trajectory prediction benchmark by ~20.9% and on the ETH/UCY benchmark by ~40.8%. Project homepage: https://karttikeya.github.io/publication/htf/
A Scalable Framework for Trajectory Prediction2019-02-27   ${\displaystyle \cong }$
Trajectory prediction (TP) is of great importance for a wide range of location-based applications in intelligent transport systems such as location-based advertising, route planning, traffic management, and early warning systems. In the last few years, the widespread use of GPS navigation systems and wireless communication technology enabled vehicles has resulted in huge volumes of trajectory data. The task of utilizing this data employing spatio-temporal techniques for trajectory prediction in an efficient and accurate manner is an ongoing research problem. Existing TP approaches are limited to short-term predictions. Moreover, they cannot handle a large volume of trajectory data for long-term prediction. To address these limitations, we propose a scalable clustering and Markov chain based hybrid framework, called Traj-clusiVAT-based TP, for both short-term and long-term trajectory prediction, which can handle a large number of overlapping trajectories in a dense road network. Traj-clusiVAT can also determine the number of clusters, which represent different movement behaviours in input trajectory data. In our experiments, we compare our proposed approach with a mixed Markov model (MMM)-based scheme, and a trajectory clustering, NETSCAN-based TP method for both short- and long-term trajectory predictions. We performed our experiments on two real, vehicle trajectory datasets, including a large-scale trajectory dataset consisting of 3.28 million trajectories obtained from 15,061 taxis in Singapore over a period of one month. Experimental results on two real trajectory datasets show that our proposed approach outperforms the existing approaches in terms of both short- and long-term prediction performances, based on prediction accuracy and distance error (in km).
CoverNet: Multimodal Behavior Prediction using Trajectory Sets2020-04-01   ${\displaystyle \cong }$
We present CoverNet, a new method for multimodal, probabilistic trajectory prediction for urban driving. Previous work has employed a variety of methods, including multimodal regression, occupancy maps, and 1-step stochastic policies. We instead frame the trajectory prediction problem as classification over a diverse set of trajectories. The size of this set remains manageable due to the limited number of distinct actions that can be taken over a reasonable prediction horizon. We structure the trajectory set to a) ensure a desired level of coverage of the state space, and b) eliminate physically impossible trajectories. By dynamically generating trajectory sets based on the agent's current state, we can further improve our method's efficiency. We demonstrate our approach on public, real-world self-driving datasets, and show that it outperforms state-of-the-art methods.
Semantic segmentation of trajectories with improved agent models for pedestrian behavior analysis2019-12-11   ${\displaystyle \cong }$
In this paper, we propose a method for semantic segmentation of pedestrian trajectories based on pedestrian behavior models, or agents. The agents model the dynamics of pedestrian movements in two-dimensional space using a linear dynamics model and common start and goal locations of trajectories. First, agent models are estimated from the trajectories obtained from image sequences. Our method is built on top of the Mixture model of Dynamic pedestrian Agents (MDA); however, the MDA's trajectory modeling and estimation are improved. Then, the trajectories are divided into semantically meaningful segments. The subsegments of a trajectory are modeled by applying a hidden Markov model using the estimated agent models. Experimental results with a real trajectory dataset show the effectiveness of the proposed method as compared to the well-known classical Ramer-Douglas-Peucker algorithm and also to the original MDA model.
SafeCritic: Collision-Aware Trajectory Prediction2019-10-15   ${\displaystyle \cong }$
Navigating complex urban environments safely is a key to realize fully autonomous systems. Predicting future locations of vulnerable road users, such as pedestrians and cyclists, thus, has received a lot of attention in the recent years. While previous works have addressed modeling interactions with the static (obstacles) and dynamic (humans) environment agents, we address an important gap in trajectory prediction. We propose SafeCritic, a model that synergizes generative adversarial networks for generating multiple "real" trajectories with reinforcement learning to generate "safe" trajectories. The Discriminator evaluates the generated candidates on whether they are consistent with the observed inputs. The Critic network is environmentally aware to prune trajectories that are in collision or are in violation with the environment. The auto-encoding loss stabilizes training and prevents mode-collapse. We demonstrate results on two large scale data sets with a considerable improvement over state-of-the-art. We also show that the Critic is able to classify the safety of trajectories.
Social-WaGDAT: Interaction-aware Trajectory Prediction via Wasserstein Graph Double-Attention Network2020-02-14   ${\displaystyle \cong }$
Effective understanding of the environment and accurate trajectory prediction of surrounding dynamic obstacles are indispensable for intelligent mobile systems (like autonomous vehicles and social robots) to achieve safe and high-quality planning when they navigate in highly interactive and crowded scenarios. Due to the existence of frequent interactions and uncertainty in the scene evolution, it is desired for the prediction system to enable relational reasoning on different entities and provide a distribution of future trajectories for each agent. In this paper, we propose a generic generative neural system (called Social-WaGDAT) for multi-agent trajectory prediction, which makes a step forward to explicit interaction modeling by incorporating relational inductive biases with a dynamic graph representation and leverages both trajectory and scene context information. We also employ an efficient kinematic constraint layer applied to vehicle trajectory prediction which not only ensures physical feasibility but also enhances model performance. The proposed system is evaluated on three public benchmark datasets for trajectory prediction, where the agents cover pedestrians, cyclists and on-road vehicles. The experimental results demonstrate that our model achieves better performance than various baseline approaches in terms of prediction accuracy.
Scalable Unsupervised Multi-Criteria Trajectory Segmentation and Driving Preference Mining2020-10-23   ${\displaystyle \cong }$
We present analysis techniques for large trajectory data sets that aim to provide a semantic understanding of trajectories reaching beyond them being point sequences in time and space. The presented techniques use a driving preference model w.r.t. road segment traversal costs, e.g., travel time and distance, to analyze and explain trajectories. In particular, we present trajectory mining techniques that can (a) find interesting points within a trajectory indicating, e.g., a via-point, and (b) recover the driving preferences of a driver based on their chosen trajectory. We evaluate our techniques on the tasks of via-point identification and personalized routing using a data set of more than 1 million vehicle trajectories collected throughout Denmark during a 3-year period. Our techniques can be implemented efficiently and are highly parallelizable, allowing them to scale to millions or billions of trajectories.
A Generic Framework for Clustering Vehicle Motion Trajectories2020-09-25   ${\displaystyle \cong }$
The development of autonomous vehicles requires having access to a large amount of data in the concerning driving scenarios. However, manual annotation of such driving scenarios is costly and subject to the errors in the rule-based trajectory labeling systems. To address this issue, we propose an effective non-parametric trajectory clustering framework consisting of five stages: (1) aligning trajectories and quantifying their pairwise temporal dissimilarities, (2) embedding the trajectory-based dissimilarities into a vector space, (3) extracting transitive relations, (4) embedding the transitive relations into a new vector space, and (5) clustering the trajectories with an optimal number of clusters. We investigate and evaluate the proposed framework on a challenging real-world dataset consisting of annotated trajectories. We observe that the proposed framework achieves promising results, despite the complexity caused by having trajectories of varying length. Furthermore, we extend the framework to validate the augmentation of the real dataset with synthetic data generated by a Generative Adversarial Network (GAN) where we examine whether the generated trajectories are consistent with the true underlying clusters.
An Unsupervised Learning Method with Convolutional Auto-Encoder for Vessel Trajectory Similarity Computation2021-01-09   ${\displaystyle \cong }$
To achieve reliable mining results for massive vessel trajectories, one of the most important challenges is how to efficiently compute the similarities between different vessel trajectories. The computation of vessel trajectory similarity has recently attracted increasing attention in the maritime data mining research community. However, traditional shape- and warping-based methods often suffer from several drawbacks such as high computational cost and sensitivity to unwanted artifacts and non-uniform sampling rates, etc. To eliminate these drawbacks, we propose an unsupervised learning method which automatically extracts low-dimensional features through a convolutional auto-encoder (CAE). In particular, we first generate the informative trajectory images by remapping the raw vessel trajectories into two-dimensional matrices while maintaining the spatio-temporal properties. Based on the massive vessel trajectories collected, the CAE can learn the low-dimensional representations of informative trajectory images in an unsupervised manner. The trajectory similarity is finally equivalent to efficiently computing the similarities between the learned low-dimensional features, which strongly correlate with the raw vessel trajectories. Comprehensive experiments on realistic data sets have demonstrated that the proposed method largely outperforms traditional trajectory similarity computation methods in terms of efficiency and effectiveness. The high-quality trajectory clustering performance could also be guaranteed according to the CAE-based trajectory similarity computation results.
Learning Probabilistic Intersection Traffic Models for Trajectory Prediction2020-02-05   ${\displaystyle \cong }$
Autonomous agents must be able to safely interact with other vehicles to integrate into urban environments. The safety of these agents is dependent on their ability to predict collisions with other vehicles' future trajectories for replanning and collision avoidance. The information needed to predict collisions can be learned from previously observed vehicle trajectories in a specific environment, generating a traffic model. The learned traffic model can then be incorporated as prior knowledge into any trajectory estimation method being used in this environment. This work presents a Gaussian process based probabilistic traffic model that is used to quantify vehicle behaviors in an intersection. The Gaussian process model provides estimates for the average vehicle trajectory, while also capturing the variance between the different paths a vehicle may take in the intersection. The method is demonstrated on a set of time-series position trajectories. These trajectories are reconstructed by removing object recognition errors and missed frames that may occur due to data source processing. To create the intersection traffic model, the reconstructed trajectories are clustered based on their source and destination lanes. For each cluster, a Gaussian process model is created to capture the average behavior and the variance of the cluster. To show the applicability of the Gaussian model, the test trajectories are classified with only partial observations. Performance is quantified by the number of observations required to correctly classify the vehicle trajectory. Both the intersection traffic modeling computations and the classification procedure are timed. These times are presented as results and demonstrate that the model can be constructed in a reasonable amount of time and the classification procedure can be used for online applications.
Vehicle Trajectory Prediction by Transfer Learning of Semi-Supervised Models2020-07-13   ${\displaystyle \cong }$
In this work we show that semi-supervised models for vehicle trajectory prediction significantly improve performance over supervised models on state-of-the-art real-world benchmarks. Moving from supervised to semi-supervised models allows scaling-up by using unlabeled data, increasing the number of images in pre-training from Millions to a Billion. We perform ablation studies comparing transfer learning of semi-supervised and supervised models while keeping all other factors equal. Within semi-supervised models we compare contrastive learning with teacher-student methods as well as networks predicting a small number of trajectories with networks predicting probabilities over a large trajectory set. Our results using both low-level and mid-level representations of the driving environment demonstrate the applicability of semi-supervised methods for real-world vehicle trajectory prediction.
Mobility Inference on Long-Tailed Sparse Trajectory2020-01-21   ${\displaystyle \cong }$
Analyzing the urban trajectory in cities has become an important topic in data mining. How can we model the human mobility consisting of stay and travel from the raw trajectory data? How can we infer such a mobility model from the single trajectory information? How can we further generalize the mobility inference to accommodate the real-world trajectory data that is sparsely sampled over time? In this paper, based on formal and rigid definitions of the stay/travel mobility, we propose a single trajectory inference algorithm that utilizes a generic long-tailed sparsity pattern in the large-scale trajectory data. The algorithm guarantees a 100\% precision in the stay/travel inference with a provable lower-bound in the recall. Furthermore, we introduce an encoder-decoder learning architecture that admits multiple trajectories as inputs. The architecture is optimized for the mobility inference problem through customized embedding and learning mechanism. Evaluations with three trajectory data sets of 40 million urban users validate the performance guarantees of the proposed inference algorithm and demonstrate the superiority of our deep learning model, in comparison to well-known sequence learning methods. On extremely sparse trajectories, the deep learning model achieves a 2$\times$ overall accuracy improvement from the single trajectory inference algorithm, through proven scalability and generalizability to large-scale versatile training data.
PlanIt: A Crowdsourcing Approach for Learning to Plan Paths from Large Scale Preference Feedback2016-01-05   ${\displaystyle \cong }$
We consider the problem of learning user preferences over robot trajectories for environments rich in objects and humans. This is challenging because the criterion defining a good trajectory varies with users, tasks and interactions in the environment. We represent trajectory preferences using a cost function that the robot learns and uses it to generate good trajectories in new environments. We design a crowdsourcing system - PlanIt, where non-expert users label segments of the robot's trajectory. PlanIt allows us to collect a large amount of user feedback, and using the weak and noisy labels from PlanIt we learn the parameters of our model. We test our approach on 122 different environments for robotic navigation and manipulation tasks. Our extensive experiments show that the learned cost function generates preferred trajectories in human environments. Our crowdsourcing system is publicly available for the visualization of the learned costs and for providing preference feedback: \url{http://planit.cs.cornell.edu}
Adversarial Generation of Informative Trajectories for Dynamics System Identification2020-03-02   ${\displaystyle \cong }$
Dynamic System Identification approaches usually heavily rely on the evolutionary and gradient-based optimisation techniques to produce optimal excitation trajectories for determining the physical parameters of robot platforms. Current optimisation techniques tend to generate single trajectories. This is expensive, and intractable for longer trajectories, thus limiting their efficacy for system identification. We propose to tackle this issue by using multiple shorter cyclic trajectories, which can be generated in parallel, and subsequently combined together to achieve the same effect as a longer trajectory. Crucially, we show how to scale this approach even further by increasing the generation speed and quality of the dataset through the use of generative adversarial network (GAN) based architectures to produce a large databases of valid and diverse excitation trajectories. To the best of our knowledge, this is the first robotics work to explore system identification with multiple cyclic trajectories and to develop GAN-based techniques for scaleably producing excitation trajectories that are diverse in both control parameter and inertial parameter spaces. We show that our approach dramatically accelerates trajectory optimisation, while simultaneously providing more accurate system identification than the conventional approach.