We propose a variant of alternating direction method of multiplier (ADMM) to solve constrained trajectory optimization problems. Our ADMM framework breaks a joint optimization into small sub-problems, leading to a low iteration cost and decentralized parameter updates. Our method inherits the theoretical properties of primal interior point method (P-IPM), i.e., guaranteed collision avoidance and homotopy preservation, while being orders of magnitude faster. We have analyzed the convergence and evaluated our method for time-optimal multi-UAV trajectory optimizations and simultaneous goal-reaching of multiple robot arms, where we take into consider kinematics-, dynamics-limits, and homotopy-preserving collision constraints. Our method highlights 10-100 times speedup, while generating trajectories of comparable qualities as state-of-the-art P-IPM solver.
Neural networks have been increasingly employed in Model Predictive Controller (MPC) to control nonlinear dynamic systems. However, MPC still poses a problem that an achievable update rate is insufficient to cope with model uncertainty and external disturbances. In this paper, we present a novel control scheme that can design an optimal tracking controller using the neural network dynamics of the MPC, making it possible to be applied as a plug-and-play extension for any existing model-based feedforward controller. We also describe how our method handles a neural network containing historical information, which does not follow a general form of dynamics. The proposed method is evaluated by its performance in classical control benchmarks with external disturbances. We also extend our control framework to be applied in an aggressive autonomous driving task with unknown friction. In all experiments, our method outperformed the compared methods by a large margin. Our controller also showed low control chattering levels, demonstrating that our feedback controller does not interfere with the optimal command of MPC.
This paper presents a novel planning and control strategy for competing with multiple vehicles in a car racing scenario. The proposed racing strategy switches between two modes. When there are no surrounding vehicles, a learning-based model predictive control (MPC) trajectory planner is used to guarantee that the ego vehicle achieves better lap timing. When the ego vehicle is competing with other surrounding vehicles to overtake, an optimization-based planner generates multiple dynamically-feasible trajectories through parallel computation. Each trajectory is optimized under a MPC formulation with different homotopic Bezier-curve reference paths lying laterally between surrounding vehicles. The time-optimal trajectory among these different homotopic trajectories is selected and a low-level MPC controller with obstacle avoidance constraints is used to guarantee system safety-critical performance. The proposed algorithm has the capability to generate collision-free trajectories and track them while enhancing the lap timing performance with steady low computational complexity, outperforming existing approaches in both timing and performance for a car racing environment. To demonstrate the performance of our racing strategy, we simulate with multiple randomly generated moving vehicles on the track and test the ego vehicle's overtake maneuvers.
A cable-driven soft-bodied robot with redundancy can conduct the trajectory tracking task and in the meanwhile fulfill some extra constraints, such as tracking through an end-effector in designated orientation, or get rid of the evitable manipulator-obstacle collision. Those constraints require rational planning of the robot motion. In this work, we derived the compressible curvature kinematics of a cable-driven soft robot which takes the compressible soft segment into account. The motion planning of the soft robot for a trajectory tracking task in constrained conditions, including fixed orientation end-effector and manipulator-obstacle collision avoidance, has been investigated. The inverse solution of cable actuation was formulated as a damped least-square optimization problem and iteratively computed off-line. The performance of trajectory tracking and the obedience to constraints were evaluated via the simulation we made open-source, as well as the prototype experiments. The method can be generalized to the similar multisegment cable-driven soft robotic systems by customizing the robot parameters for the prior motion planning of the manipulator.
In order to improve the vessel's capacity and ensure maritime traffic safety, vessel intelligent trajectory prediction plays an essential role in the vessel's smart navigation and intelligent collision avoidance system. However, current researchers only focus on short-term or long-term vessel trajectory prediction, which leads to insufficient accuracy of trajectory prediction and lack of in-depth mining of comprehensive historical trajectory data. This paper proposes an Automatic Identification System (AIS) data-driven long short-term memory (LSTM) method based on the fusion of the forward sub-network and the reverse sub-network (termed as FRA-LSTM) to predict the vessel trajectory. The forward sub-network in our method combines LSTM and attention mechanism to mine features of forward historical trajectory data. Simultaneously, the reverse sub-network combines bi-directional LSTM (BiLSTM) and attention mechanism to mine features of backward historical trajectory data. Finally, the final predicted trajectory is generated by fusing output features of the forward and reverse sub-network. Based on plenty of experiments, we prove that the accuracy of our proposed method in predicting short-term and mid-term trajectories has increased by 96.8% and 86.5% on average compared with the BiLSTM and Seq2seq. Furthermore, the average accuracy of our method is 90.1% higher than that of compared the BiLSTM and Seq2seq in predicting long-term trajectories.
We study the bilinearly coupled minimax problem: $\min_{x} \max_{y} f(x) + y^\top A x - h(y)$, where $f$ and $h$ are both strongly convex smooth functions and admit first-order gradient oracles. Surprisingly, no known first-order algorithms have hitherto achieved the lower complexity bound of $\Omega((\sqrt{\frac{L_x}{\mu_x}} + \frac{\|A\|}{\sqrt{\mu_x \mu_y}} + \sqrt{\frac{L_y}{\mu_y}}) \log(\frac1{\varepsilon}))$ for solving this problem up to an $\varepsilon$ primal-dual gap in the general parameter regime, where $L_x, L_y,\mu_x,\mu_y$ are the corresponding smoothness and strongly convexity constants. We close this gap by devising the first optimal algorithm, the Lifted Primal-Dual (LPD) method. Our method lifts the objective into an extended form that allows both the smooth terms and the bilinear term to be handled optimally and seamlessly with the same primal-dual framework. Besides optimality, our method yields a desirably simple single-loop algorithm that uses only one gradient oracle call per iteration. Moreover, when $f$ is just convex, the same algorithm applied to a smoothed objective achieves the nearly optimal iteration complexity. We also provide a direct single-loop algorithm, using the LPD method, that achieves the iteration complexity of $O(\sqrt{\frac{L_x}{\varepsilon}} + \frac{\|A\|}{\sqrt{\mu_y \varepsilon}} + \sqrt{\frac{L_y}{\varepsilon}})$. Numerical experiments on quadratic minimax problems and policy evaluation problems further demonstrate the fast convergence of our algorithm in practice.
With the explosive growth of information technology, multi-view graph data have become increasingly prevalent and valuable. Most existing multi-view clustering techniques either focus on the scenario of multiple graphs or multi-view attributes. In this paper, we propose a generic framework to cluster multi-view attributed graph data. Specifically, inspired by the success of contrastive learning, we propose multi-view contrastive graph clustering (MCGC) method to learn a consensus graph since the original graph could be noisy or incomplete and is not directly applicable. Our method composes of two key steps: we first filter out the undesirable high-frequency noise while preserving the graph geometric features via graph filtering and obtain a smooth representation of nodes; we then learn a consensus graph regularized by graph contrastive loss. Results on several benchmark datasets show the superiority of our method with respect to state-of-the-art approaches. In particular, our simple approach outperforms existing deep learning-based methods.
We study constrained reinforcement learning (CRL) from a novel perspective by setting constraints directly on state density functions, rather than the value functions considered by previous works. State density has a clear physical and mathematical interpretation, and is able to express a wide variety of constraints such as resource limits and safety requirements. Density constraints can also avoid the time-consuming process of designing and tuning cost functions required by value function-based constraints to encode system specifications. We leverage the duality between density functions and Q functions to develop an effective algorithm to solve the density constrained RL problem optimally and the constrains are guaranteed to be satisfied. We prove that the proposed algorithm converges to a near-optimal solution with a bounded error even when the policy update is imperfect. We use a set of comprehensive experiments to demonstrate the advantages of our approach over state-of-the-art CRL methods, with a wide range of density constrained tasks as well as standard CRL benchmarks such as Safety-Gym.
Recent advances in sensor and mobile devices have enabled an unprecedented increase in the availability and collection of urban trajectory data, thus increasing the demand for more efficient ways to manage and analyze the data being produced. In this survey, we comprehensively review recent research trends in trajectory data management, ranging from trajectory pre-processing, storage, common trajectory analytic tools, such as querying spatial-only and spatial-textual trajectory data, and trajectory clustering. We also explore four closely related analytical tasks commonly used with trajectory data in interactive or real-time processing. Deep trajectory learning is also reviewed for the first time. Finally, we outline the essential qualities that a trajectory management system should possess in order to maximize flexibility.
Predicting the future trajectories of multiple interacting agents in a scene has become an increasingly important problem for many different applications ranging from control of autonomous vehicles and social robots to security and surveillance. This problem is compounded by the presence of social interactions between humans and their physical interactions with the scene. While the existing literature has explored some of these cues, they mainly ignored the multimodal nature of each human's future trajectory. In this paper, we present Social-BiGAT, a graph-based generative adversarial network that generates realistic, multimodal trajectory predictions by better modelling the social interactions of pedestrians in a scene. Our method is based on a graph attention network (GAT) that learns reliable feature representations that encode the social interactions between humans in the scene, and a recurrent encoder-decoder architecture that is trained adversarially to predict, based on the features, the humans' paths. We explicitly account for the multimodal nature of the prediction problem by forming a reversible transformation between each scene and its latent noise vector, as in Bicycle-GAN. We show that our framework achieves state-of-the-art performance comparing it to several baselines on existing trajectory forecasting benchmarks.
In this work, we take a representation learning perspective on hierarchical reinforcement learning, where the problem of learning lower layers in a hierarchy is transformed into the problem of learning trajectory-level generative models. We show that we can learn continuous latent representations of trajectories, which are effective in solving temporally extended and multi-stage problems. Our proposed model, SeCTAR, draws inspiration from variational autoencoders, and learns latent representations of trajectories. A key component of this method is to learn both a latent-conditioned policy and a latent-conditioned model which are consistent with each other. Given the same latent, the policy generates a trajectory which should match the trajectory predicted by the model. This model provides a built-in prediction mechanism, by predicting the outcome of closed loop policy behavior. We propose a novel algorithm for performing hierarchical RL with this model, combining model-based planning in the learned latent space with an unsupervised exploration objective. We show that our model is effective at reasoning over long horizons with sparse rewards for several simulated tasks, outperforming standard reinforcement learning methods and prior methods for hierarchical reasoning, model-based planning, and exploration.