Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot’s geometry and multiple desired behaviors. While current robot programming tools (such as inverse kinematics, collision avoidance, and manipulation planning) often treat these problems as constrained optimization, many existing solvers focus on specific problem domains or do not exploit geometric constraints effectively. We propose an efficient first-order method, Augmented Lagrangian Spectral Projected Gradient Descent (ALSPG), which leverages geometric projections via Euclidean projections, Minkowski sums, and basis functions. We show that by using geometric constraints rather than full constraints and gradients, ALSPG significantly improves real-time performance. Compared to second-order methods like iLQR, ALSPG remains competitive in the unconstrained case. We validate our method through toy examples and extensive simulations, and demonstrate its effectiveness on a 7-axis Franka robot, a 6-axis P-Rob robot and a 1:10 scale car in real-world experiments. Source codes, experimental data and videos are available on the project webpage: https://sites.google.com/view/alspg-oc

Generating overtaking trajectories in autonomous racing is a challenging task, as the trajectory must satisfy the vehicle’s dynamics and ensure safety and real-time performance running on resource-constrained hardware. This work proposes the Fast and Safe Data-Driven Planner to address this challenge. Sparse Gaussian predictions are introduced to improve both the computational efficiency and accuracy of opponent predictions. Furthermore, the proposed approach employs a bi-level quadratic programming framework to generate an overtaking trajectory leveraging the opponent predictions. The first level uses polynomial fitting to generate a rough trajectory, from which reference states and control inputs are derived for the second level. The second level formulates a model predictive control optimization problem in the Frenet frame, generating a trajectory that satisfies both kinematic feasibility and safety. Experimental results on the F1TENTH platform show that our method outperforms the State-of-the-Art, achieving an 8.93% higher overtaking success rate, allowing the maximum opponent speed, ensuring a smoother ego trajectory, and reducing 74.04% computational time compared to the Predictive Spliner method. The code is available at: https://github.com/ZJU-DDRX/FSDP.

In this paper, we propose a safety-critical controller based on time-varying control barrier functions (CBFs) for a robot with an unicycle model in the continuous-time domain to achieve navigation and dynamic collision avoidance. Unlike previous works, our proposed approach can control both linear and angular velocity to avoid collision with obstacles, overcoming the limitation of confined control performance due to the lack of control variable. To ensure that the robot reaches its destination, we also design a control Lyapunov function (CLF). Our safety-critical controller is formulated as a quadratic program (QP) optimization problem that incorporates CLF and CBFs as constraints, enabling real-time application for navigation and dynamic collision avoidance. Numerical simulations are conducted to verify the effectiveness of our proposed approach.

Because of the scarcity of bilingual corpora, current Chinese--Vietnamese machine translation is far from satisfactory. Considering the differences between Chinese and Vietnamese, we investigate whether linguistic differences can be used to supervise machine translation and propose a method of syntax-based Chinese--Vietnamese tree-to-tree statistical machine translation with bilingual features. Analyzing the syntax differences between Chinese and Vietnamese, we define some linguistic difference-based rules, such as attributive position, time adverbial position, and locative adverbial position, and create rewards for similar rules. These rewards are integrated into the extraction of tree-to-tree translation rules, and we optimize the pruning of the search space during the decoding phase. The experiments on Chinese--Vietnamese bilingual sentence translation show that the proposed method performs better than several compared methods. Further, the results show that syntactic difference features, with search pruning, can improve the accuracy of machine translation without degrading the efficiency.