arXiv subjects

Yiqun Li

Publications and source records attributed to Yiqun Li.

At least 19 recordsLinked to original sources

arXiv2026

Error estimate of the nonuniform BDF3-L2 method for subdiffusion equations via multiscale solution decomposition

Numerical experiments reported by Quan and Wu [SIAM J Numer Anal 61 (2023) 2106-2132] show that the observed temporal convergence rates of nonuniform L2 methods for subdiffusion models are not consistent with the theoretically predicted order $3-\alpha$. This discrepancy suggests that a more refined analysis is needed and motivates the development of a nonuniform BDF3-L2 method for the subdiffusion equation. To account for the initial solution singularity, we employ the multiscale solution decomposition to decompose the original solution and approximate a smoother unknown variable that satisfies the subdiffusion model with a smoother source term. The resulting formulation, however, involves restrictive high-order boundary conditions on the source term and initial data. To overcome this difficulty, we introduce a spectral truncation technique that requires only slightly stronger regularity of the data and a controllable truncation error. We establish high-order regularity estimates of the solution to the truncated problem and develop a nonuniform BDF3-L2 method for its numerical approximation, based on which we derive a rigorous error estimate of temporal convergence order $2+\alpha$. Numerical experiments are carried out to substantiate the theoretical findings.

math.NA↗

arXiv2026

S2M-Trek: From Single to Multi-Sphere Transport via Per-Frame Deep Sets on a Wheel-Legged Robot

We study the problem of scaling dynamic loco-manipulation from a single free-rolling sphere to multiple spheres transported simultaneously on the back of a wheel-legged quadruped, without fences, grippers, or mechanical stops. Multiple identical free-rolling spheres form an unordered set with no persistent identity: their ordering may change independently at each history frame, creating a \emph{per-frame permutation symmetry} that standard history-concatenation set encoders do not explicitly enforce -- these encoders impose only a shared, diagonal permutation symmetry over the full history. We show that this symmetry mismatch leads to a concrete failure mode in curriculum-based reinforcement learning. Within the same PPO training budget, flat MLPs and branch-wise encoders plateau at or below the two-sphere stage, while a history-concatenation Deep Sets baseline (\HCDS) fails to progress past the two-sphere stage in our runs unless ball-to-slot assignments are randomised during training, suggesting that it exploits slot indices as a curriculum shortcut rather than learning identity-free multi-sphere dynamics. We propose \textbf{Per-Frame Deep Sets (\PFDS)}, which performs permutation-invariant pooling within each history frame before temporal readout; we prove that \PFDS is $\Gframe$-invariant and universally approximates continuous $\Gframe$-invariant policies. A $2{\times}2$ ablation over encoder architecture and slot randomisation separates the architectural and data-augmentation pathways, and \PFDS reaches the five-sphere stage with 100\% no-drop transport in simulation across all five random seeds. We further distill the \PFDS teacher into \TactSet via DAgger, replacing privileged sphere-state observations with a $16{\times}16$ Boolean union contact map, yielding a compact and naturally $\Gframe$-invariant tactile representation.

cs.RO↗

arXiv2026

The optimal error analysis of nonuniform L1 method for the variable-exponent subdiffusion model

This work investigates the optimal error estimate of the fully discrete scheme for the variable-exponent subdiffusion model under the nonuniform temporal mesh. We apply the perturbation method to reformulate the original model into its equivalent form, and apply the L1 scheme as well as the interpolation quadrature rule to discretize the Caputo derivative term and the convolution term in the reformulated model, respectively. We then prove the temporal convergence rates $O(N^{-\min\{2-α(0), rα(0)\}})$ under the nonuniform mesh, which improves the existing convergence results in [Zheng, CSIAM T. Appl. Math. 2025] for $r\geq \frac{2-α(0)}{α(0)}$. Numerical results are presented to substantiate the theoretical findings.

math.NA↗

arXiv2025

Variable-order fractional wave equation: Analysis, numerical approximation, and fast algorithm

We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the well-posedness of the model as well as its high order regularity estimates. To accommodate the convolution term in the reformulated model, we adopt the Ritz-Volterra finite element projection and then derive the rigorous error estimate for the fully-discretized finite element scheme. To circumvent the high computational cost from the temporal integral term, we exploit the translational invariance of the discrete coefficients associated with the convolution structure and construct a fast divide-and-conquer algorithm which reduces the computational complexity from $O(MN^2)$ to $O(MN\log^2 N)$. Numerical experiments are provided to verify the theoretical results and to demonstrate the accuracy and efficiency of the proposed method.

math.NA↗

arXiv2025

Whole-body Motion Control of an Omnidirectional Wheel-Legged Mobile Manipulator via Contact-Aware Dynamic Optimization

Wheel-legged robots with integrated manipulators hold great promise for mobile manipulation in logistics, industrial automation, and human-robot collaboration. However, unified control of such systems remains challenging due to the redundancy in degrees of freedom, complex wheel-ground contact dynamics, and the need for seamless coordination between locomotion and manipulation. In this work, we present the design and whole-body motion control of an omnidirectional wheel-legged quadrupedal robot equipped with a dexterous manipulator. The proposed platform incorporates independently actuated steering modules and hub-driven wheels, enabling agile omnidirectional locomotion with high maneuverability in structured environments. To address the challenges of contact-rich interaction, we develop a contact-aware whole-body dynamic optimization framework that integrates point-contact modeling for manipulation with line-contact modeling for wheel-ground interactions. A warm-start strategy is introduced to accelerate online optimization, ensuring real-time feasibility for high-dimensional control. Furthermore, a unified kinematic model tailored for the robot's 4WIS-4WID actuation scheme eliminates the need for mode switching across different locomotion strategies, improving control consistency and robustness. Simulation and experimental results validate the effectiveness of the proposed framework, demonstrating agile terrain traversal, high-speed omnidirectional mobility, and precise manipulation under diverse scenarios, underscoring the system's potential for factory automation, urban logistics, and service robotics in semi-structured environments.

cs.RO↗

arXiv2025

FDSPC: Fast and Direct Smooth Path Planning via Continuous Curvature Integration

In recent decades, global path planning of robot has seen significant advancements. Both heuristic search-based methods and probability sampling-based methods have shown capabilities to find feasible solutions in complex scenarios. However, mainstream global path planning algorithms often produce paths with bends, requiring additional smoothing post-processing. In this work, we propose a fast and direct path planning method based on continuous curvature integration. This method ensures path feasibility while directly generating global smooth paths with constant velocity, thus eliminating the need for post-path-smoothing. Furthermore, we compare the proposed method with existing approaches in terms of solution time, path length, memory usage, and smoothness under multiple scenarios. The proposed method is vastly superior to the average performance of state-of-the-art (SOTA) methods, especially in terms of the self-defined $\mathcal{S}_2 $ smoothness (mean angle of steering). These results demonstrate the effectiveness and superiority of our approach in several representative environments.

cs.RO↗

arXiv2025

Optimal control of variable-exponent subdiffusion

This work investigates the optimal control of the variable-exponent subdiffusion, which extends the work [Gunzburger and Wang, SIAM J. Control Optim. 2019] to the variable-exponent case to account for the multiscale and crossover diffusion behavior. To resolve the difficulties caused by the leading variable-exponent operator, we adopt the convolution method to reformulate the model into an equivalent but more tractable form, and then prove the well-posedness and weighted regularity of the optimal control. As the convolution kernels in reformulated models are indefinite-sign, non-positive-definite, and non-monotonic, we adopt the discrete convolution kernel approach in numerical analysis to show the $O(\tau(1+|\ln\tau|)+h^2)$ accuracy of the schemes for state and adjoint equations. Numerical experiments are performed to substantiate the theoretical findings.

math.OC↗

arXiv2025

Compact difference method for Euler-Bernoulli beams and plates with nonlinear nonlocal strong damping

We investigate the numerical approximation to the Euler-Bernoulli (E-B) beams and plates with nonlinear nonlocal strong damping, which describes the damped mechanical behavior of beams and plates in real applications. We discretize the damping term by the composite Simpson's rule and the six-point Simpson's formula in the beam and plate problems, respectively, and then construct the fully discrete compact difference scheme for these problems. To account for the nonlinear-nonlocal term, we design several novel discrete norms to facilitate the error estimates of the damping term and the numerical scheme. The stability, convergence, and energy dissipation properties of the proposed scheme are proved, and numerical experiments are carried out to substantiate the theoretical findings.

math.NA↗

arXiv2025

Analysis of evolution equation with variable-exponent memory modeling multiscale viscoelasticity

We investigate the well-posedness and solution regularity of an evolution equation with non-positive type variable-exponent memory, which describes multiscale viscoelasticity in materials with memory. The perturbation method is applied for model transformation, based on which the well-posedness is proved. Then the weighted solution regularity is derived, where the initial singularity is characterized by the initial value of variable exponent.

math.AP↗

arXiv2025

Scene-Aware Explainable Multimodal Trajectory Prediction

Advancements in intelligent technologies have significantly improved navigation in complex traffic environments by enhancing environment perception and trajectory prediction for automated vehicles. However, current research often overlooks the joint reasoning of scenario agents and lacks explainability in trajectory prediction models, limiting their practical use in real-world situations. To address this, we introduce the Explainable Conditional Diffusion-based Multimodal Trajectory Prediction (DMTP) model, which is designed to elucidate the environmental factors influencing predictions and reveal the underlying mechanisms. Our model integrates a modified conditional diffusion approach to capture multimodal trajectory patterns and employs a revised Shapley Value model to assess the significance of global and scenario-specific features. Experiments using the Waymo Open Motion Dataset demonstrate that our explainable model excels in identifying critical inputs and significantly outperforms baseline models in accuracy. Moreover, the factors identified align with the human driving experience, underscoring the model's effectiveness in learning accurate predictions. Code is available in our open-source repository: https://github.com/ocean-luna/Explainable-Prediction.

cs.AI↗

arXiv2025

Spatiotemporal Prediction of Secondary Crashes by Rebalancing Dynamic and Static Data with Generative Adversarial Networks

Data imbalance is a common issue in analyzing and predicting sudden traffic events. Secondary crashes constitute only a small proportion of all crashes. These secondary crashes, triggered by primary crashes, significantly exacerbate traffic congestion and increase the severity of incidents. However, the severe imbalance of secondary crash data poses significant challenges for prediction models, affecting their generalization ability and prediction accuracy. Existing methods fail to fully address the complexity of traffic crash data, particularly the coexistence of dynamic and static features, and often struggle to effectively handle data samples of varying lengths. Furthermore, most current studies predict the occurrence probability and spatiotemporal distribution of secondary crashes separately, lacking an integrated solution. To address these challenges, this study proposes a hybrid model named VarFusiGAN-Transformer, aimed at improving the fidelity of secondary crash data generation and jointly predicting the occurrence and spatiotemporal distribution of secondary crashes. The VarFusiGAN-Transformer model employs Long Short-Term Memory (LSTM) networks to enhance the generation of multivariate long-time series data, incorporating a static data generator and an auxiliary discriminator to model the joint distribution of dynamic and static features. In addition, the model's prediction module achieves simultaneous prediction of both the occurrence and spatiotemporal distribution of secondary crashes. Compared to existing methods, the proposed model demonstrates superior performance in generating high-fidelity data and improving prediction accuracy.

cs.AI↗

arXiv2024

A multiscale Abel kernel and application in viscoelastic problem

We consider the variable-exponent Abel kernel and demonstrate its multiscale nature in modeling crossover dynamics from the initial quasi-exponential behavior to long-term power-law behavior. Then we apply this to an integro-differential equation modeling, e.g. mechanical vibration of viscoelastic materials with changing material properties. We apply the Crank-Nicolson method and the linear interpolation quadrature to design a temporal second-order scheme, and develop a framework of exponentially weighted energy argument in error estimate to account for the non-positivity and non-monotonicity of the multiscale kernel. Numerical experiments are carried out to substantiate the theoretical findings and the crossover dynamics of the model.

math.NA↗

arXiv2024

Kaninfradet3D:A Road-side Camera-LiDAR Fusion 3D Perception Model based on Nonlinear Feature Extraction and Intrinsic Correlation

With the development of AI-assisted driving, numerous methods have emerged for ego-vehicle 3D perception tasks, but there has been limited research on roadside perception. With its ability to provide a global view and a broader sensing range, the roadside perspective is worth developing. LiDAR provides precise three-dimensional spatial information, while cameras offer semantic information. These two modalities are complementary in 3D detection. However, adding camera data does not increase accuracy in some studies since the information extraction and fusion procedure is not sufficiently reliable. Recently, Kolmogorov-Arnold Networks (KANs) have been proposed as replacements for MLPs, which are better suited for high-dimensional, complex data. Both the camera and the LiDAR provide high-dimensional information, and employing KANs should enhance the extraction of valuable features to produce better fusion outcomes. This paper proposes Kaninfradet3D, which optimizes the feature extraction and fusion modules. To extract features from complex high-dimensional data, the model's encoder and fuser modules were improved using KAN Layers. Cross-attention was applied to enhance feature fusion, and visual comparisons verified that camera features were more evenly integrated. This addressed the issue of camera features being abnormally concentrated, negatively impacting fusion. Compared to the benchmark, our approach shows improvements of +9.87 mAP and +10.64 mAP in the two viewpoints of the TUMTraf Intersection Dataset and an improvement of +1.40 mAP in the roadside end of the TUMTraf V2X Cooperative Perception Dataset. The results indicate that Kaninfradet3D can effectively fuse features, demonstrating the potential of applying KANs in roadside perception tasks.

cs.CV↗

arXiv2024

Weighted Sonine conditions and application

The Sonine kernel described by the classical Sonine condition of convolution form is an important class of kernels used in integral equations and nonlocal differential equations. This work extends this idea to introduce weighted Sonine conditions where the non-convolutional weight functions accommodate the inhomogeneity in practical applications. We characterize tight relations between classical Sonine condition and its weighted versions, which indicates that the non-degenerate weight functions may not introduce significant changes on the set of Sonine kernels. To demonstrate the application of weighted Sonine conditions, we employ them to derive equivalent but more feasible formulations of weighted integral equations and nonlocal differential equations to prove their well-posedness, and discuss possible application to corresponding partial differential equation models.

math.CA↗

arXiv2024

Optimal Multilayered Motion Planning for Multiple Differential Drive Mobile Robots with Hierarchical Prioritization (OM-MP)

We present a novel framework for addressing the challenges of multi-Agent planning and formation control within intricate and dynamic environments. This framework transforms the Multi-Agent Path Finding (MAPF) problem into a Multi-Agent Trajectory Planning (MATP) problem. Unlike traditional MAPF solutions, our multilayer optimization scheme consists of a global planner optimization solver, which is dedicated to determining concise global paths for each individual robot, and a local planner with an embedded optimization solver aimed at ensuring the feasibility of local robot trajectories. By implementing a hierarchical prioritization strategy, we enhance robots' efficiency and approximate the global optimal solution. Specifically, within the global planner, we employ the Augmented Graph Search (AGS) algorithm, which significantly improves the speed of solutions. Meanwhile, within the local planner optimization solver, we utilize Control Barrier functions (CBFs) and introduced an oblique cylindrical obstacle bounding box based on the time axis for obstacle avoidance and construct a single-robot locally aware-communication circle to ensure the simplicity, speed, and accuracy of locally optimized solutions. Additionally, we integrate the weight and priority of path traces to prevent deadlocks in limiting scenarios. Compared to the other state-of-the-art methods, including CBS, ECBS and other derivative algorithms, our proposed method demonstrates superior performance in terms of capacity, flexible scalability and overall task optimality in theory, as validated through simulations and experiments.

cs.RO↗

arXiv2024

PEVA-Net: Prompt-Enhanced View Aggregation Network for Zero/Few-Shot Multi-View 3D Shape Recognition

Large vision-language models have impressively promote the performance of 2D visual recognition under zero/few-shot scenarios. In this paper, we focus on exploiting the large vision-language model, i.e., CLIP, to address zero/few-shot 3D shape recognition based on multi-view representations. The key challenge for both tasks is to generate a discriminative descriptor of the 3D shape represented by multiple view images under the scenarios of either without explicit training (zero-shot 3D shape recognition) or training with a limited number of data (few-shot 3D shape recognition). We analyze that both tasks are relevant and can be considered simultaneously. Specifically, leveraging the descriptor which is effective for zero-shot inference to guide the tuning of the aggregated descriptor under the few-shot training can significantly improve the few-shot learning efficacy. Hence, we propose Prompt-Enhanced View Aggregation Network (PEVA-Net) to simultaneously address zero/few-shot 3D shape recognition. Under the zero-shot scenario, we propose to leverage the prompts built up from candidate categories to enhance the aggregation process of multiple view-associated visual features. The resulting aggregated feature serves for effective zero-shot recognition of the 3D shapes. Under the few-shot scenario, we first exploit a transformer encoder to aggregate the view-associated visual features into a global descriptor. To tune the encoder, together with the main classification loss, we propose a self-distillation scheme via a feature distillation loss by treating the zero-shot descriptor as the guidance signal for the few-shot descriptor. This scheme can significantly enhance the few-shot learning efficacy.

cs.CV↗

arXiv2024

Addressing complex boundary conditions of miscible flow and transport in two and three dimensions with application to optimal control

We investigate complex boundary conditions of the miscible displacement system in two and three space dimensions with the commonly-used Bear-Scheidegger diffusion-dispersion tensor, which describes, e.g., the porous medium flow processes in petroleum reservoir simulation or groundwater contaminant transport. Specifically, we incorporate the no-flux boundary condition for the Darcy velocity to prove that the general no-flux boundary condition for the transport equation is equivalent to the normal derivative boundary condition of the concentration, based on which we further prove several complex boundary conditions by the Bear-Scheidegger tensor and its derivative. The derived boundary conditions not only provide new insights and distinct properties of the Bear-Scheidegger diffusion-dispersion tensor, but accommodate the coupling and the nonlinearity of the miscible displacement system and the Bear-Scheidegger tensor in deriving the first-order optimality condition of the corresponding optimal control problem for practical application.

math.OC↗

arXiv2024

Fast Safe Rectangular Corridor-based Online AGV Trajectory Optimization with Obstacle Avoidance

Automated Guided Vehicles (AGVs) are essential in various industries for their efficiency and adaptability. However, planning trajectories for AGVs in obstacle-dense, unstructured environments presents significant challenges due to the nonholonomic kinematics, abundant obstacles, and the scenario's nonconvex and constrained nature. To address this, we propose an efficient trajectory planning framework for AGVs by formulating the problem as an optimal control problem. Our framework utilizes the fast safe rectangular corridor (FSRC) algorithm to construct rectangular convex corridors, representing avoidance constraints as box constraints. This eliminates redundant obstacle influences and accelerates the solution speed. Additionally, we employ the Modified Visibility Graph algorithm to speed up path planning and a boundary discretization strategy to expedite FSRC construction. Experimental results demonstrate the effectiveness and superiority of our framework, particularly in computational efficiency. Compared to advanced frameworks, our framework achieves computational efficiency gains of 1 to 2 orders of magnitude. Notably, FSRC significantly outperforms other safe convex corridor-based methods regarding computational efficiency.

cs.RO↗