The robustness of driving perception systems under unprecedented conditions is crucial for safety-critical usages. Latest advancements have prompted increasing interests towards multi-LiDAR perception. However, prevailing driving datasets predominantly utilize single-LiDAR systems and collect data devoid of adverse conditions, failing to capture the complexities of real-world environments accurately. Addressing these gaps, we proposed Place3D, a full-cycle pipeline that encompasses LiDAR placement optimization, data generation, and downstream evaluations. Our framework makes three appealing contributions. 1) To identify the most effective configurations for multi-LiDAR systems, we introduce a Surrogate Metric of the Semantic Occupancy Grids (M-SOG) to evaluate LiDAR placement quality. 2) Leveraging the M-SOG metric, we propose a novel optimization strategy to refine multi-LiDAR placements. 3) Centered around the theme of multi-condition multi-LiDAR perception, we collect a 364,000-frame dataset from both clean and adverse conditions. Extensive experiments demonstrate that LiDAR placements optimized using our approach outperform various baselines. We showcase exceptional robustness in both 3D object detection and LiDAR semantic segmentation tasks, under diverse adverse weather and sensor failure conditions. Code and benchmark toolkit are publicly available.

Role mining is a technique used to derive a role-based authorization policy from an existing policy. Given a set of users $U$, a set of permissions $P$ and a user-permission authorization relation $\mahtit{UPA}\subseteq U\times P$, a role mining algorithm seeks to compute a set of roles $R$, a user-role authorization relation $\mathit{UA}\subseteq U\times R$ and a permission-role authorization relation $\mathit{PA}\subseteq R\times P$, such that the composition of $\mathit{UA}$ and $\mathit{PA}$ is close (in some appropriate sense) to $\mathit{UPA}$. In this paper, we first introduce the Generalized Noise Role Mining problem (GNRM) -- a generalization of the MinNoise Role Mining problem -- which we believe has considerable practical relevance. Extending work of Fomin et al., we show that GNRM is fixed parameter tractable, with parameter $r + k$, where $r$ is the number of roles in the solution and $k$ is the number of discrepancies between $\mathit{UPA}$ and the relation defined by the composition of $\mathit{UA}$ and $\mathit{PA}$. We further introduce a bi-objective optimization variant of GNRM, where we wish to minimize both $r$ and $k$ subject to upper bounds $r\le \bar{r}$ and $k\le \bar{k}$, where $\bar{r}$ and $\bar{k}$ are constants. We show that the Pareto front of this bi-objective optimization problem (BO-GNRM) can be computed in fixed-parameter tractable time with parameter $\bar{r}+\bar{k}$. We then report the results of our experimental work using the integer programming solver Gurobi to solve instances of BO-GNRM. Our key findings are that (a) we obtained strong support that Gurobi's performance is fixed-parameter tractable, (b) our results suggest that our techniques may be useful for role mining in practice, based on our experiments in the context of three well-known real-world authorization policies.

Optimal estimation is a promising tool for multi-contact inertial estimation and localization. To harness its advantages in robotics, it is crucial to solve these large and challenging optimization problems efficiently. To tackle this, we (i) develop a multiple-shooting solver that exploits both temporal and parametric structures through a parametrized Riccati recursion. Additionally, we (ii) propose an inertial local manifold that ensures its full physical consistency. It also enhances convergence compared to the singularity-free log-Cholesky approach. To handle its singularities, we (iii) introduce a nullspace approach in our optimal estimation solver. We (iv) finally develop the analytical derivatives of contact dynamics for both inertial parametrizations. Our framework can successfully solve estimation problems for complex maneuvers such as brachiation in humanoids. We demonstrate its numerical capabilities across various robotics tasks and its benefits in experimental trials with the Go1 robot.

Trajectory generation for quadrotors with limited field-of-view sensors has numerous applications such as aerial exploration, coverage, inspection, videography, and target tracking. Most previous works simplify the task of optimizing yaw trajectories by either aligning the heading of the robot with its velocity, or potentially restricting the feasible space of candidate trajectories by using a limited yaw domain to circumvent angular singularities. In this paper, we propose a novel \textit{global} yaw parameterization method for trajectory optimization that allows a 360-degree yaw variation as demanded by the underlying algorithm. This approach effectively bypasses inherent singularities by including supplementary quadratic constraints and transforming the final decision variables into the desired state representation. This method significantly reduces the needed control effort, and improves optimization feasibility. Furthermore, we apply the method to several examples of different applications that require jointly optimizing over both the yaw and position trajectories. Ultimately, we present a comprehensive numerical analysis and evaluation of our proposed method in both simulation and real-world experiments.

Distributed learning is commonly used for accelerating model training by harnessing the computational capabilities of multiple-edge devices. However, in practical applications, the communication delay emerges as a bottleneck due to the substantial information exchange required between workers and a central parameter server. SignSGD with majority voting (signSGD-MV) is an effective distributed learning algorithm that can significantly reduce communication costs by one-bit quantization. However, due to heterogeneous computational capabilities, it fails to converge when the mini-batch sizes differ among workers. To overcome this, we propose a novel signSGD optimizer with \textit{federated voting} (signSGD-FV). The idea of federated voting is to exploit learnable weights to perform weighted majority voting. The server learns the weights assigned to the edge devices in an online fashion based on their computational capabilities. Subsequently, these weights are employed to decode the signs of the aggregated local gradients in such a way to minimize the sign decoding error probability. We provide a unified convergence rate analysis framework applicable to scenarios where the estimated weights are known to the parameter server either perfectly or imperfectly. We demonstrate that the proposed signSGD-FV algorithm has a theoretical convergence guarantee even when edge devices use heterogeneous mini-batch sizes. Experimental results show that signSGD-FV outperforms signSGD-MV, exhibiting a faster convergence rate, especially in heterogeneous mini-batch sizes.

In this paper, we present a novel problem coined multi-robot, multi-objective, and multi-mode routing and scheduling (M^3RS). The formulation for M^3RS is introduced for time-bound multi-robot, multi-objective routing and scheduling missions where each task has multiple execution modes. Different execution modes have distinct resource consumption, associated execution time, and quality. M^3RS assigns the optimal sequence of tasks and the execution modes to each agent. The routes and associated modes depend on user preferences for different objective criteria. The need for M^3RS comes from multi-robot applications in which a trade-off between multiple criteria arises from different task execution modes. We use M^3RS for the application of multi-robot disinfection in public locations. The objectives considered for disinfection application are disinfection quality and number of tasks completed. A mixed-integer linear programming model is proposed for M^3RS. Then, a time-efficient column generation scheme is presented to tackle the issue of computation times for larger problem instances. The advantage of using multiple modes over fixed execution mode is demonstrated using experiments on synthetic data. The results suggest that M^3RS provides flexibility to the user in terms of available solutions and performs well in joint performance metrics. The application of the proposed problem is shown for a team of disinfection robots.} The videos for the experiments are available on the project website: https://sites.google.com/view/g-robot/m3rs/ .

Recently neural radiance fields (NeRF) have been widely exploited as 3D representations for dense simultaneous localization and mapping (SLAM). Despite their notable successes in surface modeling and novel view synthesis, existing NeRF-based methods are hindered by their computationally intensive and time-consuming volume rendering pipeline. This paper presents an efficient dense RGB-D SLAM system, i.e., CG-SLAM, based on a novel uncertainty-aware 3D Gaussian field with high consistency and geometric stability. Through an in-depth analysis of Gaussian Splatting, we propose several techniques to construct a consistent and stable 3D Gaussian field suitable for tracking and mapping. Additionally, a novel depth uncertainty model is proposed to ensure the selection of valuable Gaussian primitives during optimization, thereby improving tracking efficiency and accuracy. Experiments on various datasets demonstrate that CG-SLAM achieves superior tracking and mapping performance with a notable tracking speed of up to 15 Hz. We will make our source code publicly available.

Multi-task learning solves multiple correlated tasks. However, conflicts may exist between them. In such circumstances, a single solution can rarely optimize all the tasks, leading to performance trade-offs. To arrive at a set of optimized yet well-distributed models that collectively embody different trade-offs in one algorithmic pass, this paper proposes to view Pareto multi-task learning through the lens of multi-task optimization. Multi-task learning is first cast as a multi-objective optimization problem, which is then decomposed into a diverse set of unconstrained scalar-valued subproblems. These subproblems are solved jointly using a novel multi-task gradient descent method, whose uniqueness lies in the iterative transfer of model parameters among the subproblems during the course of optimization. A theorem proving faster convergence through the inclusion of such transfers is presented. We investigate the proposed multi-task learning with multi-task optimization for solving various problem settings including image classification, scene understanding, and multi-target regression. Comprehensive experiments confirm that the proposed method significantly advances the state-of-the-art in discovering sets of Pareto-optimized models. Notably, on the large image dataset we tested on, namely NYUv2, the hypervolume convergence achieved by our method was found to be nearly two times faster than the next-best among the state-of-the-art.

We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The resulting class of objective functions encapsulates the classes of objective functions traditionally studied in optimization, which are defined based on either Lipschitz continuity of the objective or H\"{o}lder/Lipschitz continuity of its gradient. Further, the defined class contains functions that are neither Lipschitz continuous nor have a H\"{o}lder continuous gradient. When restricted to the traditional classes of optimization problems, the parameters defining the studied classes lead to more fine-grained complexity bounds, recovering traditional oracle complexity bounds in the worst case but generally leading to lower oracle complexity for functions that are not ``worst case.'' Some highlights of our results are that: (i) it is possible to obtain complexity results for both convex and nonconvex problems with the (local or global) Lipschitz constant being replaced by a constant of local subgradient variation and (ii) mean width of the subdifferential set around the optima plays a role in the complexity of nonsmooth optimization, particularly in parallel settings. A consequence of (ii) is that for any error parameter $\epsilon > 0$, parallel oracle complexity of nonsmooth Lipschitz convex optimization is lower than its sequential oracle complexity by a factor $\tilde{\Omega}\big(\frac{1}{\epsilon}\big)$ whenever the objective function is piecewise linear with polynomially many pieces in the input size. This is particularly surprising as existing parallel complexity lower bounds are based on such classes of functions. The seeming contradiction is resolved by considering the region in which the algorithm is allowed to query the objective.

Reinforcement learning (RL) has revolutionized decision-making across a wide range of domains over the past few decades. Yet, deploying RL policies in real-world scenarios presents the crucial challenge of ensuring safety. Traditional safe RL approaches have predominantly focused on incorporating predefined safety constraints into the policy learning process. However, this reliance on predefined safety constraints poses limitations in dynamic and unpredictable real-world settings where such constraints may not be available or sufficiently adaptable. Bridging this gap, we propose a novel approach that concurrently learns a safe RL control policy and identifies the unknown safety constraint parameters of a given environment. Initializing with a parametric signal temporal logic (pSTL) safety specification and a small initial labeled dataset, we frame the problem as a bilevel optimization task, intricately integrating constrained policy optimization, using a Lagrangian-variant of the twin delayed deep deterministic policy gradient (TD3) algorithm, with Bayesian optimization for optimizing parameters for the given pSTL safety specification. Through experimentation in comprehensive case studies, we validate the efficacy of this approach across varying forms of environmental constraints, consistently yielding safe RL policies with high returns. Furthermore, our findings indicate successful learning of STL safety constraint parameters, exhibiting a high degree of conformity with true environmental safety constraints. The performance of our model closely mirrors that of an ideal scenario that possesses complete prior knowledge of safety constraints, demonstrating its proficiency in accurately identifying environmental safety constraints and learning safe policies that adhere to those constraints.