Serverless Large Language Models (LLMs) have emerged as a cost-effective solution for deploying AI services by enabling a 'pay-as-you-go' pricing model through GPU resource sharing. However, cold-start latency, especially the model loading phase, has become a critical performance bottleneck, as it scales linearly with model size and severely limits the practical deployment of large-scale LLM services. This paper presents Tangram, a novel system that accelerates Serverless LLM loading through efficient GPU memory reuse. By leveraging the unused GPU memory to retain model parameters, Tangram significantly reduces model transfer time and cold-start latency. Its design includes three key components: unified GPU memory pool for tensor-level parameter sharing across models, on-demand KV cache allocation for dynamic memory management, and GPU-affinity-aware scheduling for maximizing resource utilization. These techniques collectively address the critical challenges of inefficient memory usage and the cold-start problem in Serverless LLM platforms. We have implemented a fully functional prototype, and experiments show that Tangram achieves up to 6.2 times faster loading and reduces Time-To-First-Token (TTFT) during cold-start by 23--55% over state-of-the-art methods.

We present a simple and easy-to-implement algorithm to detect plan infeasibility in kinematic motion planning. Our method involves approximating the robot's configuration space to a discrete space, where each degree of freedom has a finite set of values. The obstacle region separates the free configuration space into different connected regions. For a path to exist between the start and goal configurations, they must lie in the same connected region of the free space. Thus, to ascertain plan infeasibility, we merely need to sample adequate points from the obstacle region that isolate start and goal. Accordingly, we progressively construct the configuration space by sampling from the discretized space and updating the bitmap cells representing obstacle regions. Subsequently, we partition this partially built configuration space to identify different connected components within it and assess the connectivity of the start and goal cells. We illustrate this methodology on five different scenarios with configuration spaces having up to 5 degree-of-freedom (DOF).

Mobile manipulators typically encounter significant challenges in navigating narrow, cluttered environments due to their high-dimensional state spaces and complex kinematics. While reactive methods excel in dynamic settings, they struggle to efficiently incorporate complex, coupled constraints across the entire state space. In this work, we present a novel local reactive controller that reformulates the time-domain single-step problem into a multi-step optimization problem in the spatial domain, leveraging the propagation of a serial kinematic chain. This transformation facilitates the formulation of customized, decoupled link-specific constraints, which is further solved efficiently with augmented Lagrangian differential dynamic programming (AL-DDP). Our approach naturally absorbs spatial kinematic propagation in the forward pass and processes all link-specific constraints simultaneously during the backward pass, enhancing both constraint management and computational efficiency. Notably, in this framework, we formulate collision avoidance constraints for each link using accurate geometric models with extracted free regions, and this improves the maneuverability of the mobile manipulator in narrow, cluttered spaces. Experimental results showcase significant improvements in safety, efficiency, and task completion rates. These findings underscore the robustness of the proposed method, particularly in narrow, cluttered environments where conventional approaches could falter. The open-source project can be found at https://github.com/Chunx1nZHENG/MM-with-Whole-Body-Safety-Release.git.

In this work, we present FRTree planner, a novel robot navigation framework that leverages a tree structure of free regions, specifically designed for navigation in cluttered and unknown environments with narrow passages. The framework continuously incorporates real-time perceptive information to identify distinct navigation options and dynamically expands the tree toward explorable and traversable directions. This dynamically constructed tree incrementally encodes the geometric and topological information of the collision-free space, enabling efficient selection of the intermediate goals, navigating around dead-end situations, and avoidance of dynamic obstacles without a prior map. Crucially, our method performs a comprehensive analysis of the geometric relationship between free regions and the robot during online replanning. In particular, the planner assesses the accessibility of candidate passages based on the robot's geometries, facilitating the effective selection of the most viable intermediate goals through accessible narrow passages while minimizing unnecessary detours. By combining the free region information with a bi-level trajectory optimization tailored for robots with specific geometries, our approach generates robust and adaptable obstacle avoidance strategies in confined spaces. Through extensive simulations and real-world experiments, FRTree demonstrates its superiority over benchmark methods in generating safe, efficient motion plans through highly cluttered and unknown terrains with narrow gaps.

In this work, we propose a trajectory optimization approach for robot navigation in cluttered 3D environments. We represent the robot's geometry as a semialgebraic set defined by polynomial inequalities such that robots with general shapes can be suitably characterized. To address the robot navigation task in obstacle-dense environments, we exploit the free space directly to construct a sequence of free regions, and allocate each waypoint on the trajectory to a specific region. Then, we incorporate a uniform scaling factor for each free region, and formulate a Sums-of-Squares (SOS) optimization problem that renders the containment relationship between the robot and the free space computationally tractable. The SOS optimization problem is further reformulated to a semidefinite program (SDP), and the collision-free constraints are shown to be equivalent to limiting the scaling factor along the entire trajectory. In this context, the robot at a specific configuration is tailored to stay within the free region. Next, to solve the trajectory optimization problem with the proposed safety constraints (which are implicitly dependent on the robot configurations), we derive the analytical solution to the gradient of the minimum scaling factor with respect to the robot configuration. As a result, this seamlessly facilitates the use of gradient-based methods in efficient solving of the trajectory optimization problem. Through a series of simulations and real-world experiments, the proposed trajectory optimization approach is validated in various challenging scenarios, and the results demonstrate its effectiveness in generating collision-free trajectories in dense and intricate environments populated with obstacles.

This paper presents a novel reactive motion planning framework for navigating robots in unknown and cluttered 2D workspace. Typical existing methods are developed by enforcing the robot staying in free regions represented by the locally extracted ellipse or polygon. Instead, we navigate the robot in free space with an alternate starshaped decomposition, which is calculated directly from real-time sensor data. Additionally, a roadmap is constructed incrementally to maintain the connectivity information of the starshaped regions. Compared to the roadmap built upon connected polygons or ellipses in the conventional approaches, the concave starshaped region is better suited to capture the natural distribution of sensor data, so that the perception information can be fully exploited for robot navigation. In this sense, conservative and myopic behaviors are avoided with the proposed approach, and intricate obstacle configurations can be suitably accommodated in unknown and cluttered environments. Then, we design a heuristic exploration algorithm on the roadmap to determine the frontier points of the starshaped regions, from which short-term goals are selected to attract the robot towards the goal configuration. It is noteworthy that, a recovery mechanism is developed on the roadmap that is triggered once a non-extendable short-term goal is reached. This mechanism renders it possible to deal with dead-end situations that can be typically encountered in unknown and cluttered environments. Furthermore, safe and smooth motion within the starshaped regions is generated by employing the Dynamical System Modulation (DSM) approach on the constructed roadmap. Through comprehensive evaluation in both simulations and real-world experiments, the proposed method outperforms the benchmark methods in terms of success rate and traveling time.

Energy consumption of memory accesses dominates the compute energy in energy-constrained robots which require a compact 3D map of the environment to achieve autonomy. Recent mapping frameworks only focused on reducing the map size while incurring significant memory usage during map construction due to multi-pass processing of each depth image. In this work, we present a memory-efficient continuous occupancy map, named GMMap, that accurately models the 3D environment using a Gaussian Mixture Model (GMM). Memory-efficient GMMap construction is enabled by the single-pass compression of depth images into local GMMs which are directly fused together into a globally-consistent map. By extending Gaussian Mixture Regression to model unexplored regions, occupancy probability is directly computed from Gaussians. Using a low-power ARM Cortex A57 CPU, GMMap can be constructed in real-time at up to 60 images per second. Compared with prior works, GMMap maintains high accuracy while reducing the map size by at least 56%, memory overhead by at least 88%, DRAM access by at least 78%, and energy consumption by at least 69%. Thus, GMMap enables real-time 3D mapping on energy-constrained robots.

This work proposes a safety-critical local reactive controller that enables the robot to navigate in unknown and cluttered environments. In particular, the trajectory tracking task is formulated as a constrained polynomial optimization problem. Then, safety constraints are imposed on the control variables invoking the notion of polynomial positivity certificates in conjunction with their Sum-of-Squares (SOS) approximation, thereby confining the robot motion inside the locally extracted convex free region. It is noteworthy that, in the process of devising the proposed safety constraints, the geometry of the robot can be approximated using any shape that can be characterized with a set of polynomial functions. The optimization problem is further convexified into a semidefinite program (SDP) leveraging truncated multi-sequences (tms) and moment relaxation, which favorably facilitates the effective use of off-the-shelf conic programming solvers, such that real-time performance is attainable. Various robot navigation tasks are investigated to demonstrate the effectiveness of the proposed approach in terms of safety and tracking performance.