Simultaneous Localization and Mapping (SLAM) is one of the most important environment-perception and navigation algorithms for computer vision, robotics, and autonomous cars/drones. Hence, high quality and fast mapping becomes a fundamental problem. With the advent of 3D Gaussian Splatting (3DGS) as an explicit representation with excellent rendering quality and speed, state-of-the-art (SOTA) works introduce GS to SLAM. Compared to classical pointcloud-SLAM, GS-SLAM generates photometric information by learning from input camera views and synthesizing unseen views with high-quality textures. However, these GS-SLAM fail when moving objects occupy the scene that violates the static assumption of bundle adjustment. The failed updates of moving GS affects the static GS and contaminates the full map over the video sequence. Although some efforts have been made by concurrent works to consider moving objects for GS-SLAM, they simply detect and remove the moving regions from GS rendering ("anti" dynamic GS-SLAM), where only the static background could benefit from GS. To this end, we propose the first real-time GS-SLAM, "DynaGSLAM", that achieves high-quality online GS rendering, tracking, motion predictions of moving objects in dynamic scenes while jointly estimating accurate ego motion. Our DynaGSLAM outperforms SOTA static & "Anti" dynamic GS-SLAM on three dynamic real datasets, while keeping speed and memory efficiency in practice. https://blarklee.github.io/dynagslam/

Dense reconstruction and differentiable rendering are fundamental tightly connected operations in 3D vision and computer graphics. Recent neural implicit representations demonstrate compelling advantages in reconstruction fidelity and differentiability over conventional discrete representations such as meshes, point clouds, and voxels. However, many neural implicit models, such as neural radiance fields (NeRF) and signed distance function (SDF) networks, are inefficient in rendering due to the need to perform multiple queries along each camera ray. Moreover, NeRF and Gaussian Splatting methods offer impressive photometric reconstruction but often require careful supervision to achieve accurate geometric reconstruction. To address these challenges, we propose a novel representation called signed directional distance function (SDDF). Unlike SDF and similar to NeRF, SDDF has a position and viewing direction as input. Like SDF and unlike NeRF, SDDF directly provides distance to the observed surface rather than integrating along the view ray. As a result, SDDF achieves accurate geometric reconstruction and efficient differentiable directional distance prediction. To learn and predict scene-level SDDF efficiently, we develop a differentiable hybrid representation that combines explicit ellipsoid priors and implicit neural residuals. This allows the model to handle distance discontinuities around obstacle boundaries effectively while preserving the ability for dense high-fidelity distance prediction. Through extensive evaluation against state-of-the-art representations, we show that SDDF achieves (i) competitive SDDF prediction accuracy, (ii) faster prediction speed than SDF and NeRF, and (iii) superior geometric consistency compared to NeRF and Gaussian Splatting.

Planning and control for high-dimensional robot manipulators in cluttered dynamic environments require computational efficiency and robust safety guarantees. Inspired by recent advances in learning configuration-space distance functions (CDFs) as representations of robot bodies, we propose a unified approach for motion planning and control that formulates safety constraints as CDF barriers. A CDF barrier approximates the local free configuration space, substantially reducing the number of collision-checking operations during motion planning. However, learning a CDF barrier with a neural network and relying on online sensor observations introduces uncertainties that must be considered during control synthesis. To address this, we develop a distributionally robust CDF barrier formulation for control that accounts for modeling errors and sensor noise without assuming a known underlying distribution. Simulations and hardware experiments on a UFactory xArm6 manipulator show that our neural CDF barrier formulation enables efficient planning and robust safe control in cluttered and dynamic environments, relying only on onboard point-cloud observations.

The problem of planning sensing trajectories for a mobile robot to collect observations of a target and predict its future trajectory is known as active target tracking. Enabled by probabilistic motion models, one may solve this problem by exploring the belief space of all trajectory predictions given future sensing actions to maximise information gain. However, for multi-modal motion models the notion of information gain is often ill-defined. This paper proposes a planning approach designed around maximising information regarding the target's homotopy class, or high-level motion. We introduce homotopic information gain, a measure of the expected high-level trajectory information given by a measurement. We show that homotopic information gain is a lower bound for metric or low-level information gain, and is as sparsely distributed in the environment as obstacles are. Planning sensing trajectories to maximise homotopic information results in highly accurate trajectory estimates with fewer measurements than a metric information approach, as supported by our empirical evaluation on real and simulated pedestrian data.

Robotic manipulator applications often require efficient online motion planning. When completing multiple tasks, sequence order and choice of goal configuration can have a drastic impact on planning performance. This is well known as the robot task sequencing problem (RTSP). Existing general-purpose RTSP algorithms are susceptible to producing poor-quality solutions or failing entirely when available computation time is restricted. We propose a new multiquery task sequencing method designed to operate in semistructured environments with a combination of static and nonstatic obstacles. Our method intentionally trades off workspace generality for planning efficiency. Given a user-defined task space with static obstacles, we compute a subspace decomposition. The key idea is to establish approximate isometries known as$\epsilon$-Gromov-Hausdorff approximations that identify points that are close to one another in both task and configuration space. Importantly, we prove bounded suboptimality guarantees on the lengths of paths within these subspaces. These bounding relations further imply that paths within the same subspace can be smoothly concatenated, which we show is useful for determining efficient task sequences. We evaluate our method with several kinematic configurations in a complex simulated environment, achieving up to 3× faster motion planning and 5× lower maximum trajectory jerk compared to baselines.

We consider the coordinated escort problem, where a decentralised team of supporting robots implicitly assist the mission of higher-value principal robots. The defining challenge is how to evaluate the effect of supporting robots' actions on the principal robots' mission. To capture this effect, we define two novel auxiliary reward functions for supporting robots called satisfaction improvement and satisfaction entropy, which computes the improvement in probability of mission success, or the uncertainty thereof. Given these reward functions, we coordinate the entire team of principal and supporting robots using decentralised cross entropy method (Dec-CEM), a new extension of CEM to multi-agent systems based on the product distribution approximation. In a simulated object avoidance scenario, our planning framework demonstrates up to two-fold improvement in task satisfaction against conventional decoupled information gathering. The significance of our results is to introduce a new family of algorithmic problems that will enable important new practical applications of heterogeneous multi-robot systems.

Trajectory prediction in a cluttered environment is key to many important robotics tasks such as autonomous navigation. However, there are an infinite number of possible trajectories to consider. To simplify the space of trajectories under consideration, we utilise homotopy classes to partition the space into countably many mathematically equivalent classes. All members within a class demonstrate identical high-level motion with respect to the environment, i.e., travelling above or below an obstacle. This allows high-level prediction of a trajectory in terms of a sparse label identifying its homotopy class. We therefore present a light-weight learning framework based on variable-order Markov processes to learn and predict homotopy classes and thus high-level agent motion. By informing a Gaussian mixture model (GMM) with our homotopy class predictions, we see great improvements in low-level trajectory prediction compared to a naive GMM on a real dataset.

Whereas dedicated scene representations are required for each different task in conventional robotic systems, this article demonstrates that a unified representation can be used directly for multiple key tasks. We propose the log-Gaussian process implicit surface for mapping, odometry, and planning (Log-GPIS-MOP): a probabilistic framework for surface reconstruction, localization, and navigation based on a unified representation. Our framework applies a logarithmic transformation to a Gaussian process implicit surface (GPIS) formulation to recover a global representation that accurately captures the Euclidean distance field with gradients and, at the same time, the implicit surface. By directly estimating the distance field and its gradient through Log-GPIS inference, the proposed incremental odometry technique computes the optimal alignment of an incoming frame and fuses it globally to produce a map. Concurrently, an optimization-based planner computes a safe collision-free path using the same Log-GPIS surface representation. We validate the proposed framework on simulated and real datasets in 2-D and 3-D, and benchmark against the state-of-the-art approaches. Our experiments show that Log-GPIS-MOP produces competitive results in sequential odometry, surface mapping, and obstacle avoidance.

We present a planning framework for min-imising the deterministic worst-case error in sparse Gaus-sian process (GP) regression. We first derive a univer-sal worst-case error bound for sparse GP regression with bounded noise using interpolation theory on reproducing kernel Hilbert spaces (RKHSs). By exploiting the conditional inde-pendence (CI) assumption central to sparse GP regression, we show that the worst-case error minimisation can be achieved by solving a posterior entropy minimisation problem. In turn, the posterior entropy minimisation problem is solved using a Gaussian belief space planning algorithm. We corroborate the proposed worst-case error bound in a simple 1D example, and test the planning framework in simulation for a 2D vehicle in a complex flow field. Our results demonstrate that the proposed posterior entropy minimisation approach is effective in minimising deterministic error, and outperforms the conventional measurement entropy maximisation formulation when the inducing points are fixed.

Heterogeneous multi-robot systems are advantageous for operations in unknown environments because functionally specialised robots can gather environmental information, while others perform tasks. We de ne this decomposition as the scout–task robot architecture and show how it avoids the need to explicitly balance exploration and exploitation by permitting the system to do both simultaneously. The challenge is to guide exploration in a way that improves overall performance for time-limited tasks. We derive a novel upper confidence bound for simultaneous exploration and exploitation based on mutual information and present a general solution for scout–task coordination using decentralised Monte Carlo tree search. We evaluate the performance of our algorithms in a multi-drone surveillance scenario in which scout robots are equipped with low-resolution, long-range sensors and task robots capture detailed information using short-range sensors. The results address a new class of coordination problem for heterogeneous teams that has many practical applications.

We present a method to estimate two-dimensional, time-invariant oceanic flow fields based on data from both ensemble forecasts and online measurements. Our method produces a realistic estimate in a computationally efficient manner suitable for use in marine robotics for path planning and related applications. We use kernel methods and singular value decomposition to find a compact model of the ensemble data that is represented as a linear combination of basis flow fields and that preserves the spatial correlations present in the data. Online measurements of ocean current, taken for example by marine robots, can then be incorporated using recursive Bayesian estimation. We provide computational analysis, performance comparisons with related methods, and demonstration with real-world ensemble data to show the computational efficiency and validity of our method. Possible applications in addition to path planning include active perception for model improvement through deliberate choice of measurement locations.

Gaussian processes (GPs) enable a probabilistic approach to important estimation and classification tasks that arise in robotics applications. Meanwhile, most GP-based methods are often prohibitively slow, thereby posing a substantial barrier to practical applications. Existing "sparse" methods to speed up GPs seek to either make the model more sparse, or find ways to more efficiently manage a large covariance matrix. In this paper, we present an orthogonal approach that memoises (i.e. reuses) previous computations in GP inference. We demonstrate that a substantial speedup can be achieved by incorporating memoisation into applications in which GPs must be updated frequently. Moreover, we derive a novel online update scheme for sparse GPs that can be used in conjunction with our memoisation approach for a synergistic improvement in performance. Across three robotic vision applications, we demonstrate between 40-100% speed-up over the standard method for inference in GP mixtures.

Underwater robots are subject to position drift due to the effect of ocean currents and the lack of accurate localisation while submerged. We are interested in exploiting such position drift to estimate the ocean current in the surrounding area, thereby assisting navigation and planning. We present a Gaussian process (GP)-based expectation-maximisation (EM) algorithm that estimates the underlying ocean current using sparse GPS data obtained on the surface and dead-reckoned position estimates. We first develop a specialised GP regression scheme that exploits the incompressibility of ocean currents to counteract the underdetermined nature of the problem. We then use the proposed regression scheme in an EM algorithm that estimates the best-fitting ocean current in between each GPS fix. The proposed algorithm is validated in simulation and on a real dataset, and is shown to be capable of reconstructing the underlying ocean current field. We expect to use this algorithm to close the loop between planning and estimation for underwater navigation in unknown ocean currents.

Motion planning for underwater vehicles must consider the effect of ocean currents. We present an efficient method to compute reachability and cost between sample points in sampling-based motion planning that supports long-range planning over hundreds of kilometres in complicated flows. The idea is to search a reduced space of control inputs that consists of stream functions whose level sets, or streamlines, optimally connect two given points. Such stream functions are generated by superimposing a control input onto the underlying current flow. A streamline represents the resulting path that a vehicle would follow as it is carried along by the current given that control input. We provide rigorous analysis that shows how our method avoids exhaustive search of the control space, and demonstrate simulated examples in complicated flows including a traversal along the east coast of Australia, using actual current predictions, between Sydney and Brisbane.