arXiv subjects

Tobias Löw

Publications and source records attributed to Tobias Löw.

13 recordsLinked to original sources

arXiv2026

G-MAPP: GPU-accelerated Multi-Agent Planning and Perception for Reactive Motion Generation

Reactive motion generation in unstructured environments remains an open challenge in robotics. Due to the computational complexity of collision-free motion generation, existing methods either generate global trajectories for static scenarios, or employ models that make conservative assumptions about the environment. This paper identifies the primary bottleneck as the runtime performance demand of planning on high-fidelity environments, and the temporal integration between the perception and planning modules. Therefore, we propose a framework that does not compromise on runtime performance and world representations for perception and planning by accelerating world modeling and vector-field based planning using the GPU. This allows us to achieve faster parallel state exploration for quasi-global trajectory planning, and tighter coupling of the perception-action loop in real-time for dynamic cluttered environments with off-the-shelf depth sensors. We quantitatively evaluate the computation-time and success rate differences for the CPU and GPU versions of our planner, and perform qualitative evaluations of our coupled framework using real-world experiments on a 7-DoF Franka Emika robot. Experimental results demonstrate that our GPU-based framework achieves up to a 5x speedup over the CPU version and successfully avoids collisions across both trivial and challenging physical world scenarios.

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arXiv2026

Curve-Induced Dynamical Systems on Riemannian Manifolds and Lie Groups

Deploying robots in household environments requires safe, adaptable, and interpretable behaviors that respect the geometric structure of tasks. Often represented on Lie groups and Riemannian manifolds, this includes poses on SE(3) or symmetric positive definite matrices encoding stiffness or damping matrices. In this context, dynamical system-based approaches offer a natural framework for generating such behavior, providing stability and convergence while remaining responsive to changes in the environment. We introduce Curve-induced Dynamical systems on Smooth Manifolds (CDSM), a real-time framework for constructing dynamical systems directly on Riemannian manifolds and Lie groups. The proposed approach constructs a nominal curve on the manifold, and generates a dynamical system which combines a tangential component that drives motion along the curve and a normal component that attracts the state toward the curve. We provide a stability analysis of the resulting dynamical system and validate the method quantitatively. On an S2 benchmark, CDSM demonstrates improved trajectory accuracy, reduced path deviation, and faster generation and query times compared to state-of-the-art methods. Finally, we demonstrate the practical applicability of the framework on both a robotic manipulator, where poses on SE(3) and damping matrices on SPD(n) are adapted online, and a mobile manipulator.

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arXiv2025

Cooperative Task Spaces for Multi-Arm Manipulation Control based on Similarity Transformations

Many tasks in human environments require collaborative behavior between multiple kinematic chains, either to provide additional support for carrying big and bulky objects or to enable the dexterity that is required for in-hand manipulation. Since these complex systems often have a very high number of degrees of freedom coordinating their movements is notoriously difficult to model. In this article, we present the derivation of the theoretical foundations for cooperative task spaces of multi-arm robotic systems based on geometric primitives defined using conformal geometric algebra. Based on the similarity transformations of these cooperative geometric primitives, we derive an abstraction of complex robotic systems that enables representing these systems in a way that directly corresponds to single-arm systems. By deriving the associated analytic and geometric Jacobian matrices, we then show the straightforward integration of our approach into classical control techniques rooted in operational space control. We demonstrate this using bimanual manipulators, humanoids and multi-fingered hands in optimal control experiments for reaching desired geometric primitives and in teleoperation experiments using differential kinematics control. We then discuss how the geometric primitives naturally embed nullspace structures into the controllers that can be exploited for introducing secondary control objectives. This work, represents the theoretical foundations of this cooperative manipulation control framework, and thus the experiments are presented in an abstract way, while giving pointers towards potential future applications.

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arXiv2025

Object-centric Task Representation and Transfer using Diffused Orientation Fields

Curved objects pose a fundamental challenge for skill transfer in robotics: unlike planar surfaces, they do not admit a global reference frame. As a result, task-relevant directions such as "toward" or "along" the surface vary with position and geometry, making object-centric tasks difficult to transfer across shapes. To address this, we introduce an approach using Diffused Orientation Fields (DOF), a smooth representation of local reference frames, for transfer learning of tasks across curved objects. By expressing manipulation tasks in these smoothly varying local frames, we reduce the problem of transferring tasks across curved objects to establishing sparse keypoint correspondences. DOF is computed online from raw point cloud data using diffusion processes governed by partial differential equations, conditioned on keypoints. We evaluate DOF under geometric, topological, and localization perturbations, and demonstrate successful transfer of tasks requiring continuous physical interaction such as inspection, slicing, and peeling across varied objects. We provide our open-source codes at our website https://github.com/idiap/diffused_fields_robotics

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arXiv2025

Efficient and Real-Time Motion Planning for Robotics Using Projection-Based Optimization

Generating motions for robots interacting with objects of various shapes is a complex challenge, further complicated by the robot 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

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arXiv2025

Tactile Ergodic Coverage on Curved Surfaces

In this article, we present a feedback control method for tactile coverage tasks, such as cleaning or surface inspection. These tasks are challenging to plan due to complex continuous physical interactions. In these tasks, the coverage target and progress can be easily measured using a camera and encoded in a point cloud. We propose an ergodic coverage method that operates directly on point clouds, guiding the robot to spend more time on regions requiring more coverage. For robot control and contact behavior, we use geometric algebra to formulate a task-space impedance controller that tracks a line while simultaneously exerting a desired force along that line. We evaluate the performance of our method in kinematic simulations and demonstrate its applicability in real-world experiments on kitchenware. Our source codes, experimental data, and videos are available as open access at https://sites.google.com/view/tactile-ergodic-control/

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arXiv2024

Diffusion-based Virtual Fixtures

Virtual fixtures assist human operators in teleoperation settings by constraining their actions. This extended abstract introduces a novel virtual fixture formulation \emph{on surfaces} for tactile robotics tasks. Unlike existing methods, our approach constrains the behavior based on the position on the surface and generalizes it over the surface by considering the distance (metric) on the surface. Our method works directly on possibly noisy and partial point clouds collected via a camera. Given a set of regions on the surface together with their desired behaviors, our method diffuses the behaviors across the entire surface by taking into account the surface geometry. We demonstrate our method's ability in two simulated experiments (i) to regulate contact force magnitude or tangential speed based on surface position and (ii) to guide the robot to targets while avoiding restricted regions defined on the surface. All source codes, experimental data, and videos are available as open access at https://sites.google.com/view/diffusion-virtual-fixtures

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arXiv2023

Whole-Body Ergodic Exploration with a Manipulator Using Diffusion

This paper presents a whole-body robot control method for exploring and probing a given region of interest. The ergodic control formalism behind such an exploration behavior consists of matching the time-averaged statistics of a robot trajectory with the spatial statistics of the target distribution. Most existing ergodic control approaches assume the robots/sensors as individual point agents moving in space. We introduce an approach that decomposes the whole-body of a robotic manipulator into multiple kinematically constrained agents. Then, we generate control actions by calculating a consensus among the agents. To do so, we use an ergodic control formulation called heat equation-driven area coverage (HEDAC) and slow the diffusion using the non-stationary heat equation. Our approach extends HEDAC to applications where robots have multiple sensors on the whole-body (such as tactile skin) and use all sensors to optimally explore the given region. We show that our approach increases the exploration performance in terms of ergodicity and scales well to real-world problems. We compare our method in kinematic simulations with the state-of-the-art and demonstrate the applicability of an online exploration task with a 7-axis Franka Emika robot. Additional material available at https://sites.google.com/view/w-ee-d/

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arXiv2023

gafro: Geometric Algebra for Robotics

Geometry is a fundamental part of robotics and there have been various frameworks of representation over the years. Recently, geometric algebra has gained attention for its property of unifying many of those previous ideas into one algebra. While there are already efficient open-source implementations of geometric algebra available, none of them is targeted at robotics applications. We want to address this shortcoming with our library gafro. This article presents an overview of the implementation details as well as a tutorial of gafro, an efficient c++ library targeting robotics applications using geometric algebra. The library focuses on using conformal geometric algebra. Hence, various geometric primitives are available for computation as well as rigid body transformations. The modeling of robotic systems is also an important aspect of the library. It implements various algorithms for calculating the kinematics and dynamics of such systems as well as objectives for optimisation problems. The software stack is completed by python bindings in pygafro and a ROS interface in gafro_ros.

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arXiv2023

Extending the Cooperative Dual-Task Space in Conformal Geometric Algebra

In this work, we are presenting an extension of the cooperative dual-task space (CDTS) in conformal geometric algebra. The CDTS was first defined using dual quaternion algebra and is a well established framework for the simplified definition of tasks using two manipulators. By integrating conformal geometric algebra, we aim to further enhance the geometric expressiveness and thus simplify the modeling of various tasks. We show this formulation by first presenting the CDTS and then its extension that is based around a cooperative pointpair. This extension keeps all the benefits of the original formulation that is based on dual quaternions, but adds more tools for geometric modeling of the dual-arm tasks. We also present how this CGA-CDTS can be seamlessly integrated with an optimal control framework in geometric algebra that was derived in previous work. In the experiments, we demonstrate how to model different objectives and constraints using the CGA-CDTS. Using a setup of two Franka Emika robots we then show the effectiveness of our approach using model predictive control in real world experiments.

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arXiv2023

Geometric Projectors: Geometric Constraints based Optimization for Robot Behaviors

Generating motion for robots that interact with objects of various shapes is a complex challenge, further complicated when the robot's own geometry and multiple desired behaviors are considered. To address this issue, we introduce a new framework based on Geometric Projectors (GeoPro) for constrained optimization. This novel framework allows for the generation of task-agnostic behaviors that are compliant with geometric constraints. GeoPro streamlines the design of behaviors in both task and configuration spaces, offering diverse functionalities such as collision avoidance and goal-reaching, while maintaining high computational efficiency. We validate the efficacy of our work through simulations and Franka Emika robotic experiments, comparing its performance against state-of-the-art methodologies. This comprehensive evaluation highlights GeoPro's versatility in accommodating robots with varying dynamics and precise geometric shapes. For additional materials, please visit: https://www.xueminchi.com/publications/geopro

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arXiv2023

Projection-based first-order constrained optimization solver for robotics

Robot programming tools ranging from inverse kinematics (IK) to model predictive control (MPC) are most often described as constrained optimization problems. Even though there are currently many commercially-available second-order solvers, robotics literature recently focused on efficient implementations and improvements over these solvers for real-time robotic applications. However, most often, these implementations stay problem-specific and are not easy to access or implement, or do not exploit the geometric aspect of the robotics problems. In this work, we propose to solve these problems using a fast, easy-to-implement first-order method that fully exploits the geometric constraints via Euclidean projections, called Augmented Lagrangian Spectral Projected Gradient Descent (ALSPG). We show that 1. using projections instead of full constraints and gradients improves the performance of the solver and 2. ALSPG stays competitive to the standard second-order methods such as iLQR in the unconstrained case. We showcase these results with IK and motion planning problems on simulated examples and with an MPC problem on a 7-axis manipulator experiment.

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arXiv2023

Geometric Algebra for Optimal Control with Applications in Manipulation Tasks

Many problems in robotics are fundamentally problems of geometry, which lead to an increased research effort in geometric methods for robotics in recent years. The results were algorithms using the various frameworks of screw theory, Lie algebra and dual quaternions. A unification and generalization of these popular formalisms can be found in geometric algebra. The aim of this paper is to showcase the capabilities of geometric algebra when applied to robot manipulation tasks. In particular the modelling of cost functions for optimal control can be done uniformly across different geometric primitives leading to a low symbolic complexity of the resulting expressions and a geometric intuitiveness. We demonstrate the usefulness, simplicity and computational efficiency of geometric algebra in several experiments using a Franka Emika robot. The presented algorithms were implemented in c++20 and resulted in the publicly available library \textit{gafro}. The benchmark shows faster computation of the kinematics than state-of-the-art robotics libraries.

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