Load transportation with quadruped robots is strongly affected by the dynamics of the physical interface between the robot and the load. Passive spring-based arms reduce weight and complexity compared to active manipulators, but their spring-damper dynamics can introduce oscillatory forces that degrade locomotion stability. This paper derives an extended Zero Moment Point (ZMP) formulation that includes passive payload-interface dynamics, relating stiffness, damping, and payload mass to the stability margin. The analysis shows that underdamped configurations can resonate with locomotion harmonics. Based on this insight, we augment a Single Rigid Body Dynamics model with passive subsystem dynamics and integrate it into a Model Predictive Control framework. In simulation, the proposed controller reduces stability violations by up to 10×, from 7.0% to 0.7%, and increase locomotion efficiency by lowering horizontal ground reaction force effort by up to 15% compared to a nominal baseline. Hardware experiments with a 2 kg payload show stable locomotion under pull-release disturbances where the nominal controller fails. The same model also enables end-effector tracking through passive arm dynamics without direct arm actuation.

This paper introduces a novel Model Predictive Control (MPC) implementation for legged robot locomotion that leverages GPU parallelization. Our approach enables both temporal and state-space parallelization by incorporating a parallel associative scan to solve the primal-dual Karush-Kuhn-Tucker (KKT) system. In this way, the optimal control problem is solved in $\mathcal{O}(n\log{N} + m)$ complexity, instead of $\mathcal{O}(N(n + m)^3)$, where $n$, $m$, and $N$ are the dimension of the system state, control vector, and the length of the prediction horizon. We demonstrate the advantages of this implementation over two state-of-the-art solvers (acados and crocoddyl), achieving up to a 60\% improvement in runtime for Whole Body Dynamics (WB)-MPC and a 700\% improvement for Single Rigid Body Dynamics (SRBD)-MPC when varying the prediction horizon length. The presented formulation scales efficiently with the problem state dimensions as well, enabling the definition of a centralized controller for up to 16 legged robots that can be computed in less than 25 ms. Furthermore, thanks to the JAX implementation, the solver supports large-scale parallelization across multiple environments, allowing the possibility of performing learning with the MPC in the loop directly in GPU.

Achieving safe quadrupedal locomotion in real-world environments has attracted much attention in recent years. When walking over uneven terrain, achieving reliable estimation and realising safety-critical control based on the obtained information is still an open question. To address this challenge, especially for low-cost robots equipped solely with proprioceptive sensors (e.g., IMUs, joint encoders, and contact force sensors), this work first presents an estimation framework that generates a 2.5-D terrain map and extracts support plane parameters, which are then integrated into contact and state estimation. Then, we integrate this estimation framework into a safety-critical control pipeline by formulating control barrier functions that provide rigorous safety guarantees. Experiments demonstrate that the proposed terrain estimation method provides smooth terrain representations. Moreover, the coupled estimation framework of terrain, state, and contact reduces the mean absolute error of base position estimation by 64.8

Passive mechanical interfaces offer a lightweight alternative to actuated manipulators for quadruped payload carrying, but their impedance directly couples the payload dynamics with the locomotion pattern. This paper analyzes how passive-arm stiffness-damping selection affects payload-carrying locomotion under different gait and payload conditions. We compare damped and underdamped passive-arm impedance configurations in simulation during flat-ground locomotion. For crawl gaits, where the support polygon remains well defined, the results show that underdamped impedance increases passive-joint oscillations and can reduce the ZMP margin with respect to the support polygon. Trot is retained as a dynamic excitation case for the passive arm, but it is not used for direct ZMP-margin stability comparison. The results are summarized in gait-payload-stiffness-damping maps, where ZMP-margin reduction is evaluated for crawl gaits and trot is retained only as a passive-arm excitation case.

In modern robotic systems, scalable, flexible, and robust software architectures are critical for enabling efficient collaboration and computation across distributed hardware. This paper introduces DLS2, a truly distributed robot-centric software architecture designed for complex, highly dynamic robots. Unlike conventional middleware, the DLS2 architecture natively integrates dynamic distribution of processing, containerized microservices, seamless application migration, and real-time performance constraints without relying on centralized orchestration. DLS2 manages different abstractions of the robotic stack by defining a structured, omnipresent layer-based organization. Through a formal architectural case study and a qualitative comparison with state-of-the-art frameworks, the structural advantages of this design paradigm are highlighted, particularly in terms of fault tolerance, modularity, and resource isolation. This research lays the foundational framework for future advancements in distributed robotic systems, offering an alternative design reference for resilient multi-robot environments. The DLS2 code can be found at https://github.com/iit-DLSLab/dls2-barebone

Mobile manipulation requires coordinated control of high-dimensional, bimanual robots. Imitation learning methods have been broadly used to solve these robotic tasks, yet typically ignore the bilateral morphological symmetry inherent in such systems. We argue that morphological symmetry is an underexplored but crucial inductive bias for learning in bimanual mobile manipulation: knowing how to solve a task in one configuration directly determines how to solve its mirrored counterpart. In this paper, we formalize this symmetry prior and show that it constrains optimal bimanual policies to be ambidextrous and equivariant under reflections across the robot's sagittal plane. We introduce a ℂ_2-equivariant flow matching policy that enforces reflective symmetry either via a regularized training loss or an equivariant velocity network. Across planar and 6-DoF mobile manipulation tasks, symmetry-informed policies consistently improve sample efficiency and achieve zero-shot generalization to mirrored configurations absent from the training distribution. We further validate this zero-shot generalization capability on a real-world manipulation task with a TIAGo++ robot. Together, our findings establish morphological symmetry as an effective, generalizable, and scalable inductive bias for ambidextrous generative policy learning.

Collapsing terrains, often present in search and rescue missions or planetary exploration, pose significant challenges for quadruped robots. This paper introduces a robust locomotion framework for safe navigation over unstable surfaces by integrating terrain probing, load-bearing analysis, motion planning, and control strategies. Unlike traditional methods that rely on specialized sensors or external terrain mapping alone, our approach leverages joint measurements to assess terrain stability without hardware modifications. A Model Predictive Control (MPC) system optimizes robot motion, balancing stability and probing constraints, while a state machine coordinates terrain probing actions, enabling the robot to detect collapsible regions and dynamically adjust its footholds. Experimental results on custom-made collapsing platforms and rocky terrains demonstrate the framework's ability to traverse collapsing terrain while maintaining stability and prioritizing safety.

State estimation is essential for quadruped robots, enabling robust locomotion, navigation, and control. While many estimators have been proposed in the literature, existing implementations are often tied to specific robots or software stacks, making fair comparisons difficult. This lack of a general-purpose benchmarking framework hinders reproducibility and slows down algorithmic innovation. In this paper, we introduce Chalito, an extensible MATLAB/Python library for benchmarking filter-based state estimation algorithms in quadruped robots. Chalito imports robot models directly from URDF, supports multiple filtering approaches, and is designed to be easily extended with new methods. The framework runs on both simulated and real datasets, enabling systematic evaluation across robots and filters. To the best of our knowledge, this is the first open-source library exclusively dedicated to benchmarking filtering algorithms for quadruped robots.

Litter pollution represents a growing environmental problem affecting natural and urban ecosystems worldwide. Waste discarded in public spaces often accumulates in areas that are difficult to access, such as uneven terrains, coastal environments, parks, and roadside vegetation. Over time, these materials degrade and release harmful substances, including toxic chemicals and microplastics, which can contaminate soil and water and pose serious threats to wildlife and human health. Despite increasing awareness of the problem, litter collection is still largely performed manually by human operators, making large-scale cleanup operations labor-intensive, time-consuming, and costly. Robotic solutions have the potential to support and partially automate environmental cleanup tasks. In this work, we present a quadruped robotic system designed for autonomous litter collection in challenging outdoor scenarios. The robot combines the mobility advantages of legged locomotion with a manipulation system consisting of a robotic arm and an onboard litter container. This configuration enables the robot to detect, grasp, and store litter items while navigating through uneven terrains. The proposed system aims to demonstrate the feasibility of integrating perception, locomotion, and manipulation on a legged robotic platform for environmental cleanup tasks. Experimental evaluations conducted in outdoor scenarios highlight the effectiveness of the approach and its potential for assisting large-scale litter removal operations in environments that are difficult to reach with traditional robotic platforms. The code associated with this work can be found at: https://github.com/iit-DLSLab/trash-collection-isaaclab.

Legged robots deployed in planetary exploration and other remote environments must maintain reliable locomotion despite actuator failures and challenging terrain conditions. Although reinforcement learning has achieved strong results in legged locomotion, monolithic policies can struggle to efficiently represent the diverse control strategies required to compensate for different fault conditions. In this work, we propose a fault-aware modular control architecture that explicitly leverages fault-diagnosis information to activate specialized control experts associated with distinct actuator failure modes. Experimental results show that explicit fault-conditioned modular policies consistently outperform monolithic policies of comparable size, achieving higher locomotion performance across failure scenarios. Moreover, the proposed modular architecture retains competitive performance even under significantly reduced network capacity, highlighting its suitability for compute-constrained robotic platforms, such as those typically employed in space applications. The code associated with this work is available at: https://github.com/iit-DLSLab/fault-locomotion-isaaclab.

Kalman filter-based algorithms are fundamental for mobile robots, as they provide a computationally efficient solution to the challenging problem of state estimation. However, they rely on two main assumptions that are difficult to satisfy in practice: (a) the system dynamics must be linear with Gaussian process noise, and (b) the measurement model must also be linear with Gaussian measurement noise. Previous works have extended assumption (a) to nonlinear spaces through the Invariant Extended Kalman Filter (IEKF), showing that it retains properties similar to those of the classical Kalman filter when the system dynamics are group-affine on a Lie group. More recently, the counterpart of assumption (b) for the same nonlinear setting was addressed in [1]. By means of the proposed Iterated Invariant Extended Kalman Filter (IterIEKF), the authors of that work demonstrated that the update step exhibits several compatibility properties of the classical linear Kalman filter. In this work, we introduce a novel open-source state estimation algorithm for legged robots based on the IterIEKF. The update step of the proposed filter relies solely on proprioceptive measurements, exploiting kinematic constraints on foot velocity during contact and base-frame velocity, making it inherently robust to environmental conditions. Through extensive numerical simulations and evaluation on real-world datasets, we demonstrate that the IterIEKF outperforms the vanilla IEKF, the SO(3)-based Kalman Filter, and its iterated variant in terms of both accuracy and consistency.

We compare three state-of-the-art proprioceptive state estimators for quadruped robots: MUSE [1], the Invariant Extended Kalman Filter (IEKF) [2], and the Invariant Smoother (IS) [3], on the CYN-1 sequence of the GrandTour Dataset [4]. Our goal is to give practitioners clear guidance on accuracy and computation time: we report long-term accuracy (Absolute Trajectory Error, ATE), short-term accuracy (translational and rotational Relative Pose Error, RPE), and per-update computation time on a fixed hardware/software stack. On this dataset, RPEs are broadly similar across methods, while IEKF and IS achieve a lower ATE than MUSE. Runtime results highlight the accuracy-latency trade-offs across the three approaches. In the discussion, we outline the evaluation choices used to ensure a fair comparison and analyze factors that influence short-horizon metrics. Overall, this study provides a concise snapshot of accuracy and cost, helping readers choose an estimator that fits their application constraints, with all evaluation code and documentation released open-source at https://github.com/iit-DLSLab/state_estimation_benchmark for full reproducibility.

This paper presents a novel approach for representing proprioceptive time-series data from quadruped robots as structured two-dimensional images, enabling the use of convolutional neural networks for learning locomotion-related tasks. The proposed method encodes temporal dynamics from multiple proprioceptive signals, such as joint positions, IMU readings, and foot velocities, while preserving the robot’s morphological structure in the spatial arrangement of the image. This transformation captures inter-signal correlations and gait-dependent patterns, providing a richer feature space than direct time-series processing. We apply this concept in the problem of contact estimation, a key capability for stable and adaptive locomotion on diverse terrains. Experimental evaluations on both real-world datasets and simulated environments show that our image-based representation consistently enhances prediction accuracy and generalization over conventional sequence-based models, underscoring the potential of cross-modal encoding strategies for robotic state learning. Our method achieves superior performance on the contact dataset, improving contact state accuracy from 87.7% to 94.5% over the recently proposed MI-HGNN method, using a 15 times shorter window size.

Legged rovers provide enhanced mobility compared to wheeled platforms, enabling navigation on steep and irregular planetary terrains. However, traditional legged locomotion might be energetically inefficient and potentially dangerous to the rover on loose and inclined surfaces, such as crater walls and cave slopes. This paper introduces a preliminary study that compares the Cost of Transport (CoT) of walking and torso-based sliding locomotion for quadruped robots across different slopes, friction conditions and speed levels. By identifying intersections between walking and sliding CoT curves, we aim to define threshold conditions that may trigger transitions between the two strategies. The methodology combines physics-based simulations in Isaac Sim with particle interaction validation in ANSYS-Rocky. Our results represent an initial step towards adaptive locomotion strategies for planetary legged rovers.

Humans naturally exhibit bilateral symmetry in their gross manipulation skills, effortlessly mirroring simple actions between left and right hands. Bimanual robots-which also feature bilateral symmetry-should similarly exploit this property to perform tasks with either hand. Unlike humans, who often favor a dominant hand for fine dexterous skills, robots should ideally execute ambidextrous manipulation with equal proficiency. To this end, we introduce SYMDEX (SYMmetric DEXterity), a reinforcement learning framework for ambidextrous bi-manipulation that leverages the robot's inherent bilateral symmetry as an inductive bias. SYMDEX decomposes complex bimanual manipulation tasks into per-hand subtasks and trains dedicated policies for each. By exploiting bilateral symmetry via equivariant neural networks, experience from one arm is inherently leveraged by the opposite arm. We then distill the subtask policies into a global ambidextrous policy that is independent of the hand-task assignment. We evaluate SYMDEX on six challenging simulated manipulation tasks and demonstrate successful real-world deployment on two of them. Our approach strongly outperforms baselines on complex task in which the left and right hands perform different roles. We further demonstrate SYMDEX's scalability by extending it to a four-arm manipulation setup, where our symmetry-aware policies enable effective multi-arm collaboration and coordination. Our results highlight how structural symmetry as inductive bias in policy learning enhances sample efficiency, robustness, and generalization across diverse dexterous manipulation tasks.

This letter introduces two multi-sensor state estimation frameworks for quadruped robots, built on the Invariant Extended Kalman Filter (InEKF) and Invariant Smoother (IS). The proposed methods, named E-InEKF and E-IS, fuse kinematics, IMU, LiDAR, and GPS data to mitigate position drift, particularly along the z-axis, a common issue in proprioceptive-based approaches. We derived observation models that satisfy group-affine properties to integrate LiDAR odometry and GPS into InEKF and IS. LiDAR odometry is incorporated using Iterative Closest Point (ICP) registration on a parallel thread, preserving the computational efficiency of proprioceptive-based state estimation. We evaluate E-InEKF and E-IS with and without exteroceptive sensors, benchmarking them against LiDAR-based odometry methods in indoor and outdoor experiments using the KAIST HOUND2 robot. Our methods achieve lower Relative Position Errors (RPE) and significantly reduce Absolute Trajectory Error (ATE), with improvements of up to 28% indoors and 40% outdoors compared to LIO-SAM and FAST-LIO2. Additionally, we compare E-InEKF and E-IS in terms of computational efficiency and accuracy.

This paper introduces an innovative state estimator, MUSE (MUlti-sensor State Estimator), designed to enhance state estimation's accuracy and real-time performance in quadruped robot navigation. The proposed state estimator builds upon our previous work presented in [1]. It integrates data from a range of onboard sensors, including IMUs, encoders, cameras, and LiDARs, to deliver a comprehensive and reliable estimation of the robot's pose and motion, even in slippery scenarios. We tested MUSE on a Unitree Aliengo robot, successfully closing the locomotion control loop in difficult scenarios, including slippery and uneven terrain. Benchmarking against Pronto [2] and VILENS [3] showed 67.6% and 26.7% reductions in translational errors, respectively. Additionally, MUSE outperformed DLIO [4], a LiDAR-inertial odometry system in rotational errors and frequency, while the proprioceptive version of MUSE (P-MUSE) outperformed TSIF [5], with a 45.9% reduction in absolute trajectory error (ATE).

Legged manipulators, such as quadrupeds equipped with robotic arms, require motion planning techniques that account for their complex kinematic constraints in order to perform manipulation tasks both safely and effectively. However, trajectory optimization methods often face challenges due to the hybrid dynamics introduced by contact discontinuities, and tend to neglect leg limitations during planning for computational reasons. In this work, we propose RAKOMO, a path optimization technique that integrates the strengths of K-Order Markov Optimization (KOMO) with a kinematically-aware criterion based on the reachable region defined as reachability margin. We leverage a neural-network to predict the margin and optimize it by incorporating it in the standard KOMO formulation. This approach enables rapid convergence of gradient-based motion planning – commonly tailored for continuous systems – while adapting it effectively to legged manipulators, successfully executing loco-manipulation tasks. We benchmark RAKOMO against a baseline KOMO approach through a set of simulations for pick-and-place tasks with the HyQReal quadruped robot equipped with a Kinova Gen3 robotic arm.

Permanently Shadowed Regions (PSRs) near the lunar poles are of interest for future exploration due to their potential to contain water ice and preserve geological records. Their complex, uneven terrain favors the use of legged robots, which can traverse challenging surfaces while collecting in-situ data, and have proven effective in Earth analogs, including dark caves, when equipped with onboard lighting. While exteroceptive sensors like cameras and lidars can capture terrain geometry and even semantic information, they cannot quantify its physical interaction with the robot, a capability provided by proprioceptive sensing. We propose a terrain mapping framework for quadruped robots, which estimates elevation, foot slippage, energy cost, and stability margins from internal sensing during locomotion. These metrics are incrementally integrated into a multi-layer 2.5D gridmap that reflects terrain interaction from the robot's perspective. The system is evaluated in a simulator that mimics a lunar environment, using the 21 kg quadruped robot Aliengo, showing consistent mapping performance under lunar gravity and terrain conditions.

We present a comprehensive framework for studying and leveraging morphological symmetries in robotic systems. These are intrinsic properties of the robot's morphology, frequently observed in animal biology and robotics, which stem from the replication of kinematic structures and the symmetrical distribution of mass. We illustrate how these symmetries extend to the robot's state space and both proprioceptive and exteroceptive sensor measurements, resulting in the equivariance of the robot's equations of motion and optimal control policies. Thus, we recognize morphological symmetries as a relevant and previously unexplored physics-informed geometric prior, with significant implications for both data-driven and analytical methods used in modeling, control, estimation and design in robotics. For data-driven methods, we demonstrate that morphological symmetries can enhance the sample efficiency and generalization of machine learning models through data augmentation, or by applying equivariant/invariant constraints on the model's architecture. In the context of analytical methods, we employ abstract harmonic analysis to decompose the robot's dynamics into a superposition of lower-dimensional, independent dynamics. We substantiate our claims with both synthetic and real-world experiments conducted on bipedal and quadrupedal robots. Lastly, we introduce the repository MorphoSymm to facilitate the practical use of the theory and applications outlined in this work.