arXiv subjects

Giulio Turrisi

Publications and source records attributed to Giulio Turrisi.

At least 19 recordsLinked to original sources

arXiv2026

SKooP: Symmetric Koopman Predictions for Faster and More Generalizable Legged Robot Locomotion with Reinforcement Learning

Reinforcement learning (RL) algorithms classically suffer from poor sample efficiency. In robotics, a recent line of work has emerged addressing this problem by encoding physics priors in the learning process. However, most of these approaches are validated on well-defined, low-dimensional benchmark systems rather than high-dimensional robots with complex nonlinear dynamics. In this paper, we introduce \textit{SKooP (Symmetric Koopman Predictions)}, an approach combining the advantages of morphological symmetries with those of a Koopman model learned via autoencoder to enhance policy learning. SKooP learns a Koopman model of the system dynamics alongside the policy. The resulting Koopman predictions are used as privileged observations for the critic, allowing the agent to learn based on smoother, more informative features. We also incorporate group symmetries into the actor, critic, encoder and decoder networks to produce a highly equivariant policy. The SKooP approach is validated via in-depth analysis of the learned Koopman models and symmetric policies to showcase how each of these influences the agent's performance. We also show that the learned policies are transferable to different simulation environments. Our results show that SKooP consistently reduces convergence time and increases the learned reward for multiple challenging bipedal locomotion tasks on a quadruped robot. Project page: https://evelyd.github.io/SymmetricKoopmanPredictions

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arXiv2026

Mixture-of-Experts RL for Fault-Tolerant Legged Locomotion

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.

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arXiv2026

Morphologically Equivariant Flow Matching for Bimanual Mobile Manipulation

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 $\mathbb{C}_2$-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.

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arXiv2026

BinWalker: Development and Field Evaluation of a Quadruped Manipulator Platform for Sustainable Litter Collection

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.

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arXiv2025

Proprioceptive Image: An Image Representation of Proprioceptive Data from Quadruped Robots for Contact Estimation Learning

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.

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arXiv2025

CroSTAta: Cross-State Transition Attention Transformer for Robotic Manipulation

Learning robotic manipulation policies through supervised learning from demonstrations remains challenging when policies encounter execution variations not explicitly covered during training. While incorporating historical context through attention mechanisms can improve robustness, standard approaches process all past states in a sequence without explicitly modeling the temporal structure that demonstrations may include, such as failure and recovery patterns. We propose a Cross-State Transition Attention Transformer that employs a novel State Transition Attention (STA) mechanism to modulate standard attention weights based on learned state evolution patterns, enabling policies to better adapt their behavior based on execution history. Our approach combines this structured attention with temporal masking during training, where visual information is randomly removed from recent timesteps to encourage temporal reasoning from historical context. Evaluation in simulation shows that STA consistently outperforms standard attention approach and temporal modeling methods like TCN and LSTM networks, achieving more than 2x improvement over cross-attention on precision-critical tasks. The source code and data can be accessed at https://github.com/iit-DLSLab/croSTAta

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arXiv2025

BC-MPPI: A Probabilistic Constraint Layer for Safe Model-Predictive Path-Integral Control

Model Predictive Path Integral (MPPI) control has recently emerged as a fast, gradient-free alternative to model-predictive control in highly non-linear robotic tasks, yet it offers no hard guarantees on constraint satisfaction. We introduce Bayesian-Constraints MPPI (BC-MPPI), a lightweight safety layer that attaches a probabilistic surrogate to every state and input constraint. At each re-planning step the surrogate returns the probability that a candidate trajectory is feasible; this joint probability scales the weight given to a candidate, automatically down-weighting rollouts likely to collide or exceed limits and pushing the sampling distribution toward the safe subset; no hand-tuned penalty costs or explicit sample rejection required. We train the surrogate from 1000 offline simulations and deploy the controller on a quadrotor in MuJoCo with both static and moving obstacles. Across K in [100,1500] rollouts BC-MPPI preserves safety margins while satisfying the prescribed probability of violation. Because the surrogate is a stand-alone, version-controlled artefact and the runtime safety score is a single scalar, the approach integrates naturally with verification-and-validation pipelines for certifiable autonomous systems.

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arXiv2025

Guided Reinforcement Learning for Omnidirectional 3D Jumping in Quadruped Robots

Jumping poses a significant challenge for quadruped robots, despite being crucial for many operational scenarios. While optimisation methods exist for controlling such motions, they are often time-consuming and demand extensive knowledge of robot and terrain parameters, making them less robust in real-world scenarios. Reinforcement learning (RL) is emerging as a viable alternative, yet conventional end-to-end approaches lack efficiency in terms of sample complexity, requiring extensive training in simulations, and predictability of the final motion, which makes it difficult to certify the safety of the final motion. To overcome these limitations, this paper introduces a novel guided reinforcement learning approach that leverages physical intuition for efficient and explainable jumping, by combining B\'ezier curves with a Uniformly Accelerated Rectilinear Motion (UARM) model. Extensive simulation and experimental results clearly demonstrate the advantages of our approach over existing alternatives.

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arXiv2025

Feedback-MPPI: Fast Sampling-Based MPC via Rollout Differentiation -- Adios low-level controllers

Model Predictive Path Integral control is a powerful sampling-based approach suitable for complex robotic tasks due to its flexibility in handling nonlinear dynamics and non-convex costs. However, its applicability in real-time, highfrequency robotic control scenarios is limited by computational demands. This paper introduces Feedback-MPPI (F-MPPI), a novel framework that augments standard MPPI by computing local linear feedback gains derived from sensitivity analysis inspired by Riccati-based feedback used in gradient-based MPC. These gains allow for rapid closed-loop corrections around the current state without requiring full re-optimization at each timestep. We demonstrate the effectiveness of F-MPPI through simulations and real-world experiments on two robotic platforms: a quadrupedal robot performing dynamic locomotion on uneven terrain and a quadrotor executing aggressive maneuvers with onboard computation. Results illustrate that incorporating local feedback significantly improves control performance and stability, enabling robust, high-frequency operation suitable for complex robotic systems.

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arXiv2025

Primal-Dual iLQR for GPU-Accelerated Learning and Control in Legged Robots

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 $\mathcal{O}(\log^2(n)\log{N} + \log^2(m))$ 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. The code associated with this work can be found at https://github.com/iit-DLSLab/mpx.

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arXiv2025

On-Line Learning for Planning and Control of Underactuated Robots with Uncertain Dynamics

We present an iterative approach for planning and controlling motions of underactuated robots with uncertain dynamics. At its core, there is a learning process which estimates the perturbations induced by the model uncertainty on the active and passive degrees of freedom. The generic iteration of the algorithm makes use of the learned data in both the planning phase, which is based on optimization, and the control phase, where partial feedback linearization of the active dofs is performed on the model updated on-line. The performance of the proposed approach is shown by comparative simulations and experiments on a Pendubot executing various types of swing-up maneuvers. Very few iterations are typically needed to generate dynamically feasible trajectories and the tracking control that guarantees their accurate execution, even in the presence of large model uncertainties.

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arXiv2024

Adaptive Non-linear Centroidal MPC with Stability Guarantees for Robust Locomotion of Legged Robots

Nonlinear model predictive locomotion controllers based on the reduced centroidal dynamics are nowadays ubiquitous in legged robots. These schemes, even if they assume an inherent simplification of the robot's dynamics, were shown to endow robots with a step-adjustment capability in reaction to small pushes, and, moreover, in the case of uncertain parameters - as unknown payloads - they were shown to be able to provide some practical, albeit limited, robustness. In this work, we provide rigorous certificates of their closed loop stability via a reformulation of the centroidal MPC controller. This is achieved thanks to a systematic procedure inspired by the machinery of adaptive control, together with ideas coming from Control Lyapunov functions. Our reformulation, in addition, provides robustness for a class of unmeasured constant disturbances. To demonstrate the generality of our approach, we validated our formulation on a new generation of humanoid robots - the 56.7 kg ergoCub, as well as on a commercially available 21 kg quadruped robot, Aliengo.

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arXiv2024

Non-Gaited Legged Locomotion with Monte-Carlo Tree Search and Supervised Learning

Legged robots are able to navigate complex terrains by continuously interacting with the environment through careful selection of contact sequences and timings. However, the combinatorial nature behind contact planning hinders the applicability of such optimization problems on hardware. In this work, we present a novel approach that optimizes gait sequences and respective timings for legged robots in the context of optimization-based controllers through the use of sampling-based methods and supervised learning techniques. We propose to bootstrap the search by learning an optimal value function in order to speed-up the gait planning procedure making it applicable in real-time. To validate our proposed method, we showcase its performance both in simulation and on hardware using a 22 kg electric quadruped robot. The method is assessed on different terrains, under external perturbations, and in comparison to a standard control approach where the gait sequence is fixed a priori.

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arXiv2024

PACC: A Passive-Arm Approach for High-Payload Collaborative Carrying with Quadruped Robots Using Model Predictive Control

In this paper, we introduce the concept of using passive arm structures with intrinsic impedance for robot-robot and human-robot collaborative carrying with quadruped robots. The concept is meant for a leader-follower task and takes a minimalist approach that focuses on exploiting the robots' payload capabilities and reducing energy consumption, without compromising the robot locomotion capabilities. We introduce a preliminary arm mechanical design and describe how to use its joint displacements to guide the robot's motion. To control the robot's locomotion, we propose a decentralized Model Predictive Controller that incorporates an approximation of the arm dynamics and the estimation of the external forces from the collaborative carrying. We validate the overall system experimentally by performing both robot-robot and human-robot collaborative carrying on a stair-like obstacle and on rough terrain.

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arXiv2024

Leveraging Symmetry in RL-based Legged Locomotion Control

Model-free reinforcement learning is a promising approach for autonomously solving challenging robotics control problems, but faces exploration difficulty without information of the robot's kinematics and dynamics morphology. The under-exploration of multiple modalities with symmetric states leads to behaviors that are often unnatural and sub-optimal. This issue becomes particularly pronounced in the context of robotic systems with morphological symmetries, such as legged robots for which the resulting asymmetric and aperiodic behaviors compromise performance, robustness, and transferability to real hardware. To mitigate this challenge, we can leverage symmetry to guide and improve the exploration in policy learning via equivariance/invariance constraints. In this paper, we investigate the efficacy of two approaches to incorporate symmetry: modifying the network architectures to be strictly equivariant/invariant, and leveraging data augmentation to approximate equivariant/invariant actor-critics. We implement the methods on challenging loco-manipulation and bipedal locomotion tasks and compare with an unconstrained baseline. We find that the strictly equivariant policy consistently outperforms other methods in sample efficiency and task performance in simulation. In addition, symmetry-incorporated approaches exhibit better gait quality, higher robustness and can be deployed zero-shot in real-world experiments.

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arXiv2024

Accelerating Model Predictive Control for Legged Robots through Distributed Optimization

This paper presents a novel approach to enhance Model Predictive Control (MPC) for legged robots through Distributed Optimization. Our method focuses on decomposing the robot dynamics into smaller, parallelizable subsystems, and utilizing the Alternating Direction Method of Multipliers (ADMM) to ensure consensus among them. Each subsystem is managed by its own Optimal Control Problem, with ADMM facilitating consistency between their optimizations. This approach not only decreases the computational time but also allows for effective scaling with more complex robot configurations, facilitating the integration of additional subsystems such as articulated arms on a quadruped robot. We demonstrate, through numerical evaluations, the convergence of our approach on two systems with increasing complexity. In addition, we showcase that our approach converges towards the same solution when compared to a state-of-the-art centralized whole-body MPC implementation. Moreover, we quantitatively compare the computational efficiency of our method to the centralized approach, revealing up to a 75% reduction in computational time. Overall, our approach offers a promising avenue for accelerating MPC solutions for legged robots, paving the way for more effective utilization of the computational performance of modern hardware.

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arXiv2024

On the Benefits of GPU Sample-Based Stochastic Predictive Controllers for Legged Locomotion

Quadrupedal robots excel in mobility, navigating complex terrains with agility. However, their complex control systems present challenges that are still far from being fully addressed. In this paper, we introduce the use of Sample-Based Stochastic control strategies for quadrupedal robots, as an alternative to traditional optimal control laws. We show that Sample-Based Stochastic methods, supported by GPU acceleration, can be effectively applied to real quadruped robots. In particular, in this work, we focus on achieving gait frequency adaptation, a notable challenge in quadrupedal locomotion for gradient-based methods. To validate the effectiveness of Sample-Based Stochastic controllers we test two distinct approaches for quadrupedal robots and compare them against a conventional gradient-based Model Predictive Control system. Our findings, validated both in simulation and on a real 21Kg Aliengo quadruped, demonstrate that our method is on par with a traditional Model Predictive Control strategy when the robot is subject to zero or moderate disturbance, while it surpasses gradient-based methods in handling sustained external disturbances, thanks to the straightforward gait adaptation strategy that is possible to achieve within their formulation.

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arXiv2024

Morphological Symmetries in Robotics

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.

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