Aristotelis Papatheodorou, Wolfgang Merkt, Alexander L. Mitchell, Ioannis Havoutis
The current state-of-the-art gradient-based optimisation frameworks are able to produce impressive dynamic manoeuvres such as linear and rotational jumps. However, these methods, which optimise over the full rigid-body dynamics of the robot, often require precise foothold locations apriori, while real-time performance is not guaranteed without elaborate regularisation and tuning of the cost function. In contrast, we investigate the advantages of a task-space optimisation framework, with special focus on acrobatic motions. Our proposed formulation exploits the system's high-order nonlinearities, such as the nonholonomy of the angular momentum, in order to produce feasible, high-acceleration manoeuvres. By leveraging the full-centroidal dynamics of the quadruped ANYmal C and directly optimising its footholds and contact forces, the framework is capable of producing efficient motion plans with low computational overhead. Finally, we deploy our proposed framework on the ANYmal C platform, and demonstrate its true capabilities through real-world experiments, with the successful execution of high-acceleration motions, such as linear and rotational jumps. Extensive analysis of these shows that the robot's dynamics can be exploited to surpass its hardware limitations of having a high mass and low-torque limits.
Pranav Vaidhyanathan, Aristotelis Papatheodorou, Mark T. Mitchison, Natalia Ares, Ioannis Havoutis
Scalable and generalizable physics-aware deep learning has long been considered a significant challenge with various applications across diverse domains ranging from robotics to molecular dynamics. Central to almost all physical systems are symplectic forms, the geometric backbone that underpins fundamental invariants like energy and momentum. In this work, we introduce a novel deep learning framework, MetaSym. In particular, MetaSym combines a strong symplectic inductive bias obtained from a symplectic encoder, and an autoregressive decoder with meta-attention. This principled design ensures that core physical invariants remain intact, while allowing flexible, data efficient adaptation to system heterogeneities. We benchmark MetaSym with highly varied and realistic datasets, such as a high-dimensional spring-mesh system Otness et al. (2021), an open quantum system with dissipation and measurement backaction, and robotics-inspired quadrotor dynamics. Crucially, we fine-tune and deploy MetaSym on real-world quadrotor data, demonstrating robustness to sensor noise and real-world uncertainty. Across all tasks, MetaSym achieves superior few-shot adaptation and outperforms larger state-of-the-art (SOTA) models.
Guillaume Gagné-Labelle, Vassil Atanassov, Ioannis Havoutis
Climbing, crouching, bridging gaps, and walking up stairs are just a few of the advantages that quadruped robots have over wheeled robots, making them more suitable for navigating rough and unstructured terrain. However, executing such manoeuvres requires precise temporal coordination and complex agent-environment interactions. Moreover, legged locomotion is inherently more prone to slippage and tripping, and the classical approach of modeling such cases to design a robust controller thus quickly becomes impractical. In contrast, reinforcement learning offers a compelling solution by enabling optimal control through trial and error. We present a generalist reinforcement learning algorithm for quadrupedal agents in dynamic motion scenarios. The learned policy rivals state-of-the-art specialist policies trained using a mixture of experts approach, while using only 25% as many agents during training. Our experiments also highlight the key components of the generalist locomotion policy and the primary factors contributing to its success.
Jose Rojas, Aristotelis Papatheodorou, Sergi Martinez, Andrea Patrizi, Ioannis Havoutis, Carlos Mastalli
We introduce ODYN, a novel all-shifted primal-dual non-interior-point quadratic programming (QP) solver designed to efficiently handle challenging dense and sparse QPs. ODYN combines all-shifted nonlinear complementarity problem (NCP) functions with proximal method of multipliers to robustly address ill-conditioned and degenerate problems, without requiring linear independence of the constraints. It exhibits strong warm-start performance and is well suited to both general-purpose optimization, and robotics and AI applications, including model-based control, estimation, and kernel-based learning methods. We provide an open-source implementation and benchmark ODYN on the Maros-Mészáros test set, demonstrating state-of-the-art convergence performance in small-to-high-scale problems. The results highlight ODYN's superior warm-starting capabilities, which are critical in sequential and real-time settings common in robotics and AI. These advantages are further demonstrated by deploying ODYN as the backend of an SQP-based predictive control framework (OdynSQP), as the implicitly differentiable optimization layer for deep learning (ODYNLayer), and the optimizer of a contact-dynamics simulation (ODYNSim).
David Rytz, Suyoung Choi, Wanming Yu, Wolfgang Merkt, Jemin Hwangbo, Ioannis Havoutis
This article presents Platform Adaptive Locomotion (PAL), a unified control method for quadrupedal robots with different morphologies and dynamics. We leverage deep reinforcement learning to train a single locomotion policy on procedurally generated robots. The policy maps proprioceptive robot state information and base velocity commands into desired joint actuation targets, which are conditioned using a latent embedding of the temporally local system dynamics. We explore two conditioning strategies - one using a GRU-based dynamics encoder and another using a morphology-based property estimator - and show that morphology-aware conditioning outperforms temporal dynamics encoding regarding velocity task tracking for our hardware test on ANYmal C. Our results demonstrate that both approaches achieve robust zero-shot transfer across multiple unseen simulated quadrupeds. Furthermore, we demonstrate the need for careful robot reference modelling during training: exposing the policy to a diverse set of robot morphologies and dynamics leads to improved generalization, reducing the velocity tracking error by up to 30% compared to the baseline method. Despite PAL not surpassing the best-performing reference-free controller in all cases, our analysis uncovers critical design choices and informs improvements to the state of the art.
Chia-Man Hung, Shaohong Zhong, Walter Goodwin, Oiwi Parker Jones, Martin Engelcke, Ioannis Havoutis, Ingmar Posner
We present a novel approach to path planning for robotic manipulators, in which paths are produced via iterative optimisation in the latent space of a generative model of robot poses. Constraints are incorporated through the use of constraint satisfaction classifiers operating on the same space. Optimisation leverages gradients through our learned models that provide a simple way to combine goal reaching objectives with constraint satisfaction, even in the presence of otherwise non-differentiable constraints. Our models are trained in a task-agnostic manner on randomly sampled robot poses. In baseline comparisons against a number of widely used planners, we achieve commensurate performance in terms of task success, planning time and path length, performing successful path planning with obstacle avoidance on a real 7-DoF robot arm.
Alexander L. Mitchell, Wolfgang Merkt, Mathieu Geisert, Siddhant Gangapurwala, Martin Engelcke, Oiwi Parker Jones, Ioannis Havoutis, Ingmar Posner
Quadruped locomotion is rapidly maturing to a degree where robots now routinely traverse a variety of unstructured terrains. However, while gaits can be varied typically by selecting from a range of pre-computed styles, current planners are unable to vary key gait parameters continuously while the robot is in motion. The synthesis, on-the-fly, of gaits with unexpected operational characteristics or even the blending of dynamic manoeuvres lies beyond the capabilities of the current state-of-the-art. In this work we address this limitation by learning a latent space capturing the key stance phases of a particular gait, via a generative model trained on a single trot style. This encourages disentanglement such that application of a drive signal to a single dimension of the latent state induces holistic plans synthesising a continuous variety of trot styles. In fact properties of this drive signal map directly to gait parameters such as cadence, footstep height and full stance duration. The use of a generative model facilitates the detection and mitigation of disturbances to provide a versatile and robust planning framework. We evaluate our approach on a real ANYmal quadruped robot and demonstrate that our method achieves a continuous blend of dynamic trot styles whilst being robust and reactive to external perturbations.
Chia-Man Hung, Li Sun, Yizhe Wu, Ioannis Havoutis, Ingmar Posner
End-to-end visuomotor control is emerging as a compelling solution for robot manipulation tasks. However, imitation learning-based visuomotor control approaches tend to suffer from a common limitation, lacking the ability to recover from an out-of-distribution state caused by compounding errors. In this paper, instead of using tactile feedback or explicitly detecting the failure through vision, we investigate using the uncertainty of a policy neural network. We propose a novel uncertainty-based approach to detect and recover from failure cases. Our hypothesis is that policy uncertainties can implicitly indicate the potential failures in the visuomotor control task and that robot states with minimum uncertainty are more likely to lead to task success. To recover from high uncertainty cases, the robot monitors its uncertainty along a trajectory and explores possible actions in the state-action space to bring itself to a more certain state. Our experiments verify this hypothesis and show a significant improvement on task success rate: 12% in pushing, 15% in pick-and-reach and 22% in pick-and-place.
Alexander L. Mitchell, Wolfgang Merkt, Mathieu Geisert, Siddhant Gangapurwala, Martin Engelcke, Oiwi Parker Jones, Ioannis Havoutis, Ingmar Posner
Quadruped locomotion is rapidly maturing to a degree where robots are able to realise highly dynamic manoeuvres. However, current planners are unable to vary key gait parameters of the in-swing feet midair. In this work we address this limitation and show that it is pivotal in increasing controller robustness by learning a latent space capturing the key stance phases constituting a particular gait. This is achieved via a generative model trained on a single trot style, which encourages disentanglement such that application of a drive signal to a single dimension of the latent state induces holistic plans synthesising a continuous variety of trot styles. We demonstrate that specific properties of the drive signal map directly to gait parameters such as cadence, footstep height and full stance duration. Due to the nature of our approach these synthesised gaits are continuously variable online during robot operation. The use of a generative model facilitates the detection and mitigation of disturbances to provide a versatile and robust planning framework. We evaluate our approach on two versions of the real ANYmal quadruped robots and demonstrate that our method achieves a continuous blend of dynamic trot styles whilst being robust and reactive to external perturbations.
Siddhant Gangapurwala, Mathieu Geisert, Romeo Orsolino, Maurice Fallon, Ioannis Havoutis
We present a unified model-based and data-driven approach for quadrupedal planning and control to achieve dynamic locomotion over uneven terrain. We utilize on-board proprioceptive and exteroceptive feedback to map sensory information and desired base velocity commands into footstep plans using a reinforcement learning (RL) policy. This RL policy is trained in simulation over a wide range of procedurally generated terrains. When ran online, the system tracks the generated footstep plans using a model-based motion controller. We evaluate the robustness of our method over a wide variety of complex terrains. It exhibits behaviors which prioritize stability over aggressive locomotion. Additionally, we introduce two ancillary RL policies for corrective whole-body motion tracking and recovery control. These policies account for changes in physical parameters and external perturbations. We train and evaluate our framework on a complex quadrupedal system, ANYmal version B, and demonstrate transferability to a larger and heavier robot, ANYmal C, without requiring retraining.
Alexander L. Mitchell, Martin Engelcke, Oiwi Parker Jones, David Surovik, Siddhant Gangapurwala, Oliwier Melon, Ioannis Havoutis, Ingmar Posner
Traditional approaches to quadruped control frequently employ simplified, hand-derived models. This significantly reduces the capability of the robot since its effective kinematic range is curtailed. In addition, kinodynamic constraints are often non-differentiable and difficult to implement in an optimisation approach. In this work, these challenges are addressed by framing quadruped control as optimisation in a structured latent space. A deep generative model captures a statistical representation of feasible joint configurations, whilst complex dynamic and terminal constraints are expressed via high-level, semantic indicators and represented by learned classifiers operating upon the latent space. As a consequence, complex constraints are rendered differentiable and evaluated an order of magnitude faster than analytical approaches. We validate the feasibility of locomotion trajectories optimised using our approach both in simulation and on a real-world ANYmal quadruped. Our results demonstrate that this approach is capable of generating smooth and realisable trajectories. To the best of our knowledge, this is the first time latent space control has been successfully applied to a complex, real robot platform.
Alexander L. Mitchell, Wolfgang Merkt, Aristotelis Papatheodorou, Ioannis Havoutis, Ingmar Posner
The current state-of-the-art in quadruped locomotion is able to produce a variety of complex motions. These methods either rely on switching between a discrete set of skills or learn a distribution across gaits using complex black-box models. Alternatively, we present Gaitor, which learns a disentangled and 2D representation across locomotion gaits. This learnt representation forms a planning space for closed-loop control delivering continuous gait transitions and perceptive terrain traversal. Gaitor's latent space is readily interpretable and we discover that during gait transitions, novel unseen gaits emerge. The latent space is disentangled with respect to footswing heights and lengths. This means that these gait characteristics can be varied independently in the 2D latent representation. Together with a simple terrain encoding and a learnt planner operating in the latent space, Gaitor can take motion commands including desired gait type and swing characteristics all while reacting to uneven terrain. We evaluate Gaitor in both simulation and the real world on the ANYmal C platform. To the best of our knowledge, this is the first work learning a unified and interpretable latent space for multiple gaits, resulting in continuous blending between different locomotion modes on a real quadruped robot. An overview of the methods and results in this paper is found at https://youtu.be/eVFQbRyilCA.
Siddhant Gangapurwala, Alexander Mitchell, Ioannis Havoutis
Deep reinforcement learning (RL) uses model-free techniques to optimize task-specific control policies. Despite having emerged as a promising approach for complex problems, RL is still hard to use reliably for real-world applications. Apart from challenges such as precise reward function tuning, inaccurate sensing and actuation, and non-deterministic response, existing RL methods do not guarantee behavior within required safety constraints that are crucial for real robot scenarios. In this regard, we introduce guided constrained policy optimization (GCPO), an RL framework based upon our implementation of constrained proximal policy optimization (CPPO) for tracking base velocity commands while following the defined constraints. We also introduce schemes which encourage state recovery into constrained regions in case of constraint violations. We present experimental results of our training method and test it on the real ANYmal quadruped robot. We compare our approach against the unconstrained RL method and show that guided constrained RL offers faster convergence close to the desired optimum resulting in an optimal, yet physically feasible, robotic control behavior without the need for precise reward function tuning.
Aristotelis Papatheodorou, Pranav Vaidhyanathan, Natalia Ares, Ioannis Havoutis
Physics-informed deep learning has achieved remarkable progress by embedding geometric priors, such as Hamiltonian symmetries and variational principles, into neural networks, enabling structure-preserving models that extrapolate with high accuracy. However, in systems with dissipation and holonomic constraints, ubiquitous in legged locomotion and multibody robotics, the canonical symplectic form becomes degenerate, undermining the very invariants that guarantee stability and long-term prediction. In this work, we tackle this foundational limitation by introducing Presymplectification Networks (PSNs), the first framework to learn the symplectification lift via Dirac structures, restoring a non-degenerate symplectic geometry by embedding constrained systems into a higher-dimensional manifold. Our architecture combines a recurrent encoder with a flow-matching objective to learn the augmented phase-space dynamics end-to-end. We then attach a lightweight Symplectic Network (SympNet) to forecast constrained trajectories while preserving energy, momentum, and constraint satisfaction. We demonstrate our method on the dynamics of the ANYmal quadruped robot, a challenging contact-rich, multibody system. To the best of our knowledge, this is the first framework that effectively bridges the gap between constrained, dissipative mechanical systems and symplectic learning, unlocking a whole new class of geometric machine learning models, grounded in first principles yet adaptable from data.
Pranav Vaidhyanathan, Aristotelis Papatheodorou, David R. M. Arvidsson-Shukur, Mark T. Mitchison, Natalia Ares, Ioannis Havoutis
Dec 17, 2025·quant-ph·PDF Dynamic programming is a cornerstone of graph-based optimization. While effective, it scales unfavorably with problem size. In this work, we present QuantGraph, a two-stage quantum-enhanced framework that casts local and global graph-optimization problems as quantum searches over discrete trajectory spaces. The solver is designed to operate efficiently by first finding a sequence of locally optimal transitions in the graph (local stage), without considering full trajectories. The accumulated cost of these transitions acts as a threshold that prunes the search space (up to 60% reduction for certain examples). The subsequent global stage, based on this threshold, refines the solution. Both stages utilize variants of the Grover-adaptive-search algorithm. To achieve scalability and robustness, we draw on principles from control theory and embed QuantGraph's global stage within a receding-horizon model-predictive-control scheme. This classical layer stabilizes and guides the quantum search, improving precision and reducing computational burden. In practice, the resulting closed-loop system exhibits robust behavior and lower overall complexity. Notably, for a fixed query budget, QuantGraph attains a 2x increase in control-discretization precision while still benefiting from Grover-search's inherent quadratic speedup compared to classical methods.
Carlos Mastalli, Ioannis Havoutis, Michele Focchi, Darwin G. Caldwell, Claudio Semini
Planning whole-body motions while taking into account the terrain conditions is a challenging problem for legged robots since the terrain model might produce many local minima. Our coupled planning method uses stochastic and derivatives-free search to plan both foothold locations and horizontal motions due to the local minima produced by the terrain model. It jointly optimizes body motion, step duration and foothold selection, and it models the terrain as a cost-map. Due to the novel attitude planning method, the horizontal motion plans can be applied to various terrain conditions. The attitude planner ensures the robot stability by imposing limits to the angular acceleration. Our whole-body controller tracks compliantly trunk motions while avoiding slippage, as well as kinematic and torque limits. Despite the use of a simplified model, which is restricted to flat terrain, our approach shows remarkable capability to deal with a wide range of non-coplanar terrains. The results are validated by experimental trials and comparative evaluations in a series of terrains of progressively increasing complexity.
Wolfgang Merkt, Vladimir Ivan, Traiko Dinev, Ioannis Havoutis, Sethu Vijayakumar
Shooting methods are an efficient approach to solving nonlinear optimal control problems. As they use local optimization, they exhibit favorable convergence when initialized with a good warm-start but may not converge at all if provided with a poor initial guess. Recent work has focused on providing an initial guess from a learned model trained on samples generated during an offline exploration of the problem space. However, in practice the solutions contain discontinuities introduced by system dynamics or the environment. Additionally, in many cases multiple equally suitable, i.e., multi-modal, solutions exist to solve a problem. Classic learning approaches smooth across the boundary of these discontinuities and thus generalize poorly. In this work, we apply tools from algebraic topology to extract information on the underlying structure of the solution space. In particular, we introduce a method based on persistent homology to automatically cluster the dataset of precomputed solutions to obtain different candidate initial guesses. We then train a Mixture-of-Experts within each cluster to predict state and control trajectories to warm-start the optimal control solver and provide a comparison with modality-agnostic learning. We demonstrate our method on a cart-pole toy problem and a quadrotor avoiding obstacles, and show that clustering samples based on inherent structure improves the warm-start quality.
Carlo Tiseo, Vladimir Ivan, Wolfgang Merkt, Ioannis Havoutis, Michael Mistry, Sethu Vijayakumar
Path planning and collision avoidance are challenging in complex and highly variable environments due to the limited horizon of events. In literature, there are multiple model- and learning-based approaches that require significant computational resources to be effectively deployed and they may have limited generality. We propose a planning algorithm based on a globally stable passive controller that can plan smooth trajectories using limited computational resources in challenging environmental conditions. The architecture combines the recently proposed fractal impedance controller with elastic bands and regions of finite time invariance. As the method is based on an impedance controller, it can also be used directly as a force/torque controller. We validated our method in simulation to analyse the ability of interactive navigation in challenging concave domains via the issuing of via-points, and its robustness to low bandwidth feedback. A swarm simulation using 11 agents validated the scalability of the proposed method. We have performed hardware experiments on a holonomic wheeled platform validating smoothness and robustness of interaction with dynamic agents (i.e., humans and robots). The computational complexity of the proposed local planner enables deployment with low-power micro-controllers lowering the energy consumption compared to other methods that rely upon numeric optimisation.
Carlos Mastalli, Ioannis Havoutis, Alexander W. Winkler, Darwin G. Caldwell, Claudio Semini
We present a legged motion planning approach for quadrupedal locomotion over challenging terrain. We decompose the problem into body action planning and footstep planning. We use a lattice representation together with a set of defined body movement primitives for computing a body action plan. The lattice representation allows us to plan versatile movements that ensure feasibility for every possible plan. To this end, we propose a set of rules that define the footstep search regions and footstep sequence given a body action. We use Anytime Repairing A* (ARA*) search that guarantees bounded suboptimal plans. Our main contribution is a planning approach that generates on-line versatile movements. Experimental trials demonstrate the performance of our planning approach in a set of challenging terrain conditions. The terrain information and plans are computed on-line and on-board.
Alexander W. Winkler, Carlos Mastalli, Ioannis Havoutis, Michele Focchi, Darwin G. Caldwell, Claudio Semini
We present a framework for dynamic quadrupedal locomotion over challenging terrain, where the choice of appropriate footholds is crucial for the success of the behaviour. We build a model of the environment on-line and on-board using an efficient occupancy grid representation. We use Any-time-Repairing A* (ARA*) to search over a tree of possible actions, choose a rough body path and select the locally-best footholds accordingly. We run a n-step lookahead optimization of the body trajectory using a dynamic stability metric, the Zero Moment Point (ZMP), that generates natural dynamic whole-body motions. A combination of floating-base inverse dynamics and virtual model control accurately executes the desired motions on an actively compliant system. Experimental trials show that this framework allows us to traverse terrains at nearly 6 times the speed of our previous work, evaluated over the same set of trials.