Residual Dynamics Learning

We present RACER, a hierarchical control framework for wheel-based quadruped racing that combines an MPPI planner with a learned residual dynamics model and a low-level RL velocity tracker. The planner augments a nominal unicycle kinematic model with a neural residual term to capture the closed-loop tracking behavior of the RL policy. To train this residual model under limited real-world data, we propose Low-Rank Residual Adaptation (LoRRA), a two-stage approach that pre-trains on large-scale simulation data for broad coverage and then fine-tunes on a small real-world dataset with a low-rank constraint. In simulation, we empirically validate our engineering choices by showing (A) Residual dynamics improve the overall performance of our pipeline by capturing the tracking error of RL velocity tracker at high-speed cornering. (B) Residual dynamics trained with both source-domain and target-domain data gives racing performance significantly better than the residual dynamics trained with only target-domain data. (C) Low-rank constraint at target-domain adaptation gives higher success rates and higher performance than full-tune and from-scratch when domain gap in ground coefficient or joint gain increases.

Model Predictive Control (MPC) provides a structured and constraint-aware mechanism for decision-making, but its reliance on optimization-friendly analytical dynamics models limits its use in tasks with contacts and other hard-to-model state dependencies. Model-free reinforcement learning avoids explicit modeling assumptions but typically requires large amounts of interaction data. We present a learning-based MPC framework that combines the data efficiency and structure of local model-based planning with learned components that compensate for incomplete dynamics and finite-horizon myopia. The method augments a nominal analytical model with a residual dynamics network that learns missing state-dependent effects from data and combines the resulting planner with a learned action-value critic that injects long-horizon MDP structure into the local iLQR optimization. To make this practical at reinforcement-learning scale, we develop a GPU-accelerated batched iLQR solver that evaluates learned dynamics and critic networks inside the optimal-control loop and solves thousands of trajectory-optimization problems in parallel. The complete system is integrated into a robotics simulator, enabling scalable model-based reinforcement learning under incomplete dynamics. Experiments on biased and incompletely modeled control tasks show that the approach improves closed-loop control performance while preserving the model-based structure needed for efficient constrained trajectory optimization.

A robot should be able to learn through experiments how unfamiliar objects behave and interact, then plan with that knowledge. It need not start from scratch: physics engines supply knowledge of motion and contact, but can omit entire mechanisms, such as glue curing, water heating, or wind. We present EMPIRIC, an agent that learns a residual world model: a physics engine extended with code for the missing mechanisms. The learned programs can introduce new forces, constraints, and hidden state, and Bayesian inference estimates their parameters and states from noisy observations. The resulting model lets the agent predict the outcomes of actions, choose informative experiments, and revise its hypotheses when predictions fail. Across five simulated domains, EMPIRIC learns interpretable, reusable models, and solves more tasks with fewer environment interactions than all three baselines. On a physical robot, it learns wind forces and domino masses to solve a manipulation task. Website and code: https://yichao-liang.github.io/empiric

Online residual learning can reduce model mismatch in predictive control, but passive data collection may fail to adequately cover states that become important later in the task. Task-agnostic active learning targets uncertain or informative regions, but information acquired in such regions does not necessarily improve task performance. This paper introduces Task-Oriented Information Acquisition (ToIA), an active-learning criterion for model predictive path integral control (MPPI) with online Gaussian process (GP) residual learning. For each sampled control sequence, ToIA estimates how much an observation obtained early in the rollout would reduce predictive uncertainty at later states on the same rollout, and weights this reduction by the rollout's relevance to the task. The score is evaluated over the existing MPPI rollout batch without sampling future observations or re-optimizing control under hypothetical posterior updates. In simulated off-road navigation across held-out maps with heterogeneous terrain, ToIA improved the goal-reaching success rate over passive GP learning by 19.3 and 27.4 percentage points and outperformed task-agnostic active-learning baselines across dense and sparse online-learning intervals. An ablation study indicates that task relevance is particularly important under sparse model updates. The implementation supports online control at 20 Hz on an NVIDIA RTX 2080 Ti.

Training multi-agent drone-swarm policies directly in high-fidelity (HF) rigid-body physics is accurate but computationally expensive. This cost scales poorly with team size, as each additional agent multiplies contact-resolution complexity and sharply raises the in-simulation crash rate. To address this, we propose a mixed-fidelity training scheme that eliminates HF reinforcement learning entirely. A single shared, decentralized policy is optimized inside a fully-differentiable, JAX-native low-fidelity (LF) point-mass simulator. The simulator is corrected by a small, per-agent bagged residual ensemble fit once, offline, using short calibration flights in the HF simulator. Because calibration requires only one isolated drone, the data collection budget does not compound with team size. Reference trajectories are generated by rolling out an existing LF-only policy and tracked in the HF simulator by a zero-training PD controller. Evaluated across four cooperative drone tasks and team sizes from 3 to 18, the residual-corrected policy outperforms an uncorrected LF baseline in all combinations, and a from-scratch HF policy in 22 of 24 combinations tested. It trails an HF-finetuned policy by a margin that narrows steadily with team size. Ultimately, the proposed method achieves near-equivalent performance at the largest team sizes at a fraction of the computational cost, completely avoiding the high crash rates typical of HF training.

Simulating deformable objects is essential for a wide range of robotic manipulation applications, yet accurately predicting their dynamics remains challenging. We propose Physics-Guided Residual Dynamics (PGRD), a hybrid simulation framework that combines the advantages of physics-based and learning-based approaches. Specifically, PGRD combines an optimizable spring-mass simulator as a backbone with a learned neural network that predicts residual corrections to the physics-based predictions. We adopt a velocity-based formulation to ensure stable simulation and a sliding-window transformer architecture to capture temporal dependencies. We show that PGRD produces more accurate results than both purely physics-based and learning-based methods on a set of diverse real-world deformable objects. We further demonstrate the utility of PGRD in two applications: manipulation planning via Model Predictive Control, including a language-conditioned setting with a generated goal image; and interactive simulation via action-conditioned video prediction by 3D Gaussian Splatting.

Quadrotors flying in tight formations are severely affected by turbulent aerodynamic interactions, such as downwash, that can cause catastrophic collisions if left unmodeled. To compensate for these effects, we propose a physics-informed residual dynamics learning framework that captures complex aerodynamic interactions while ensuring the joint multi-quadrotor system remains differentially flat. We leverage this preserved flatness to design a computationally efficient feedback linearization controller that is easily tunable with linear control techniques and cancels aerodynamic disturbances via feedforward compensation. Hardware experiments demonstrate our framework reduces average tracking errors by 31% compared to nominal baselines. Crucially, our lightweight approach matches the tracking performance of state-of-the-art nonlinear model predictive control (NMPC) while requiring an order of magnitude less computation. We are the first to show that stable, tight formation flight can be achieved with under 30 seconds of training data and a 5ms loop rate, unlocking high-fidelity aerodynamic compensation for compute-constrained flight stacks.

Robots deployed in the real world rarely operate under a single fixed dynamics model: wind changes, payloads vary, batteries drain, contacts shift, and hardware wears. Yet most learning-based controllers are trained once and deployed as if learning were complete. This prevents the robot from using deployment experience to further improve task performance. In this work, we propose a continual learning framework that uses real-world experience to improve robot policies under hidden and recurring dynamics. Our method learns a condition-aware dynamics model from real state-action trajectories by combining an analytical physics prior with a neural residual for unmodeled effects. A recurrent encoder infers the current hidden condition from recent interaction, and this estimate conditions both the residual model and the policy. Policy learning is performed via differentiable simulation using diverse learned dynamics sampled from the latent model. At deployment, these sampled conditions are replaced by conditions inferred online from recent real interaction, allowing the policy to recover recurring dynamics by recognition rather than residual re-fitting. Through extensive simulation studies and real-world experiments, we demonstrate that the framework improves policy performance under diverse unobserved disturbances. On real quadrotor trajectory tracking under changing wind, the policy recovers from recurring disturbances in roughly 1s, about 5x faster than online residual re-fitting. It also reduces large-disturbance hover and tracking errors by 65.7% and 53.3% over the state-of-the-art online adaptation approaches

Accurate dynamics models are essential for model-based robotic control, yet nominal Euler--Lagrange models often become inaccurate in the presence of payload variation, unmodeled coupling, friction, aerodynamic effects, and changing operating conditions. Most learning-based correction methods improve prediction accuracy by introducing a single additive residual, but do not preserve the internal mechanical structure of Euler--Lagrange systems. This leads to models that do not preserve symmetry, positive-definiteness, or the coupling between inertia and velocity-dependent terms, which can result in physically inconsistent predictions and reduced reliability when embedded in model-based controllers. We propose a structure-preserving residual learning framework that decomposes model mismatch into an inertia correction, the corresponding induced Coriolis term, and a generalized-force residual. The mechanical component is learned under physical constraints, while the disturbance-sensitive component is represented through a sparse history-dependent latent interaction model and adapted online using Bayesian linear regression. This separation preserves key mechanical structure while restricting adaptation to the part of the dynamics most affected by changing conditions. Experiments across multiple robotic platforms, including mobile, aerial, and manipulator systems, show that the proposed method improves dynamics prediction and trajectory tracking under coupled and time-varying dynamics. These results highlight the value of combining structured residual modeling, compact latent interaction selection, and selective online adaptation for real-world model-based control.

Accurate dynamics models are critical for aerial manipulators operating under complex tasks such as payload transport. However, modeling these systems remains fundamentally challenging due to strong quadrotor-manipulator coupling, delayed aerodynamic interactions, and regime-dependent dynamics variations arising from payload changes and manipulator reconfiguration. These effects produce residual dynamics that are simultaneously cross-coupled, history-dependent, and nonstationary, causing both analytical models and purely offline learned models to degrade during deployment. To address these challenges, we propose a structured encoder-decoder framework for adaptive residual dynamics learning in aerial manipulators. The proposed nonlinear latent encoder captures cross-variable coupling and temporal dependencies from state-input histories, while a lightweight linear latent decoder enables online adaptation under regime-dependent nonstationary dynamics. The linear-in-parameter decoder structure permits closed-form Bayesian adaptation together with consistency-driven covariance inflation, enabling rapid and stable adaptation to both transient and slowly varying dynamics changes while remaining compatible with real-time model predictive control (MPC). Experimental results on a real aerial manipulation platform demonstrate improved residual prediction accuracy, faster adaptation under changing operating conditions, and enhanced MPC-based trajectory tracking performance. These results highlight the importance of jointly modeling coupled temporal dynamics and deployment-time nonstationarity for reliable aerial manipulation.

Data-driven Model Predictive Control (MPC) has lately been the core research subject in the field of control theory. The combination of an optimal control framework with deep learning paradigms opens up the possibility to accurately track control tasks without the need for complex analytical models. However, the system dynamics are often nuanced and the neural model lacks the potential to understand physical properties such as inertia and conservation of energy. In this work, we propose a novel energy-based regularization loss function which is applied to the training of a neural model that learns the residual dynamics of an omnidirectional aerial robot. Our energy-based regularization encourages the neural network to cause control corrections that stabilize the energy of the system. The residual dynamics are integrated into the MPC framework and improve the positional mean absolute error (MAE) over three real-world experiments by 23% compared to an analytical MPC. We also compare our method to a standard neural MPC implementation without regularization and primarily achieve a significantly increased flight stability implicitly due to the energy regularization and up to 15% lower MAE. Our code is available under: https://github.com/johanneskbl/jsk_aerial_robot/tree/develop/neural_MPC.

Classical proportional--integral--derivative (PID) control remains widely used in industrial control systems, while model predictive control (MPC) is actively studied to achieve higher performance for systems with nonlinear dynamics. Model predictive path integral (MPPI) control is a sampling-based MPC method that optimizes control inputs without gradient calculations and can handle non-differentiable models and objective functions. However, conventional MPPI directly samples control-input sequences, which can produce large temporal input increments and causes the optimization dimension to grow with the prediction horizon. This study proposes MPPI--PID control, which uses MPPI to optimize PID gains online instead of directly optimizing the control-input sequences. By replacing high-dimensional input-sequence optimization with low-dimensional gain-space optimization while retaining the PID structure, the proposed formulation improves sampling efficiency and promotes smoother control inputs. Theoretical analyses are provided for a unified path-integral update, the relation between optimization dimension and effective sample size, and the temporal correlation of input perturbations induced by the PID structure. The method is evaluated on a learning-based path following of a mini forklift using a residual-learning dynamics model that combines a physical model and a neural network identified from real-machine driving data. Numerical results show that MPPI--PID improves tracking performance over fixed-gain PID, yields smaller input increments than conventional MPPI, and maintains favorable performance under reduced sampling budgets.