arXiv subjects

Hongkai Dai

Publications and source records attributed to Hongkai Dai.

At least 19 recordsLinked to original sources

arXiv2026

OGPO: Sample Efficient Full-Finetuning of Generative Control Policies

Generative control policies (GCPs), such as diffusion- and flow-based control policies, have emerged as effective parameterizations for robot learning. This work introduces Off-policy Generative Policy Optimization (OGPO), a sample-efficient algorithm for finetuning GCPs that maintains off-policy critic networks to maximize data reuse and propagate policy gradients through the full generative process of the policy via a modified PPO objective, using critics as the terminal reward. OGPO achieves state-of-the-art performance on manipulation tasks spanning multi-task settings, high-precision insertion, and dexterous control. To our knowledge, it is also the only method that can fine-tune poorly-initialized behavior cloning policies to near full task-success with no expert data in the online replay buffer, and does so with few task-specific hyperparameter tuning. Through extensive empirical investigations, we demonstrate that OGPO drastically outperforms methods alternatives on policy steering and learning residual corrections, and identify the key mechanisms behind its performance. We further introduce practical stabilization tricks, including success-buffer regularization, two-sided conservative advantages, and Q-variance reduction, to mitigate critic over-exploitation across state- and pixel-based settings. Beyond proposing OGPO, we conduct a systematic empirical study of GCP finetuning, identifying the stabilizing mechanisms and failure modes that govern successful off-policy full-policy improvement.

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arXiv2025

A Careful Examination of Large Behavior Models for Multitask Dexterous Manipulation

Robot manipulation has seen tremendous progress in recent years, with imitation learning policies enabling successful performance of dexterous and hard-to-model tasks. Concurrently, scaling data and model size has led to the development of capable language and vision foundation models, motivating large-scale efforts to create general-purpose robot foundation models. While these models have garnered significant enthusiasm and investment, meaningful evaluation of real-world performance remains a challenge, limiting both the pace of development and inhibiting a nuanced understanding of current capabilities. In this paper, we rigorously evaluate multitask robot manipulation policies, referred to as Large Behavior Models (LBMs), by extending the Diffusion Policy paradigm across a corpus of simulated and real-world robot data. We propose and validate an evaluation pipeline to rigorously analyze the capabilities of these models with statistical confidence. We compare against single-task baselines through blind, randomized trials in a controlled setting, using both simulation and real-world experiments. We find that multi-task pretraining makes the policies more successful and robust, and enables teaching complex new tasks more quickly, using a fraction of the data when compared to single-task baselines. Moreover, performance predictably increases as pretraining scale and diversity grows. Project page: https://toyotaresearchinstitute.github.io/lbm1/

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arXiv2025

Steerable Scene Generation with Post Training and Inference-Time Search

Training robots in simulation requires diverse 3D scenes that reflect the specific challenges of downstream tasks. However, scenes that satisfy strict task requirements, such as high-clutter environments with plausible spatial arrangement, are rare and costly to curate manually. Instead, we generate large-scale scene data using procedural models that approximate realistic environments for robotic manipulation, and adapt it to task-specific goals. We do this by training a unified diffusion-based generative model that predicts which objects to place from a fixed asset library, along with their SE(3) poses. This model serves as a flexible scene prior that can be adapted using reinforcement learning-based post training, conditional generation, or inference-time search, steering generation toward downstream objectives even when they differ from the original data distribution. Our method enables goal-directed scene synthesis that respects physical feasibility and scales across scene types. We introduce a novel MCTS-based inference-time search strategy for diffusion models, enforce feasibility via projection and simulation, and release a dataset of over 44 million SE(3) scenes spanning five diverse environments. Website with videos, code, data, and model weights: https://steerable-scene-generation.github.io/

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arXiv2024

Diffusion Policy Policy Optimization

We introduce Diffusion Policy Policy Optimization, DPPO, an algorithmic framework including best practices for fine-tuning diffusion-based policies (e.g. Diffusion Policy) in continuous control and robot learning tasks using the policy gradient (PG) method from reinforcement learning (RL). PG methods are ubiquitous in training RL policies with other policy parameterizations; nevertheless, they had been conjectured to be less efficient for diffusion-based policies. Surprisingly, we show that DPPO achieves the strongest overall performance and efficiency for fine-tuning in common benchmarks compared to other RL methods for diffusion-based policies and also compared to PG fine-tuning of other policy parameterizations. Through experimental investigation, we find that DPPO takes advantage of unique synergies between RL fine-tuning and the diffusion parameterization, leading to structured and on-manifold exploration, stable training, and strong policy robustness. We further demonstrate the strengths of DPPO in a range of realistic settings, including simulated robotic tasks with pixel observations, and via zero-shot deployment of simulation-trained policies on robot hardware in a long-horizon, multi-stage manipulation task. Website with code: diffusion-ppo.github.io

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arXiv2024

Verification and Synthesis of Compatible Control Lyapunov and Control Barrier Functions

Safety and stability are essential properties of control systems. Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) are powerful tools to ensure safety and stability respectively. However, previous approaches typically verify and synthesize the CBFs and CLFs separately, satisfying their respective constraints, without proving that the CBFs and CLFs are compatible with each other, namely at every state, there exists control actions within the input limits that satisfy both the CBF and CLF constraints simultaneously. Ignoring the compatibility criteria might cause the CLF-CBF-QP controller to fail at runtime. There exists some recent works that synthesized compatible CLF and CBF, but relying on nominal polynomial or rational controllers, which is just a sufficient but not necessary condition for compatibility. In this work, we investigate verification and synthesis of compatible CBF and CLF independent from any nominal controllers. We derive exact necessary and sufficient conditions for compatibility, and further formulate Sum-Of-Squares programs for the compatibility verification. Based on our verification framework, we also design a nominal-controller-free synthesis method, which can effectively expands the compatible region, in which the system is guaranteed to be both safe and stable. We evaluate our method on a non-linear toy problem, and also a 3D quadrotor to demonstrate its scalability. The code is open-sourced at \url{https://github.com/hongkai-dai/compatible_clf_cbf}.

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arXiv2024

Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulation

Learning-based neural network (NN) control policies have shown impressive empirical performance in a wide range of tasks in robotics and control. However, formal (Lyapunov) stability guarantees over the region-of-attraction (ROA) for NN controllers with nonlinear dynamical systems are challenging to obtain, and most existing approaches rely on expensive solvers such as sums-of-squares (SOS), mixed-integer programming (MIP), or satisfiability modulo theories (SMT). In this paper, we demonstrate a new framework for learning NN controllers together with Lyapunov certificates using fast empirical falsification and strategic regularizations. We propose a novel formulation that defines a larger verifiable region-of-attraction (ROA) than shown in the literature, and refines the conventional restrictive constraints on Lyapunov derivatives to focus only on certifiable ROAs. The Lyapunov condition is rigorously verified post-hoc using branch-and-bound with scalable linear bound propagation-based NN verification techniques. The approach is efficient and flexible, and the full training and verification procedure is accelerated on GPUs without relying on expensive solvers for SOS, MIP, nor SMT. The flexibility and efficiency of our framework allow us to demonstrate Lyapunov-stable output feedback control with synthesized NN-based controllers and NN-based observers with formal stability guarantees, for the first time in literature. Source code at https://github.com/Verified-Intelligence/Lyapunov_Stable_NN_Controllers

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arXiv2023

Fighting Uncertainty with Gradients: Offline Reinforcement Learning via Diffusion Score Matching

Gradient-based methods enable efficient search capabilities in high dimensions. However, in order to apply them effectively in offline optimization paradigms such as offline Reinforcement Learning (RL) or Imitation Learning (IL), we require a more careful consideration of how uncertainty estimation interplays with first-order methods that attempt to minimize them. We study smoothed distance to data as an uncertainty metric, and claim that it has two beneficial properties: (i) it allows gradient-based methods that attempt to minimize uncertainty to drive iterates to data as smoothing is annealed, and (ii) it facilitates analysis of model bias with Lipschitz constants. As distance to data can be expensive to compute online, we consider settings where we need amortize this computation. Instead of learning the distance however, we propose to learn its gradients directly as an oracle for first-order optimizers. We show these gradients can be efficiently learned with score-matching techniques by leveraging the equivalence between distance to data and data likelihood. Using this insight, we propose Score-Guided Planning (SGP), a planning algorithm for offline RL that utilizes score-matching to enable first-order planning in high-dimensional problems, where zeroth-order methods were unable to scale, and ensembles were unable to overcome local minima. Website: https://sites.google.com/view/score-guided-planning/home

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arXiv2023

Approximate Optimal Controller Synthesis for Cart-Poles and Quadrotors via Sums-of-Squares

Sums-of-squares (SOS) optimization is a promising tool to synthesize certifiable controllers for nonlinear dynamical systems. Building upon prior works, we demonstrate that SOS can synthesize dynamic controllers with bounded suboptimal performance for various underactuated robotic systems by finding good approximations of the value function. We summarize a unified SOS framework to synthesize both under- and over- approximations of the value function for continuous-time, control-affine systems, use these approximations to generate approximate optimal controllers, and perform regional analysis on the closed-loop system driven by these controllers. We then extend the formulation to handle hybrid systems with contacts. We demonstrate that our method can generate tight under- and over- approximations of the value function with low-degree polynomials, which are used to provide stabilizing controllers for continuous-time systems including the inverted pendulum, the cart-pole, and the quadrotor as well as a hybrid system, the planar pusher. To the best of our knowledge, this is the first time that a SOS-based time-invariant controller can swing up and stabilize a cart-pole, and push the planar slider to the desired pose.

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arXiv2023

Certified Polyhedral Decompositions of Collision-Free Configuration Space

Understanding the geometry of collision-free configuration space (C-free) in the presence of task-space obstacles is an essential ingredient for collision-free motion planning. While it is possible to check for collisions at a point using standard algorithms, to date no practical method exists for computing C-free regions with rigorous certificates due to the complexity of mapping task-space obstacles through the kinematics. In this work, we present the first to our knowledge rigorous method for approximately decomposing a rational parametrization of C-free into certified polyhedral regions. Our method, called C-IRIS (C-space Iterative Regional Inflation by Semidefinite programming), generates large, convex polytopes in a rational parameterization of the configuration space which are rigorously certified to be collision-free. Such regions have been shown to be useful for both optimization-based and randomized motion planning. Based on convex optimization, our method works in arbitrary dimensions, only makes assumptions about the convexity of the obstacles in the task space, and is fast enough to scale to realistic problems in manipulation. We demonstrate our algorithm's ability to fill a non-trivial amount of collision-free C-space in several 2-DOF examples where the C-space can be visualized, as well as the scalability of our algorithm on a 7-DOF KUKA iiwa, a 6-DOF UR3e and 12-DOF bimanual manipulators. An implementation of our algorithm is open-sourced in Drake. We furthermore provide examples of our algorithm in interactive Python notebooks.

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arXiv2023

AdaptSim: Task-Driven Simulation Adaptation for Sim-to-Real Transfer

Simulation parameter settings such as contact models and object geometry approximations are critical to training robust robotic policies capable of transferring from simulation to real-world deployment. Previous approaches typically handcraft distributions over such parameters (domain randomization), or identify parameters that best match the dynamics of the real environment (system identification). However, there is often an irreducible gap between simulation and reality: attempting to match the dynamics between simulation and reality across all states and tasks may be infeasible and may not lead to policies that perform well in reality for a specific task. Addressing this issue, we propose AdaptSim, a new task-driven adaptation framework for sim-to-real transfer that aims to optimize task performance in target (real) environments -- instead of matching dynamics between simulation and reality. First, we meta-learn an adaptation policy in simulation using reinforcement learning for adjusting the simulation parameter distribution based on the current policy's performance in a target environment. We then perform iterative real-world adaptation by inferring new simulation parameter distributions for policy training, using a small amount of real data. We perform experiments in three robotic tasks: (1) swing-up of linearized double pendulum, (2) dynamic table-top pushing of a bottle, and (3) dynamic scooping of food pieces with a spatula. Our extensive simulation and hardware experiments demonstrate AdaptSim achieving 1-3x asymptotic performance and $\sim$2x real data efficiency when adapting to different environments, compared to methods based on Sys-ID and directly training the task policy in target environments. Website: https://irom-lab.github.io/AdaptSim/

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arXiv2022

Convex synthesis and verification of control-Lyapunov and barrier functions with input constraints

Control Lyapunov functions (CLFs) and control barrier functions (CBFs) are widely used tools for synthesizing controllers subject to stability and safety constraints. Paired with online optimization, they provide stabilizing control actions that satisfy input constraints and avoid unsafe regions of state-space. Designing CLFs and CBFs with rigorous performance guarantees is computationally challenging. To certify existence of control actions, current techniques not only design a CLF/CBF, but also a nominal controller. This can make the synthesis task more expensive, and performance estimation more conservative. In this work, we characterize polynomial CLFs/CBFs using sum-of-squares conditions, which can be directly certified using convex optimization. This yields a CLF and CBF synthesis technique that does not rely on a nominal controller. We then present algorithms for iteratively enlarging estimates of the stabilizable and safe regions. We demonstrate our algorithms on a 2D toy system, a pendulum and a quadrotor.

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arXiv2022

Finding and Optimizing Certified, Collision-Free Regions in Configuration Space for Robot Manipulators

Configuration space (C-space) has played a central role in collision-free motion planning, particularly for robot manipulators. While it is possible to check for collisions at a point using standard algorithms, to date no practical method exists for computing collision-free C-space regions with rigorous certificates due to the complexities of mapping task-space obstacles through the kinematics. In this work, we present the first to our knowledge method for generating such regions and certificates through convex optimization. Our method, called C-Iris (C-space Iterative Regional Inflation by Semidefinite programming), generates large, convex polytopes in a rational parametrization of the configuration space which are guaranteed to be collision-free. Such regions have been shown to be useful for both optimization-based and randomized motion planning. Our regions are generated by alternating between two convex optimization problems: (1) a simultaneous search for a maximal-volume ellipse inscribed in a given polytope and a certificate that the polytope is collision-free and (2) a maximal expansion of the polytope away from the ellipse which does not violate the certificate. The volume of the ellipse and size of the polytope are allowed to grow over several iterations while being collision-free by construction. Our method works in arbitrary dimensions, only makes assumptions about the convexity of the obstacles in the task space, and scales to realistic problems in manipulation. We demonstrate our algorithm's ability to fill a non-trivial amount of collision-free C-space in a 3-DOF example where the C-space can be visualized, as well as the scalability of our algorithm on a 7-DOF KUKA iiwa and a 12-DOF bimanual manipulator.

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arXiv2021

Lyapunov-stable neural-network control

Deep learning has had a far reaching impact in robotics. Specifically, deep reinforcement learning algorithms have been highly effective in synthesizing neural-network controllers for a wide range of tasks. However, despite this empirical success, these controllers still lack theoretical guarantees on their performance, such as Lyapunov stability (i.e., all trajectories of the closed-loop system are guaranteed to converge to a goal state under the control policy). This is in stark contrast to traditional model-based controller design, where principled approaches (like LQR) can synthesize stable controllers with provable guarantees. To address this gap, we propose a generic method to synthesize a Lyapunov-stable neural-network controller, together with a neural-network Lyapunov function to simultaneously certify its stability. Our approach formulates the Lyapunov condition verification as a mixed-integer linear program (MIP). Our MIP verifier either certifies the Lyapunov condition, or generates counter examples that can help improve the candidate controller and the Lyapunov function. We also present an optimization program to compute an inner approximation of the region of attraction for the closed-loop system. We apply our approach to robots including an inverted pendulum, a 2D and a 3D quadrotor, and showcase that our neural-network controller outperforms a baseline LQR controller. The code is open sourced at \url{https://github.com/StanfordASL/neural-network-lyapunov}.

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arXiv2021

Dexterous Manipulation Primitives for the Real Robot Challenge

This report describes our approach for Phase 3 of the Real Robot Challenge. To solve cuboid manipulation tasks of varying difficulty, we decompose each task into the following primitives: moving the fingers to the cuboid to grasp it, turning it on the table to minimize orientation error, and re-positioning it to the goal position. We use model-based trajectory optimization and control to plan and execute these primitives. These grasping, turning, and re-positioning primitives are sequenced with a state-machine that determines which primitive to execute given the current object state and goal. Our method shows robust performance over multiple runs with randomized initial and goal positions. With this approach, our team placed second in the challenge, under the anonymous name "sombertortoise" on the leaderboard. Example runs of our method solving each of the four levels can be seen in this video (https://www.youtube.com/watch?v=I65Kwu9PGmg&list=PLt9QxrtaftrHGXcp4Oh8-s_OnQnBnLtei&index=1).

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arXiv2019

A Convex-Combinatorial Model for Planar Caging

Caging is a promising tool which allows a robot to manipulate an object without directly reasoning about the contact dynamics involved. Furthermore, caging also provides useful guarantees in terms of robustness to uncertainty, and often serves as a way-point to a grasp. Unfortunately, previous work on caging is often based on computational geometry or discrete topology tools, causing restriction on gripper geometry, and difficulty on integration into larger manipulation frameworks. In this paper, we develop a convex-combinatorial model to characterize caging from an optimization perspective. More specifically, we study the configuration space of the object, where the fingers act as obstacles that enclose the configuration of the object. The convex-combinatorial nature of this approach provides guarantees on optimality, convergence and scalability, and its optimization nature makes it adaptable for further applications on robot manipulation tasks.

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arXiv2019

Simultaneous Contact, Gait and Motion Planning for Robust Multi-Legged Locomotion via Mixed-Integer Convex Optimization

Traditional motion planning approaches for multi-legged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or non-convex optimization with intractable computation time. In this paper, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a pre-specified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robot's torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where non-convexity and flat terrain assumptions might lead to sub-optimal or unstable plans. Our method increases the motion generality while keeping a low computation time.

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arXiv2018

Application of Wrench based Feasibility Analysis to the Online Trajectory Optimization of Legged Robots

Motion planning in multi-contact scenarios has recently gathered interest within the legged robotics community, however actuator force/torque limits are rarely considered. We believe that these limits gain paramount importance when the complexity of the terrains to be traversed increases. We build on previous research from the field of robotic grasping to propose two new six-dimensional bounded polytopes named the Actuation Wrench Polytope (AWP) and the Feasible Wrench Polytope (FWP). We define the AWP as the set of all the wrenches that a robot can generate while considering its actuation limits. This considers the admissible contact forces that the robot can generate given its current configuration and actuation capabilities. The Contact Wrench Cone (CWC), instead, includes features of the environment such as the contact normal or the friction coefficient. The intersection of the AWP and of the CWC results in a convex polytope, the FWP, which turns out to be more descriptive of the real robot capabilities than existing simplified models, while maintaining the same compact representation. We explain how to efficiently compute the vertex-description of the FWP that is then used to evaluate a feasibility factor that we adapted from the field of robotic grasping. This allows us to optimize for robustness to external disturbance wrenches. Based on this, we present an implementation of a motion planner for our quadruped robot HyQ that provides online Center of Mass (CoM) trajectories that are guaranteed to be statically stable and actuation consistent.

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arXiv2017

The Actuation-consistent Wrench Polytope (AWP) and the Feasible Wrench Polytope (FWP)

The motivation of our current research is to devise motion planners for legged locomotion that are able to exploit the robot's actuation capabilities. This means, when possible, to minimize joint torques or to propel as much as admissible when required. For this reason we define two new 6 dimensional bounded polytopes that we name Actuation-consistent Wrench Polytope (AWP) and Feasible Wrench Polytope (FWP). These objects turn out to be very useful in motion planning for the definition of constraints on the accelerations of the Center of Mass of the robot that respect the friction cones and the actuation limits. The AWP and the FWP could be used also in the robot design phase to size the actuators of the system based on some predefined reference motion.

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