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In this work, we introduce general purpose touch representations for the increasingly accessible class of vision-based tactile sensors. Such sensors have led to many recent advances in robot manipulation as they markedly complement vision, yet solutions today often rely on task and sensor specific handcrafted perception models. Collecting real data at scale with task centric ground truth labels, like contact forces and slip, is a challenge further compounded by sensors of various form factor differing in aspects like lighting and gel markings. To tackle this we turn to self-supervised learning (SSL) that has demonstrated remarkable performance in computer vision. We present Sparsh, a family of SSL models that can support various vision-based tactile sensors, alleviating the need for custom labels through pre-training on 460k+ tactile images with masking and self-distillation in pixel and latent spaces. We also build TacBench, to facilitate standardized benchmarking across sensors and models, comprising of six tasks ranging from comprehending tactile properties to enabling physical perception and manipulation planning. In evaluations, we find that SSL pre-training for touch representation outperforms task and sensor-specific end-to-end training by 95.1% on average over TacBench, and Sparsh (DINO) and Sparsh (IJEPA) are the most competitive, indicating the merits of learning in latent space for tactile images. Project page: https://sparsh-ssl.github.io/, Comment: Conference on Robot Learning (CoRL), 2024

In order to mitigate the sample complexity of real-world reinforcement learning, common practice is to first train a policy in a simulator where samples are cheap, and then deploy this policy in the real world, with the hope that it generalizes effectively. Such \emph{direct sim2real} transfer is not guaranteed to succeed, however, and in cases where it fails, it is unclear how to best utilize the simulator. In this work, we show that in many regimes, while direct sim2real transfer may fail, we can utilize the simulator to learn a set of \emph{exploratory} policies which enable efficient exploration in the real world. In particular, in the setting of low-rank MDPs, we show that coupling these exploratory policies with simple, practical approaches -- least-squares regression oracles and naive randomized exploration -- yields a polynomial sample complexity in the real world, an exponential improvement over direct sim2real transfer, or learning without access to a simulator. To the best of our knowledge, this is the first evidence that simulation transfer yields a provable gain in reinforcement learning in settings where direct sim2real transfer fails. We validate our theoretical results on several realistic robotic simulators and a real-world robotic sim2real task, demonstrating that transferring exploratory policies can yield substantial gains in practice as well., Comment: NeurIPS 2024

We focus on agile, continuous, and terrain-adaptive jumping of quadrupedal robots in discontinuous terrains such as stairs and stepping stones. Unlike single-step jumping, continuous jumping requires accurately executing highly dynamic motions over long horizons, which is challenging for existing approaches. To accomplish this task, we design a hierarchical learning and control framework, which consists of a learned heightmap predictor for robust terrain perception, a reinforcement-learning-based centroidal-level motion policy for versatile and terrain-adaptive planning, and a low-level model-based leg controller for accurate motion tracking. In addition, we minimize the sim-to-real gap by accurately modeling the hardware characteristics. Our framework enables a Unitree Go1 robot to perform agile and continuous jumps on human-sized stairs and sparse stepping stones, for the first time to the best of our knowledge. In particular, the robot can cross two stair steps in each jump and completes a 3.5m long, 2.8m high, 14-step staircase in 4.5 seconds. Moreover, the same policy outperforms baselines in various other parkour tasks, such as jumping over single horizontal or vertical discontinuities. Experiment videos can be found at https://yxyang.github.io/jumping_cod/, Comment: Website: https://yxyang.github.io/jumping_cod/

Current developments in autonomous off-road driving are steadily increasing performance through higher speeds and more challenging, unstructured environments. However, this operating regime subjects the vehicle to larger inertial effects, where consideration of higher-order states is necessary to avoid failures such as rollovers or excessive impact forces. Aggressive driving through Model Predictive Control (MPC) in these conditions requires dynamics models that accurately predict safety-critical information. This work aims to empirically quantify this aggressive operating regime and its effects on the performance of current models. We evaluate three dynamics models of varying complexity on two distinct off-road driving datasets: one simulated and the other real-world. By conditioning trajectory data on higher-order states, we show that model accuracy degrades with aggressiveness and simpler models degrade faster. These models are also validated across datasets, where accuracies over safety-critical states are reported and provide benchmarks for future work., Comment: Accepted to ICRA 2024 Workshop on Resilient Off-road Autonomy

Quadrupedal robots have emerged as versatile agents capable of locomoting and manipulating in complex environments. Traditional designs typically rely on the robot's inherent body parts or incorporate top-mounted arms for manipulation tasks. However, these configurations may limit the robot's operational dexterity, efficiency and adaptability, particularly in cluttered or constrained spaces. In this work, we present LocoMan, a dexterous quadrupedal robot with a novel morphology to perform versatile manipulation in diverse constrained environments. By equipping a Unitree Go1 robot with two low-cost and lightweight modular 3-DoF loco-manipulators on its front calves, LocoMan leverages the combined mobility and functionality of the legs and grippers for complex manipulation tasks that require precise 6D positioning of the end effector in a wide workspace. To harness the loco-manipulation capabilities of LocoMan, we introduce a unified control framework that extends the whole-body controller (WBC) to integrate the dynamics of loco-manipulators. Through experiments, we validate that the proposed whole-body controller can accurately and stably follow desired 6D trajectories of the end effector and torso, which, when combined with the large workspace from our design, facilitates a diverse set of challenging dexterous loco-manipulation tasks in confined spaces, such as opening doors, plugging into sockets, picking objects in narrow and low-lying spaces, and bimanual manipulation., Comment: Project page: https://linchangyi1.github.io/LocoMan

We focus on the problem of long-range dynamic replanning for off-road autonomous vehicles, where a robot plans paths through a previously unobserved environment while continuously receiving noisy local observations. An effective approach for planning under sensing uncertainty is determinization, where one converts a stochastic world into a deterministic one and plans under this simplification. This makes the planning problem tractable, but the cost of following the planned path in the real world may be different than in the determinized world. This causes collisions if the determinized world optimistically ignores obstacles, or causes unnecessarily long routes if the determinized world pessimistically imagines more obstacles. We aim to be robust to uncertainty over potential worlds while still achieving the efficiency benefits of determinization. We evaluate algorithms for dynamic replanning on a large real-world dataset of challenging long-range planning problems from the DARPA RACER program. Our method, Dynamic Replanning via Evaluating and Aggregating Multiple Samples (DREAMS), outperforms other determinization-based approaches in terms of combined traversal time and collision cost. https://sites.google.com/cs.washington.edu/dreams/

Reliable estimation of terrain traversability is critical for the successful deployment of autonomous systems in wild, outdoor environments. Given the lack of large-scale annotated datasets for off-road navigation, strictly-supervised learning approaches remain limited in their generalization ability. To this end, we introduce a novel, image-based self-supervised learning method for traversability prediction, leveraging a state-of-the-art vision foundation model for improved out-of-distribution performance. Our method employs contrastive representation learning using both human driving data and instance-based segmentation masks during training. We show that this simple, yet effective, technique drastically outperforms recent methods in predicting traversability for both on- and off-trail driving scenarios. We compare our method with recent baselines on both a common benchmark as well as our own datasets, covering a diverse range of outdoor environments and varied terrain types. We also demonstrate the compatibility of resulting costmap predictions with a model-predictive controller. Finally, we evaluate our approach on zero- and few-shot tasks, demonstrating unprecedented performance for generalization to new environments. Videos and additional material can be found here: https://sites.google.com/view/visual-traversability-learning., Comment: ICRA 2024; 8 pages

Terrain traversability in unstructured off-road autonomy has traditionally relied on semantic classification, resource-intensive dynamics models, or purely geometry-based methods to predict vehicle-terrain interactions. While inconsequential at low speeds, uneven terrain subjects our full-scale system to safety-critical challenges at operating speeds of 7--10 m/s. This study focuses particularly on uneven terrain such as hills, banks, and ditches. These common high-risk geometries are capable of disabling the vehicle and causing severe passenger injuries if poorly traversed. We introduce a physics-based framework for identifying traversability constraints on terrain dynamics. Using this framework, we derive two fundamental constraints, each with a focus on mitigating rollover and ditch-crossing failures while being fully parallelizable in the sample-based Model Predictive Control (MPC) framework. In addition, we present the design of our planning and control system, which implements our parallelized constraints in MPC and utilizes a low-level controller to meet the demands of our aggressive driving without prior information about the environment and its dynamics. Through real-world experimentation and traversal of hills and ditches, we demonstrate that our approach captures fundamental elements of safe and aggressive autonomy over uneven terrain. Our approach improves upon geometry-based methods by completing comprehensive off-road courses up to 22% faster while maintaining safe operation., Comment: Accepted to R:SS 2024

Precise arbitrary trajectory tracking for quadrotors is challenging due to unknown nonlinear dynamics, trajectory infeasibility, and actuation limits. To tackle these challenges, we present Deep Adaptive Trajectory Tracking (DATT), a learning-based approach that can precisely track arbitrary, potentially infeasible trajectories in the presence of large disturbances in the real world. DATT builds on a novel feedforward-feedback-adaptive control structure trained in simulation using reinforcement learning. When deployed on real hardware, DATT is augmented with a disturbance estimator using L1 adaptive control in closed-loop, without any fine-tuning. DATT significantly outperforms competitive adaptive nonlinear and model predictive controllers for both feasible smooth and infeasible trajectories in unsteady wind fields, including challenging scenarios where baselines completely fail. Moreover, DATT can efficiently run online with an inference time less than 3.2 ms, less than 1/4 of the adaptive nonlinear model predictive control baseline

A major challenge in robotics is to design robust policies which enable complex and agile behaviors in the real world. On one end of the spectrum, we have model-free reinforcement learning (MFRL), which is incredibly flexible and general but often results in brittle policies. In contrast, model predictive control (MPC) continually re-plans at each time step to remain robust to perturbations and model inaccuracies. However, despite its real-world successes, MPC often under-performs the optimal strategy. This is due to model quality, myopic behavior from short planning horizons, and approximations due to computational constraints. And even with a perfect model and enough compute, MPC can get stuck in bad local optima, depending heavily on the quality of the optimization algorithm. To this end, we propose Deep Model Predictive Optimization (DMPO), which learns the inner-loop of an MPC optimization algorithm directly via experience, specifically tailored to the needs of the control problem. We evaluate DMPO on a real quadrotor agile trajectory tracking task, on which it improves performance over a baseline MPC algorithm for a given computational budget. It can outperform the best MPC algorithm by up to 27% with fewer samples and an end-to-end policy trained with MFRL by 19%. Moreover, because DMPO requires fewer samples, it can also achieve these benefits with 4.3X less memory. When we subject the quadrotor to turbulent wind fields with an attached drag plate, DMPO can adapt zero-shot while still outperforming all baselines. Additional results can be found at https://tinyurl.com/mr2ywmnw., Comment: Main paper is 6 pages with 4 figures and 1 table. Code available at: https://github.com/jisacks/dmpo

Robotic manipulation tasks such as object insertion typically involve interactions between object and environment, namely extrinsic contacts. Prior work on Neural Contact Fields (NCF) use intrinsic tactile sensing between gripper and object to estimate extrinsic contacts in simulation. However, its effectiveness and utility in real-world tasks remains unknown. In this work, we improve NCF to enable sim-to-real transfer and use it to train policies for mug-in-cupholder and bowl-in-dishrack insertion tasks. We find our model NCF-v2, is capable of estimating extrinsic contacts in the real-world. Furthermore, our insertion policy with NCF-v2 outperforms policies without it, achieving 33% higher success and 1.36x faster execution on mug-in-cupholder, and 13% higher success and 1.27x faster execution on bowl-in-dishrack., Comment: Under review

We present CAJun, a novel hierarchical learning and control framework that enables legged robots to jump continuously with adaptive jumping distances. CAJun consists of a high-level centroidal policy and a low-level leg controller. In particular, we use reinforcement learning (RL) to train the centroidal policy, which specifies the gait timing, base velocity, and swing foot position for the leg controller. The leg controller optimizes motor commands for the swing and stance legs according to the gait timing to track the swing foot target and base velocity commands using optimal control. Additionally, we reformulate the stance leg optimizer in the leg controller to speed up policy training by an order of magnitude. Our system combines the versatility of learning with the robustness of optimal control. By combining RL with optimal control methods, our system achieves the versatility of learning while enjoys the robustness from control methods, making it easily transferable to real robots. We show that after 20 minutes of training on a single GPU, CAJun can achieve continuous, long jumps with adaptive distances on a Go1 robot with small sim-to-real gaps. Moreover, the robot can jump across gaps with a maximum width of 70cm, which is over 40% wider than existing methods., Comment: Please visit https://yxyang.github.io/cajun/ for additional results

Autocurricular training is an important sub-area of multi-agent reinforcement learning~(MARL) that allows multiple agents to learn emergent skills in an unsupervised co-evolving scheme. The robotics community has experimented autocurricular training with physically grounded problems, such as robust control and interactive manipulation tasks. However, the asymmetric nature of these tasks makes the generation of sophisticated policies challenging. Indeed, the asymmetry in the environment may implicitly or explicitly provide an advantage to a subset of agents which could, in turn, lead to a low-quality equilibrium. This paper proposes a novel game-theoretic algorithm, Stackelberg Multi-Agent Deep Deterministic Policy Gradient (ST-MADDPG), which formulates a two-player MARL problem as a Stackelberg game with one player as the `leader' and the other as the `follower' in a hierarchical interaction structure wherein the leader has an advantage. We first demonstrate that the leader's advantage from ST-MADDPG can be used to alleviate the inherent asymmetry in the environment. By exploiting the leader's advantage, ST-MADDPG improves the quality of a co-evolution process and results in more sophisticated and complex strategies that work well even against an unseen strong opponent.

Jumping is essential for legged robots to traverse through difficult terrains. In this work, we propose a hierarchical framework that combines optimal control and reinforcement learning to learn continuous jumping motions for quadrupedal robots. The core of our framework is a stance controller, which combines a manually designed acceleration controller with a learned residual policy. As the acceleration controller warm starts policy for efficient training, the trained policy overcomes the limitation of the acceleration controller and improves the jumping stability. In addition, a low-level whole-body controller converts the body pose command from the stance controller to motor commands. After training in simulation, our framework can be deployed directly to the real robot, and perform versatile, continuous jumping motions, including omni-directional jumps at up to 50cm high, 60cm forward, and jump-turning at up to 90 degrees. Please visit our website for more results: https://sites.google.com/view/learning-to-jump., Comment: To be presented at L4DC 2023

Simulating vision-based tactile sensors enables learning models for contact-rich tasks when collecting real world data at scale can be prohibitive. However, modeling the optical response of the gel deformation as well as incorporating the dynamics of the contact makes sim2real challenging. Prior works have explored data augmentation, fine-tuning, or learning generative models to reduce the sim2real gap. In this work, we present the first method to leverage probabilistic diffusion models for capturing complex illumination changes from gel deformations. Our tactile diffusion model is able to generate realistic tactile images from simulated contact depth bridging the reality gap for vision-based tactile sensing. On real braille reading task with a DIGIT sensor, a classifier trained with our diffusion model achieves 75.74% accuracy outperforming classifiers trained with simulation and other approaches. Project page: https://github.com/carolinahiguera/Tactile-Diffusion

Effective use of camera-based vision systems is essential for robust performance in autonomous off-road driving, particularly in the high-speed regime. Despite success in structured, on-road settings, current end-to-end approaches for scene prediction have yet to be successfully adapted for complex outdoor terrain. To this end, we present TerrainNet, a vision-based terrain perception system for semantic and geometric terrain prediction for aggressive, off-road navigation. The approach relies on several key insights and practical considerations for achieving reliable terrain modeling. The network includes a multi-headed output representation to capture fine- and coarse-grained terrain features necessary for estimating traversability. Accurate depth estimation is achieved using self-supervised depth completion with multi-view RGB and stereo inputs. Requirements for real-time performance and fast inference speeds are met using efficient, learned image feature projections. Furthermore, the model is trained on a large-scale, real-world off-road dataset collected across a variety of diverse outdoor environments. We show how TerrainNet can also be used for costmap prediction and provide a detailed framework for integration into a planning module. We demonstrate the performance of TerrainNet through extensive comparison to current state-of-the-art baselines for camera-only scene prediction. Finally, we showcase the effectiveness of integrating TerrainNet within a complete autonomous-driving stack by conducting a real-world vehicle test in a challenging off-road scenario.

Sampling-based Model Predictive Control (MPC) is a flexible control framework that can reason about non-smooth dynamics and cost functions. Recently, significant work has focused on the use of machine learning to improve the performance of MPC, often through learning or fine-tuning the dynamics or cost function. In contrast, we focus on learning to optimize more effectively. In other words, to improve the update rule within MPC. We show that this can be particularly useful in sampling-based MPC, where we often wish to minimize the number of samples for computational reasons. Unfortunately, the cost of computational efficiency is a reduction in performance; fewer samples results in noisier updates. We show that we can contend with this noise by learning how to update the control distribution more effectively and make better use of the few samples that we have. Our learned controllers are trained via imitation learning to mimic an expert which has access to substantially more samples. We test the efficacy of our approach on multiple simulated robotics tasks in sample-constrained regimes and demonstrate that our approach can outperform a MPC controller with the same number of samples., Comment: Proceedings of the IEEE Conference on Robotics and Automation (ICRA), 2022. Paper is 6 pages with 2 figures and 2 tables

Sampling-based methods have become a cornerstone of contemporary approaches to Model Predictive Control (MPC), as they make no restrictions on the differentiability of the dynamics or cost function and are straightforward to parallelize. However, their efficacy is highly dependent on the quality of the sampling distribution itself, which is often assumed to be simple, like a Gaussian. This restriction can result in samples which are far from optimal, leading to poor performance. Recent work has explored improving the performance of MPC by sampling in a learned latent space of controls. However, these methods ultimately perform all MPC parameter updates and warm-starting between time steps in the control space. This requires us to rely on a number of heuristics for generating samples and updating the distribution and may lead to sub-optimal performance. Instead, we propose to carry out all operations in the latent space, allowing us to take full advantage of the learned distribution. Specifically, we frame the learning problem as bi-level optimization and show how to train the controller with backpropagation-through-time. By using a normalizing flow parameterization of the distribution, we can leverage its tractable density to avoid requiring differentiability of the dynamics and cost function. Finally, we evaluate the proposed approach on simulated robotics tasks and demonstrate its ability to surpass the performance of prior methods and scale better with a reduced number of samples., Comment: Accepted at the Conference on Robot Learning (CoRL), 2022. Main paper is 9 pages with 4 figures. Appendix is 12 pages with 11 figures and 1 table

Collision-free motion generation in unknown environments is a core building block for robot manipulation. Generating such motions is challenging due to multiple objectives; not only should the solutions be optimal, the motion generator itself must be fast enough for real-time performance and reliable enough for practical deployment. A wide variety of methods have been proposed ranging from local controllers to global planners, often being combined to offset their shortcomings. We present an end-to-end neural model called Motion Policy Networks (M$\pi$Nets) to generate collision-free, smooth motion from just a single depth camera observation. M$\pi$Nets are trained on over 3 million motion planning problems in over 500,000 environments. Our experiments show that M$\pi$Nets are significantly faster than global planners while exhibiting the reactivity needed to deal with dynamic scenes. They are 46% better than prior neural planners and more robust than local control policies. Despite being only trained in simulation, M$\pi$Nets transfer well to the real robot with noisy partial point clouds. Code and data are publicly available at https://mpinets.github.io., Comment: To be published in the Conference on Robot Learning (CoRL) 2022. 10 pages with 4 figures. Appendix has 10 pages and 1 figure

We present Neural Contact Fields, a method that brings together neural fields and tactile sensing to address the problem of tracking extrinsic contact between object and environment. Knowing where the external contact occurs is a first step towards methods that can actively control it in facilitating downstream manipulation tasks. Prior work for localizing environmental contacts typically assume a contact type (e.g. point or line), does not capture contact/no-contact transitions, and only works with basic geometric-shaped objects. Neural Contact Fields are the first method that can track arbitrary multi-modal extrinsic contacts without making any assumptions about the contact type. Our key insight is to estimate the probability of contact for any 3D point in the latent space of object shapes, given vision-based tactile inputs that sense the local motion resulting from the external contact. In experiments, we find that Neural Contact Fields are able to localize multiple contact patches without making any assumptions about the geometry of the contact, and capture contact/no-contact transitions for known categories of objects with unseen shapes in unseen environment configurations. In addition to Neural Contact Fields, we also release our YCB-Extrinsic-Contact dataset of simulated extrinsic contact interactions to enable further research in this area. Project page: https://github.com/carolinahiguera/NCF, Comment: 2023 International Conference on Robotics and Automation (ICRA)

The semantics of the environment, such as the terrain type and property, reveals important information for legged robots to adjust their behaviors. In this work, we present a framework that learns semantics-aware locomotion skills from perception for quadrupedal robots, such that the robot can traverse through complex offroad terrains with appropriate speeds and gaits using perception information. Due to the lack of high-fidelity outdoor simulation, our framework needs to be trained directly in the real world, which brings unique challenges in data efficiency and safety. To ensure sample efficiency, we pre-train the perception model with an off-road driving dataset. To avoid the risks of real-world policy exploration, we leverage human demonstration to train a speed policy that selects a desired forward speed from camera image. For maximum traversability, we pair the speed policy with a gait selector, which selects a robust locomotion gait for each forward speed. Using only 40 minutes of human demonstration data, our framework learns to adjust the speed and gait of the robot based on perceived terrain semantics, and enables the robot to walk over 6km without failure at close-to-optimal speed.

In this paper, we focus on the problem of integrating Energy-based Models (EBM) as guiding priors for motion optimization. EBMs are a set of neural networks that can represent expressive probability density distributions in terms of a Gibbs distribution parameterized by a suitable energy function. Due to their implicit nature, they can easily be integrated as optimization factors or as initial sampling distributions in the motion optimization problem, making them good candidates to integrate data-driven priors in the motion optimization problem. In this work, we present a set of required modeling and algorithmic choices to adapt EBMs into motion optimization. We investigate the benefit of including additional regularizers in the learning of the EBMs to use them with gradient-based optimizers and we present a set of EBM architectures to learn generalizable distributions for manipulation tasks. We present multiple cases in which the EBM could be integrated for motion optimization and evaluate the performance of learned EBMs as guiding priors for both simulated and real robot experiments., Comment: 17 pages, accepted at IEEE/RSJ IROS 2022, paper website: https://sites.google.com/view/implicit-priors/home

This project aims to motivate research in competitive human-robot interaction by creating a robot competitor that can challenge human users in certain scenarios such as physical exercise and games. With this goal in mind, we introduce the Fencing Game, a human-robot competition used to evaluate both the capabilities of the robot competitor and user experience. We develop the robot competitor through iterative multi-agent reinforcement learning and show that it can perform well against human competitors. Our user study additionally found that our system was able to continuously create challenging and enjoyable interactions that significantly increased human subjects' heart rates. The majority of human subjects considered the system to be entertaining and desirable for improving the quality of their exercise., Comment: Conference on Robot Learning. PMLR, 2022

Nonprehensile manipulation involves long horizon underactuated object interactions and physical contact with different objects that can inherently introduce a high degree of uncertainty. In this work, we introduce a novel Real-to-Sim reward analysis technique, called Riemannian Motion Predictive Control (RMPC), to reliably imagine and predict the outcome of taking possible actions for a real robotic platform. Our proposed RMPC benefits from Riemannian motion policy and second order dynamic model to compute the acceleration command and control the robot at every location on the surface. Our approach creates a 3D object-level recomposed model of the real scene where we can simulate the effect of different trajectories. We produce a closed-loop controller to reactively push objects in a continuous action space. We evaluate the performance of our RMPC approach by conducting experiments on a real robot platform as well as simulation and compare against several baselines. We observe that RMPC is robust in cluttered as well as occluded environments and outperforms the baselines., Comment: To appear at International Symposium on Experimental Robotics (ISER)

Efficient and reliable generation of global path plans are necessary for safe execution and deployment of autonomous systems. In order to generate planning graphs which adequately resolve the topology of a given environment, many sampling-based motion planners resort to coarse, heuristically-driven strategies which often fail to generalize to new and varied surroundings. Further, many of these approaches are not designed to contend with partial-observability. We posit that such uncertainty in environment geometry can, in fact, help drive the sampling process in generating feasible, and probabilistically-safe planning graphs. We propose a method for Probabilistic Roadmaps which relies on particle-based Variational Inference to efficiently cover the posterior distribution over feasible regions in configuration space. Our approach, Stein Variational Probabilistic Roadmap (SV-PRM), results in sample-efficient generation of planning-graphs and large improvements over traditional sampling approaches. We demonstrate the approach on a variety of challenging planning problems, including real-world probabilistic occupancy maps and high-dof manipulation problems common in robotics., Comment: Pre-print

Lazy graph search algorithms are efficient at solving motion planning problems where edge evaluation is the computational bottleneck. These algorithms work by lazily computing the shortest potentially feasible path, evaluating edges along that path, and repeating until a feasible path is found. The order in which edges are selected is critical to minimizing the total number of edge evaluations: a good edge selector chooses edges that are not only likely to be invalid, but also eliminates future paths from consideration. We wish to learn such a selector by leveraging prior experience. We formulate this problem as a Markov Decision Process (MDP) on the state of the search problem. While solving this large MDP is generally intractable, we show that we can compute oracular selectors that can solve the MDP during training. With access to such oracles, we use imitation learning to find effective policies. If new search problems are sufficiently similar to problems solved during training, the learned policy will choose a good edge evaluation ordering and solve the motion planning problem quickly. We evaluate our algorithms on a wide range of 2D and 7D problems and show that the learned selector outperforms baseline commonly used heuristics. We further provide a novel theoretical analysis of lazy search in a Bayesian framework as well as regret guarantees on our imitation learning based approach to motion planning., Comment: Extended journal version accepted for publication at Autonomous Robots; 17 pages. arXiv admin note: substantial text overlap with arXiv:1907.07238

Classical mechanical systems are central to controller design in energy shaping methods of geometric control. However, their expressivity is limited by position-only metrics and the intimate link between metric and geometry. Recent work on Riemannian Motion Policies (RMPs) has shown that shedding these restrictions results in powerful design tools, but at the expense of theoretical stability guarantees. In this work, we generalize classical mechanics to what we call geometric fabrics, whose expressivity and theory enable the design of systems that outperform RMPs in practice. Geometric fabrics strictly generalize classical mechanics forming a new physics of behavior by first generalizing them to Finsler geometries and then explicitly bending them to shape their behavior while maintaining stability. We develop the theory of fabrics and present both a collection of controlled experiments examining their theoretical properties and a set of robot system experiments showing improved performance over a well-engineered and hardened implementation of RMPs, our current state-of-the-art in controller design.

Many Imitation and Reinforcement Learning approaches rely on the availability of expert-generated demonstrations for learning policies or value functions from data. Obtaining a reliable distribution of trajectories from motion planners is non-trivial, since it must broadly cover the space of states likely to be encountered during execution while also satisfying task-based constraints. We propose a sampling strategy based on variational inference to generate distributions of feasible, low-cost trajectories for high-dof motion planning tasks. This includes a distributed, particle-based motion planning algorithm which leverages a structured graphical representations for inference over multi-modal posterior distributions. We also make explicit connections to both approximate inference for trajectory optimization and entropy-regularized reinforcement learning., Comment: RSS 2021 Workshop on Integrating Planning and Learning

Many sequential decision problems involve finding a policy that maximizes total reward while obeying safety constraints. Although much recent research has focused on the development of safe reinforcement learning (RL) algorithms that produce a safe policy after training, ensuring safety during training as well remains an open problem. A fundamental challenge is performing exploration while still satisfying constraints in an unknown Markov decision process (MDP). In this work, we address this problem for the chance-constrained setting. We propose a new algorithm, SAILR, that uses an intervention mechanism based on advantage functions to keep the agent safe throughout training and optimizes the agent's policy using off-the-shelf RL algorithms designed for unconstrained MDPs. Our method comes with strong guarantees on safety during both training and deployment (i.e., after training and without the intervention mechanism) and policy performance compared to the optimal safety-constrained policy. In our experiments, we show that SAILR violates constraints far less during training than standard safe RL and constrained MDP approaches and converges to a well-performing policy that can be deployed safely without intervention. Our code is available at https://github.com/nolanwagener/safe_rl., Comment: Appearing in ICML 2021. 29 pages, 8 figures

Imitation learning (IL) is a frequently used approach for data-efficient policy learning. Many IL methods, such as Dataset Aggregation (DAgger), combat challenges like distributional shift by interacting with oracular experts. Unfortunately, assuming access to oracular experts is often unrealistic in practice; data used in IL frequently comes from offline processes such as lead-through or teleoperation. In this paper, we present a novel imitation learning technique called Collocation for Demonstration Encoding (CoDE) that operates on only a fixed set of trajectory demonstrations. We circumvent challenges with methods like back-propagation-through-time by introducing an auxiliary trajectory network, which takes inspiration from collocation techniques in optimal control. Our method generalizes well and more accurately reproduces the demonstrated behavior with fewer guiding trajectories when compared to standard behavioral cloning methods. We present simulation results on a 7-degree-of-freedom (DoF) robotic manipulator that learns to exhibit lifting, target-reaching, and obstacle avoidance behaviors.

Sampling-based model-predictive control (MPC) is a promising tool for feedback control of robots with complex, non-smooth dynamics, and cost functions. However, the computationally demanding nature of sampling-based MPC algorithms has been a key bottleneck in their application to high-dimensional robotic manipulation problems in the real world. Previous methods have addressed this issue by running MPC in the task space while relying on a low-level operational space controller for joint control. However, by not using the joint space of the robot in the MPC formulation, existing methods cannot directly account for non-task space related constraints such as avoiding joint limits, singular configurations, and link collisions. In this paper, we develop a system for fast, joint space sampling-based MPC for manipulators that is efficiently parallelized using GPUs. Our approach can handle task and joint space constraints while taking less than 8ms~(125Hz) to compute the next control command. Further, our method can tightly integrate perception into the control problem by utilizing learned cost functions from raw sensor data. We validate our approach by deploying it on a Franka Panda robot for a variety of dynamic manipulation tasks. We study the effect of different cost formulations and MPC parameters on the synthesized behavior and provide key insights that pave the way for the application of sampling-based MPC for manipulators in a principled manner. We also provide highly optimized, open-source code to be used by the wider robot learning and control community. Videos of experiments can be found at: https://sites.google.com/view/manipulation-mpc, Comment: Accepted for oral presentation at the Conference on Robot Learning (CoRL), 2021. Code available at: https://github.com/NVlabs/storm

We focus on the problem of developing energy efficient controllers for quadrupedal robots. Animals can actively switch gaits at different speeds to lower their energy consumption. In this paper, we devise a hierarchical learning framework, in which distinctive locomotion gaits and natural gait transitions emerge automatically with a simple reward of energy minimization. We use evolutionary strategies (ES) to train a high-level gait policy that specifies gait patterns of each foot, while the low-level convex MPC controller optimizes the motor commands so that the robot can walk at a desired velocity using that gait pattern. We test our learning framework on a quadruped robot and demonstrate automatic gait transitions, from walking to trotting and to fly-trotting, as the robot increases its speed. We show that the learned hierarchical controller consumes much less energy across a wide range of locomotion speed than baseline controllers., Comment: Published in CoRL 2021. Website: Website: https://sites.google.com/view/fast-and-efficient Code: https://github.com/yxyang/fast_and_efficient

Model Predictive Control (MPC) is a classic tool for optimal control of complex, real-world systems. Although it has been successfully applied to a wide range of challenging tasks in robotics, it is fundamentally limited by the prediction horizon, which, if too short, will result in myopic decisions. Recently, several papers have suggested using a learned value function as the terminal cost for MPC. If the value function is accurate, it effectively allows MPC to reason over an infinite horizon. Unfortunately, Reinforcement Learning (RL) solutions to value function approximation can be difficult to realize for robotics tasks. In this paper, we suggest a more efficient method for value function approximation that applies to goal-directed problems, like reaching and navigation. In these problems, MPC is often formulated to track a path or trajectory returned by a planner. However, this strategy is brittle in that unexpected perturbations to the robot will require replanning, which can be costly at runtime. Instead, we show how the intermediate data structures used by modern planners can be interpreted as an approximate value function. We show that that this value function can be used by MPC directly, resulting in more efficient and resilient behavior at runtime., Comment: 7 pages, 8 figures. To appear in the proceedings of the International Conference on Robotics and Automation (ICRA) 2021

Model predictive control (MPC) schemes have a proven track record for delivering aggressive and robust performance in many challenging control tasks, coping with nonlinear system dynamics, constraints, and observational noise. Despite their success, these methods often rely on simple control distributions, which can limit their performance in highly uncertain and complex environments. MPC frameworks must be able to accommodate changing distributions over system parameters, based on the most recent measurements. In this paper, we devise an implicit variational inference algorithm able to estimate distributions over model parameters and control inputs on-the-fly. The method incorporates Stein Variational gradient descent to approximate the target distributions as a collection of particles, and performs updates based on a Bayesian formulation. This enables the approximation of complex multi-modal posterior distributions, typically occurring in challenging and realistic robot navigation tasks. We demonstrate our approach on both simulated and real-world experiments requiring real-time execution in the face of dynamically changing environments., Comment: Corresponding author: lucas.barcelos@sydney.edu.au

We consider the problem of learning motion policies for acceleration-based robotics systems with a structured policy class specified by RMPflow. RMPflow is a multi-task control framework that has been successfully applied in many robotics problems. Using RMPflow as a structured policy class in learning has several benefits, such as sufficient expressiveness, the flexibility to inject different levels of prior knowledge as well as the ability to transfer policies between robots. However, implementing a system for end-to-end learning RMPflow policies faces several computational challenges. In this work, we re-examine the message passing algorithm of RMPflow and propose a more efficient alternate algorithm, called RMP2, that uses modern automatic differentiation tools (such as TensorFlow and PyTorch) to compute RMPflow policies. Our new design retains the strengths of RMPflow while bringing in advantages from automatic differentiation, including 1) easy programming interfaces to designing complex transformations; 2) support of general directed acyclic graph (DAG) transformation structures; 3) end-to-end differentiability for policy learning; 4) improved computational efficiency. Because of these features, RMP2 can be treated as a structured policy class for efficient robot learning which is suitable encoding domain knowledge. Our experiments show that using structured policy class given by RMP2 can improve policy performance and safety in reinforcement learning tasks for goal reaching in cluttered space.

Generating robot motion that fulfills multiple tasks simultaneously is challenging due to the geometric constraints imposed by the robot. In this paper, we propose to solve multi-task problems through learning structured policies from human demonstrations. Our structured policy is inspired by RMPflow, a framework for combining subtask policies on different spaces. The policy structure provides the user an interface to 1) specifying the spaces that are directly relevant to the completion of the tasks, and 2) designing policies for certain tasks that do not need to be learned. We derive an end-to-end learning objective function that is suitable for the multi-task problem, emphasizing the deviation of motions on task spaces. Furthermore, the motion generated from the learned policy class is guaranteed to be stable. We validate the effectiveness of our proposed learning framework through qualitative and quantitative evaluations on three robotic tasks on a 7-DOF Rethink Sawyer robot.

Model-Predictive Control (MPC) is a powerful tool for controlling complex, real-world systems that uses a model to make predictions about future behavior. For each state encountered, MPC solves an online optimization problem to choose a control action that will minimize future cost. This is a surprisingly effective strategy, but real-time performance requirements warrant the use of simple models. If the model is not sufficiently accurate, then the resulting controller can be biased, limiting performance. We present a framework for improving on MPC with model-free reinforcement learning (RL). The key insight is to view MPC as constructing a series of local Q-function approximations. We show that by using a parameter $\lambda$, similar to the trace decay parameter in TD($\lambda$), we can systematically trade-off learned value estimates against the local Q-function approximations. We present a theoretical analysis that shows how error from inaccurate models in MPC and value function estimation in RL can be balanced. We further propose an algorithm that changes $\lambda$ over time to reduce the dependence on MPC as our estimates of the value function improve, and test the efficacy our approach on challenging high-dimensional manipulation tasks with biased models in simulation. We demonstrate that our approach can obtain performance comparable with MPC with access to true dynamics even under severe model bias and is more sample efficient as compared to model-free RL., Comment: 15 pages

Decision making under uncertainty is critical to real-world, autonomous systems. Model Predictive Control (MPC) methods have demonstrated favorable performance in practice, but remain limited when dealing with complex probability distributions. In this paper, we propose a generalization of MPC that represents a multitude of solutions as posterior distributions. By casting MPC as a Bayesian inference problem, we employ variational methods for posterior computation, naturally encoding the complexity and multi-modality of the decision making problem. We present a Stein variational gradient descent method to estimate the posterior directly over control parameters, given a cost function and observed state trajectories. We show that this framework leads to successful planning in challenging, non-convex optimal control problems., Comment: Accepted to Conference on Robot Learning (CoRL) 2020

Billions of people use chopsticks, a simple yet versatile tool, for fine manipulation of everyday objects. The small, curved, and slippery tips of chopsticks pose a challenge for picking up small objects, making them a suitably complex test case. This paper leverages human demonstrations to develop an autonomous chopsticks-equipped robotic manipulator. Due to the lack of accurate models for fine manipulation, we explore model-free imitation learning, which traditionally suffers from the covariate shift phenomenon that causes poor generalization. We propose two approaches to reduce covariate shift, neither of which requires access to an interactive expert or a model, unlike previous approaches. First, we alleviate single-step prediction errors by applying an invariant operator to increase the data support at critical steps for grasping. Second, we generate synthetic corrective labels by adding bounded noise and combining parametric and non-parametric methods to prevent error accumulation. We demonstrate our methods on a real chopstick-equipped robot that we built, and observe the agent's success rate increase from 37.3% to 80%, which is comparable to the human expert performance of 82.6%., Comment: Submitted to ICRA 2021

This paper describes the pragmatic design and construction of geometric fabrics for shaping a robot's task-independent nominal behavior, capturing behavioral components such as obstacle avoidance, joint limit avoidance, redundancy resolution, global navigation heuristics, etc. Geometric fabrics constitute the most concrete incarnation of a new mathematical formulation for reactive behavior called optimization fabrics. Fabrics generalize recent work on Riemannian Motion Policies (RMPs); they add provable stability guarantees and improve design consistency while promoting the intuitive acceleration-based principles of modular design that make RMPs successful. We describe a suite of mathematical modeling tools that practitioners can employ in practice and demonstrate both how to mitigate system complexity by constructing behaviors layer-wise and how to employ these tools to design robust, strongly-generalizing, policies that solve practical problems one would expect to find in industry applications. Our system exhibits intelligent global navigation behaviors expressed entirely as provably stable fabrics with zero planning or state machine governance.

We present a hierarchical framework that combines model-based control and reinforcement learning (RL) to synthesize robust controllers for a quadruped (the Unitree Laikago). The system consists of a high-level controller that learns to choose from a set of primitives in response to changes in the environment and a low-level controller that utilizes an established control method to robustly execute the primitives. Our framework learns a controller that can adapt to challenging environmental changes on the fly, including novel scenarios not seen during training. The learned controller is up to 85~percent more energy efficient and is more robust compared to baseline methods. We also deploy the controller on a physical robot without any randomization or adaptation scheme., Comment: supplementary video: https://youtu.be/JJOmFZKpYTo

Generating robot motion for multiple tasks in dynamic environments is challenging, requiring an algorithm to respond reactively while accounting for complex nonlinear relationships between tasks. In this paper, we develop a novel policy synthesis algorithm, RMPflow, based on geometrically consistent transformations of Riemannian Motion Policies (RMPs). RMPs are a class of reactive motion policies that parameterize non-Euclidean behaviors as dynamical systems in intrinsically nonlinear task spaces. Given a set of RMPs designed for individual tasks, RMPflow can combine these policies to generate an expressive global policy, while simultaneously exploiting sparse structure for computational efficiency. We study the geometric properties of RMPflow and provide sufficient conditions for stability. Finally, we experimentally demonstrate that accounting for the natural Riemannian geometry of task policies can simplify classically difficult problems, such as planning through clutter on high-DOF manipulation systems., Comment: arXiv admin note: substantial text overlap with arXiv:1811.07049

Online imitation learning (IL) is an algorithmic framework that leverages interactions with expert policies for efficient policy optimization. Here policies are optimized by performing online learning on a sequence of loss functions that encourage the learner to mimic expert actions, and if the online learning has no regret, the agent can provably learn an expert-like policy. Online IL has demonstrated empirical successes in many applications and interestingly, its policy improvement speed observed in practice is usually much faster than existing theory suggests. In this work, we provide an explanation of this phenomenon. Let $\xi$ denote the policy class bias and assume the online IL loss functions are convex, smooth, and non-negative. We prove that, after $N$ rounds of online IL with stochastic feedback, the policy improves in $\tilde{O}(1/N + \sqrt{\xi/N})$ in both expectation and high probability. In other words, we show that adopting a sufficiently expressive policy class in online IL has two benefits: both the policy improvement speed increases and the performance bias decreases., Comment: 22 pages, 2 figures

Robotic tasks often require motions with complex geometric structures. We present an approach to learn such motions from a limited number of human demonstrations by exploiting the regularity properties of human motions e.g. stability, smoothness, and boundedness. The complex motions are encoded as rollouts of a stable dynamical system, which, under a change of coordinates defined by a diffeomorphism, is equivalent to a simple, hand-specified dynamical system. As an immediate result of using diffeomorphisms, the stability property of the hand-specified dynamical system directly carry over to the learned dynamical system. Inspired by recent works in density estimation, we propose to represent the diffeomorphism as a composition of simple parameterized diffeomorphisms. Additional structure is imposed to provide guarantees on the smoothness of the generated motions. The efficacy of this approach is demonstrated through validation on an established benchmark as well demonstrations collected on a real-world robotic system., Comment: 2nd Annual Conference on Learning for Dynamics and Control (L4DC) 2020 -- Revised Version

Model-free Reinforcement Learning (RL) works well when experience can be collected cheaply and model-based RL is effective when system dynamics can be modeled accurately. However, both assumptions can be violated in real world problems such as robotics, where querying the system can be expensive and real-world dynamics can be difficult to model. In contrast to RL, Model Predictive Control (MPC) algorithms use a simulator to optimize a simple policy class online, constructing a closed-loop controller that can effectively contend with real-world dynamics. MPC performance is usually limited by factors such as model bias and the limited horizon of optimization. In this work, we present a novel theoretical connection between information theoretic MPC and entropy regularized RL and develop a Q-learning algorithm that can leverage biased models. We validate the proposed algorithm on sim-to-sim control tasks to demonstrate the improvements over optimal control and reinforcement learning from scratch. Our approach paves the way for deploying reinforcement learning algorithms on real systems in a systematic manner., Comment: Extended version (15 pages) of paper accepted at the 2nd Learning for Dynamics and Control (L4DC) Conference, 2020

Learning from offline task demonstrations is a problem of great interest in robotics. For simple short-horizon manipulation tasks with modest variation in task instances, offline learning from a small set of demonstrations can produce controllers that successfully solve the task. However, leveraging a fixed batch of data can be problematic for larger datasets and longer-horizon tasks with greater variations. The data can exhibit substantial diversity and consist of suboptimal solution approaches. In this paper, we propose Implicit Reinforcement without Interaction at Scale (IRIS), a novel framework for learning from large-scale demonstration datasets. IRIS factorizes the control problem into a goal-conditioned low-level controller that imitates short demonstration sequences and a high-level goal selection mechanism that sets goals for the low-level and selectively combines parts of suboptimal solutions leading to more successful task completions. We evaluate IRIS across three datasets, including the RoboTurk Cans dataset collected by humans via crowdsourcing, and show that performant policies can be learned from purely offline learning. Additional results at https://sites.google.com/stanford.edu/iris/ .

Effective human-robot collaboration requires informed anticipation. The robot must anticipate the human's actions, but also react quickly and intuitively when its predictions are wrong. The robot must plan its actions to account for the human's own plan, with the knowledge that the human's behavior will change based on what the robot actually does. This cyclical game of predicting a human's future actions and generating a corresponding motion plan is extremely difficult to model using standard techniques. In this work, we describe a novel Model Predictive Control (MPC)-based framework for finding optimal trajectories in a collaborative, multi-agent setting, in which we simultaneously plan for the robot while predicting the actions of its external collaborators. We use human-robot handovers to demonstrate that with a strong model of the collaborator, our framework produces fluid, reactive human-robot interactions in novel, cluttered environments. Our method efficiently generates coordinated trajectories, and achieves a high success rate in handover, even in the presence of significant sensor noise., Comment: 3 figures, 7 pages

RMPflow is a recently proposed policy-fusion framework based on differential geometry. While RMPflow has demonstrated promising performance, it requires the user to provide sensible subtask policies as Riemannian motion policies (RMPs: a motion policy and an importance matrix function), which can be a difficult design problem in its own right. We propose RMPfusion, a variation of RMPflow, to address this issue. RMPfusion supplements RMPflow with weight functions that can hierarchically reshape the Lyapunov functions of the subtask RMPs according to the current configuration of the robot and environment. This extra flexibility can remedy imperfect subtask RMPs provided by the user, improving the combined policy's performance. These weight functions can be learned by back-propagation. Moreover, we prove that, under mild restrictions on the weight functions, RMPfusion always yields a globally Lyapunov-stable motion policy. This implies that we can treat RMPfusion as a structured policy class in policy optimization that is guaranteed to generate stable policies, even during the immature phase of learning. We demonstrate these properties of RMPfusion in imitation learning experiments both in simulation and on a real-world robot., Comment: Conference on Robot Learning (CoRL), 2019

Efficient planning in dynamic and uncertain environments is a fundamental challenge in robotics. In the context of trajectory optimization, the feasibility of paths can change as the environment evolves. Therefore, it can be beneficial to reason about multiple possible paths simultaneously. We build on prior work that considers graph-based trajectories to find solutions in multiple homotopy classes concurrently. Specifically, we extend this previous work to an online setting where the unreachable (in time) part of the graph is pruned and the remaining graph is reoptimized at every time step. As the robot moves within the graph on the path that is most promising, the pruning and reoptimization allows us to retain candidate paths that may become more viable in the future as the environment changes, essentially enabling the robot to dynamically switch between numerous homotopy classes. We compare our approach against prior work without the homotopy switching capability and show improved performance across several metrics in simulation with a 2D robot in multiple dynamic environments under noisy measurements and execution., Comment: Accepted to the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2019. 7 pages, 6 figures

Modern trajectory optimization based approaches to motion planning are fast, easy to implement, and effective on a wide range of robotics tasks. However, trajectory optimization algorithms have parameters that are typically set in advance (and rarely discussed in detail). Setting these parameters properly can have a significant impact on the practical performance of the algorithm, sometimes making the difference between finding a feasible plan or failing at the task entirely. We propose a method for leveraging past experience to learn how to automatically adapt the parameters of Gaussian Process Motion Planning (GPMP) algorithms. Specifically, we propose a differentiable extension to the GPMP2 algorithm, so that it can be trained end-to-end from data. We perform several experiments that validate our algorithm and illustrate the benefits of our proposed learning-based approach to motion planning., Comment: 7 pages, Proceedings of the IEEE Conference on Robotics and Automation (ICRA), 2020