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Non-prehensile manipulation enables fast interactions with objects by circumventing the need to grasp and ungrasp as well as handling objects that cannot be grasped through force closure. Current approaches to non-prehensile manipulation focus on static contacts, avoiding the underactuation that comes with sliding. However, the ability to control sliding contact, essentially removing the no-slip constraint, opens up new possibilities in dynamic manipulation. In this paper, we explore a challenging dynamic non-prehensile manipulation task that requires the consideration of the full spectrum of hybrid contact modes. We leverage recent methods in contact-implicit MPC to handle the multi-modal planning aspect of the task. We demonstrate, with careful consideration of integration between the simple model used for MPC and the low-level tracking controller, how contact-implicit MPC can be adapted to dynamic tasks. Surprisingly, despite the known inaccuracies of frictional rigid contact models, our method is able to react to these inaccuracies while still quickly performing the task. Moreover, we do not use common aids such as reference trajectories or motion primitives, highlighting the generality of our approach. To the best of our knowledge, this is the first application of contact-implicit MPC to a dynamic manipulation task in three dimensions., Comment: Project website: https://dynamic-controlled-sliding.github.io/

Robotic manipulation can greatly benefit from the data efficiency, robustness, and predictability of model-based methods if robots can quickly generate models of novel objects they encounter. This is especially difficult when effects like complex joint friction lack clear first-principles models and are usually ignored by physics simulators. Further, numerically-stiff contact dynamics can make common model-building approaches struggle. We propose a method to simultaneously learn contact and continuous dynamics of a novel, possibly multi-link object by observing its motion through contact-rich trajectories. We formulate a system identification process with a loss that infers unmeasured contact forces, penalizing their violation of physical constraints and laws of motion given current model parameters. Our loss is unlike prediction-based losses used in differentiable simulation. Using a new dataset of real articulated object trajectories and an existing cube toss dataset, our method outperforms differentiable simulation and end-to-end alternatives with more data efficiency. See our project page for code, datasets, and media: https://sites.google.com/view/continuous-contact-nets/home, Comment: 13 pages, 5 figures. Accepted to Conference on Robot Learning (CoRL) 2023. Project webpage with code, datasets, media, and OpenReview link at https://sites.google.com/view/continuous-contact-nets/home

The hybrid nature of multi-contact robotic systems, due to making and breaking contact with the environment, creates significant challenges for high-quality control. Existing model-based methods typically rely on either good prior knowledge of the multi-contact model or require significant offline model tuning effort, thus resulting in low adaptability and robustness. In this paper, we propose a real-time adaptive multi-contact model predictive control framework, which enables online adaption of the hybrid multi-contact model and continuous improvement of the control performance for contact-rich tasks. This framework includes an adaption module, which continuously learns a residual of the hybrid model to minimize the gap between the prior model and reality, and a real-time multi-contact MPC controller. We demonstrated the effectiveness of the framework in synthetic examples, and applied it on hardware to solve contact-rich manipulation tasks, where a robot uses its end-effector to roll different unknown objects on a table to track given paths. The hardware experiments show that with a rough prior model, the multi-contact MPC controller adapts itself on-the-fly with an adaption rate around 20 Hz and successfully manipulates previously unknown objects with non-smooth surface geometries., Comment: Wei-Cheng Huang and Alp Aydinoglu contributed equally to this work. ICRA 2024 Final Submission

Model-based approaches for planning and control for bipedal locomotion have a long history of success. It can provide stability and safety guarantees while being effective in accomplishing many locomotion tasks. Model-free reinforcement learning, on the other hand, has gained much popularity in recent years due to computational advancements. It can achieve high performance in specific tasks, but it lacks physical interpretability and flexibility in re-purposing the policy for a different set of tasks. For instance, we can initially train a neural network (NN) policy using velocity commands as inputs. However, to handle new task commands like desired hand or footstep locations at a desired walking velocity, we must retrain a new NN policy. In this work, we attempt to bridge the gap between these two bodies of work on a bipedal platform. We formulate a model-based reinforcement learning problem to learn a reduced-order model (ROM) within a model predictive control (MPC). Results show a 49% improvement in viable task region size and a 21% reduction in motor torque cost. All videos and code are available at https://sites.google.com/view/ymchen/research/rl-for-roms.

In contact-rich tasks, the hybrid, multi-modal nature of contact dynamics poses great challenges in model representation, planning, and control. Recent efforts have attempted to address these challenges via data-driven methods, learning dynamical models in combination with model predictive control. Those methods, while effective, rely solely on minimizing forward prediction errors to hope for better task performance with MPC controllers. This weak correlation can result in data inefficiency as well as limitations to overall performance. In response, we propose a novel strategy: using a policy gradient algorithm to find a simplified dynamics model that explicitly maximizes task performance. Specifically, we parameterize the stochastic policy as the perturbed output of the MPC controller, thus, the learned model representation can directly associate with the policy or task performance. We apply the proposed method to contact-rich tasks where a three-fingered robotic hand manipulates previously unknown objects. Our method significantly enhances task success rate by up to 15% in manipulating diverse objects compared to the existing method while sustaining data efficiency. Our method can solve some tasks with success rates of 70% or higher using under 30 minutes of data. All videos and codes are available at https://sites.google.com/view/lcs-rl., Comment: The work will be presented in ICRA2024

Bipedal robots promise the ability to traverse rough terrain quickly and efficiently, and indeed, humanoid robots can now use strong ankles and careful foot placement to traverse discontinuous terrain. However, more agile underactuated bipeds have small feet and weak ankles, and must constantly adjust their planned footstep position to maintain balance. We introduce a new model-predictive footstep controller which jointly optimizes over the robot's discrete choice of stepping surface, impending footstep position sequence, ankle torque in the sagittal plane, and center of mass trajectory, to track a velocity command. The controller is formulated as a single Mixed Integer Quadratic Program (MIQP) which is solved at 50-200 Hz, depending on terrain complexity. We implement a state of the art real-time elevation mapping and convex terrain decomposition framework to inform the controller of its surroundings in the form on convex polygons representing steppable terrain. We investigate the capabilities and challenges of our approach through hardware experiments on the underactuated biped Cassie.

This work presents an instance-agnostic learning framework that fuses vision with dynamics to simultaneously learn shape, pose trajectories, and physical properties via the use of geometry as a shared representation. Unlike many contact learning approaches that assume motion capture input and a known shape prior for the collision model, our proposed framework learns an object's geometric and dynamic properties from RGBD video, without requiring either category-level or instance-level shape priors. We integrate a vision system, BundleSDF, with a dynamics system, ContactNets, and propose a cyclic training pipeline to use the output from the dynamics module to refine the poses and the geometry from the vision module, using perspective reprojection. Experiments demonstrate our framework's ability to learn the geometry and dynamics of rigid and convex objects and improve upon the current tracking framework., Comment: IROS 2023 Workshop on Leveraging Models for Contact-Rich Manipulation

We propose a hybrid model predictive control algorithm, consensus complementarity control (C3), for systems that make and break contact with their environment. Many state-of-the-art controllers for tasks which require initiating contact with the environment, such as locomotion and manipulation, require a priori mode schedules or are too computationally complex to run at real-time rates. We present a method based on the alternating direction method of multipliers (ADMM) that is capable of high-speed reasoning over potential contact events. Via a consensus formulation, our approach enables parallelization of the contact scheduling problem. We validate our results on five numerical examples, including four high-dimensional frictional contact problems, and a physical experimentation on an underactuated multi-contact system. We further demonstrate the effectiveness of our method on a physical experiment accomplishing a high-dimensional, multi-contact manipulation task with a robot arm., Comment: T-RO submission. Continuation of the work: arXiv:2109.07076v2

When legged robots impact their environment executing dynamic motions, they undergo large changes in their velocities in a short amount of time. Measuring and applying feedback to these velocities is challenging, further complicated by uncertainty in the impact model and impact timing. This work proposes a general framework for adapting feedback control during impact by projecting the control objectives to a subspace that is invariant to the impact event. The resultant controller is robust to uncertainties in the impact event while maintaining maximum control authority over the impact-invariant subspace. We demonstrate the improved performance of the projection over other commonly used heuristics on a walking controller for a planar five-link-biped. The projection is also applied to jumping, box jumping, and running controllers for the compliant 3D bipedal robot, Cassie. The modification is easily applied to these various controllers and is a critical component to deploying on the physical robot. Code and video of the experiments are available at https://impact-invariant-control.github.io/., Comment: Project Website: https://impact-invariant-control.github.io/. arXiv admin note: text overlap with arXiv:2103.06907

Reduced-order models (ROM) are popular in online motion planning due to their simplicity. A good ROM for control captures critical task-relevant aspects of the full dynamics while remaining low dimensional. However, planning within the reduced-order space unavoidably constrains the full model, and hence we sacrifice the full potential of the robot. In the community of legged locomotion, this has lead to a search for better model extensions, but many of these extensions require human intuition, and there has not existed a principled way of evaluating the model performance and discovering new models. In this work, we propose a model optimization algorithm that automatically synthesizes reduced-order models, optimal with respect to a user-specified distribution of tasks and corresponding cost functions. To demonstrate our work, we optimized models for a bipedal robot Cassie. We show in simulation that the optimal ROM reduces the cost of Cassie's joint torques by up to 23% and increases its walking speed by up to 54%. We also show hardware result that the real robot walks on flat ground with 10% lower torque cost. All videos and code can be found at https://sites.google.com/view/ymchen/research/optimal-rom.

In contact-rich tasks, like dexterous manipulation, the hybrid nature of making and breaking contact creates challenges for model representation and control. For example, choosing and sequencing contact locations for in-hand manipulation, where there are thousands of potential hybrid modes, is not generally tractable. In this paper, we are inspired by the observation that far fewer modes are actually necessary to accomplish many tasks. Building on our prior work learning hybrid models, represented as linear complementarity systems, we find a reduced-order hybrid model requiring only a limited number of task-relevant modes. This simplified representation, in combination with model predictive control, enables real-time control yet is sufficient for achieving high performance. We demonstrate the proposed method first on synthetic hybrid systems, reducing the mode count by multiple orders of magnitude while achieving task performance loss of less than 5%. We also apply the proposed method to a three-fingered robotic hand manipulating a previously unknown object. With no prior knowledge, we achieve state-of-the-art closed-loop performance within a few minutes of online learning, by collecting only a few thousand environment samples., Comment: Reproducing code: https://github.com/wanxinjin/Task-Driven-Hybrid-Reduction. This is a preprint. The published version can be accessed at IEEE Transactions on Robotics

In a world designed for legs, quadrupeds, bipeds, and humanoids have the opportunity to impact emerging robotics applications from logistics, to agriculture, to home assistance. The goal of this survey is to cover the recent progress toward these applications that has been driven by model-based optimization for the real-time generation and control of movement. The majority of the research community has converged on the idea of generating locomotion control laws by solving an optimal control problem (OCP) in either a model-based or data-driven manner. However, solving the most general of these problems online remains intractable due to complexities from intermittent unidirectional contacts with the environment, and from the many degrees of freedom of legged robots. This survey covers methods that have been pursued to make these OCPs computationally tractable, with specific focus on how environmental contacts are treated, how the model can be simplified, and how these choices affect the numerical solution methods employed. The survey focuses on model-based optimization, covering its recent use in a stand alone fashion, and suggesting avenues for combination with learning-based formulations to further accelerate progress in this growing field., Comment: submitted for initial review; comments welcome

Complex multibody legged robots can have complex rotational control challenges. In this paper, we propose a concise way to understand and formulate a \emph{whole-body orientation} that (i) depends on system configuration only and not a history of motion, (ii) can be representative of the orientation of the entire system while not being attached to any specific link, and (iii) has a rate of change that approximates total system angular momentum. We relate this orientation coordinate to past work, and discuss and demonstrate, including on hardware, several different uses for it.

This paper investigates the learning, or system identification, of a class of piecewise-affine dynamical systems known as linear complementarity systems (LCSs). We propose a violation-based loss which enables efficient learning of the LCS parameterization, without prior knowledge of the hybrid mode boundaries, using gradient-based methods. The proposed violation-based loss incorporates both dynamics prediction loss and a novel complementarity - violation loss. We show several properties attained by this loss formulation, including its differentiability, the efficient computation of first- and second-order derivatives, and its relationship to the traditional prediction loss, which strictly enforces complementarity. We apply this violation-based loss formulation to learn LCSs with tens of thousands of (potentially stiff) hybrid modes. The results demonstrate a state-of-the-art ability to identify piecewise-affine dynamics, outperforming methods which must differentiate through non-smooth linear complementarity problems., Comment: 10 pages

Inspired by recent strides in empirical efficacy of implicit learning in many robotics tasks, we seek to understand the theoretical benefits of implicit formulations in the face of nearly discontinuous functions, common characteristics for systems that make and break contact with the environment such as in legged locomotion and manipulation. We present and motivate three formulations for learning a function: one explicit and two implicit. We derive generalization bounds for each of these three approaches, exposing where explicit and implicit methods alike based on prediction error losses typically fail to produce tight bounds, in contrast to other implicit methods with violation-based loss definitions that can be fundamentally more robust to steep slopes. Furthermore, we demonstrate that this violation implicit loss can tightly bound graph distance, a quantity that often has physical roots and handles noise in inputs and outputs alike, instead of prediction losses which consider output noise only. Our insights into the generalizability and physical relevance of violation implicit formulations match evidence from prior works and are validated through a toy problem, inspired by rigid-contact models and referenced throughout our theoretical analysis., Comment: Accepted to the 4th annual Learning for Dynamics and Control (L4DC) Conference, to be published in Proceedings of Machine Learning Research (PMLR). 23 pages, 3 figures

A realistic simulation environment is an essential tool in every roboticist's toolkit, with uses ranging from planning and control to training policies with reinforcement learning. Despite the centrality of simulation in modern robotics, little work has been done to compare the performance of robotics simulators against real-world data, especially for scenarios involving dynamic motions with high speed impact events. Handling dynamic contact is the computational bottleneck for most simulations, and thus the modeling and algorithmic choices surrounding impacts and friction form the largest distinctions between popular tools. Here, we evaluate the ability of several simulators to reproduce real-world trajectories involving impacts. Using experimental data, we identify system-specific contact parameters of popular simulators Drake, MuJoCo, and Bullet, analyzing the effects of modeling choices around these parameters. For the simple example of a cube tossed onto a table, simulators capture inelastic impacts well while failing to capture elastic impacts. For the higher-dimensional case of a Cassie biped landing from a jump, the simulators capture the bulk motion well but the accuracy is limited by numerous model differences between the real robot and the simulators., Comment: 8 pages, 6 figures, Accepted to IROS + RAL 2022

We propose a hybrid model predictive control algorithm, consensus complementarity control (C3), for systems that make and break contact with their environment. Many state-of-the-art controllers for tasks which require initiating contact with the environment, such as locomotion and manipulation, require a priori mode schedules or are so computationally complex that they cannot run at real-time rates. We present a method, based on the alternating direction method of multipliers (ADMM), capable of highspeed reasoning over potential contact events. Via a consensus formulation, our approach enables parallelization of the contact scheduling problem. We validate our results on three numerical examples, including two frictional contact problems, and physical experimentation on an underactuated multi-contact system., Comment: The work will be presented in ICRA2022

Frictional contact has been extensively studied as the core underlying behavior of legged locomotion and manipulation, and its nearly-discontinuous nature makes planning and control difficult even when an accurate model of the robot is available. Here, we present empirical evidence that learning an accurate model in the first place can be confounded by contact, as modern deep learning approaches are not designed to capture this non-smoothness. We isolate the effects of contact's non-smoothness by varying the mechanical stiffness of a compliant contact simulator. Even for a simple system, we find that stiffness alone dramatically degrades training processes, generalization, and data-efficiency. Our results raise serious questions about simulated testing environments which do not accurately reflect the stiffness of rigid robotic hardware. Significant additional investigation will be necessary to fully understand and mitigate these effects, and we suggest several avenues for future study.

Robotic manipulation and locomotion often entail nearly-simultaneous collisions -- such as heel and toe strikes during a foot step -- with outcomes that are extremely sensitive to the order in which impacts occur. Robotic simulators commonly lack the accuracy to predict this ordering, and instead pick one with a heuristic. This discrepancy degrades performance when model-based controllers and policies learned in simulation are placed on a real robot. We reconcile this issue with a set-valued rigid-body model which generates a broad set of physically reasonable outcomes of simultaneous frictional impacts. We first extend Routh's impact model to multiple impacts by reformulating it as a differential inclusion (DI), and show that any solution will resolve all impacts in finite time. By considering time as a state, we embed this model into another DI which captures the continuous-time evolution of rigid body dynamics, and guarantee existence of solutions. We finally cast simulation of simultaneous impacts as a linear complementarity problem (LCP), and develop an algorithm for tight approximation of the post-impact velocity set with probabilistic guarantees. We demonstrate our approach on several examples drawn from manipulation and legged locomotion.

When legged robots impact their environment, they undergo large changes in their velocities in a small amount of time. Measuring and applying feedback to these velocities is challenging, and is further complicated due to uncertainty in the impact model and impact timing. This work proposes a general framework for adapting feedback control during impact by projecting the control objectives to a subspace that is invariant to the impact event. The resultant controller is robust to uncertainties in the impact event while maintaining maximum control authority over the impact invariant subspace. We demonstrate the utility of the projection on a walking controller for a planar five-link-biped and on a jumping controller for a compliant 3D bipedal robot, Cassie. The effectiveness of our method is shown to translate well on hardware., Comment: 8 pages, 6 figures, Accepted in IROS 2021

Complementarity problems, a class of mathematical optimization problems with orthogonality constraints, are widely used in many robotics tasks, such as locomotion and manipulation, due to their ability to model non-smooth phenomena (e.g., contact dynamics). In this paper, we propose a method to analyze the stability of complementarity systems with neural network controllers. First, we introduce a method to represent neural networks with rectified linear unit (ReLU) activations as the solution to a linear complementarity problem. Then, we show that systems with ReLU network controllers have an equivalent linear complementarity system (LCS) description. Using the LCS representation, we turn the stability verification problem into a linear matrix inequality (LMI) feasibility problem. We demonstrate the approach on several examples, including multi-contact problems and friction models with non-unique solutions.

Common methods for learning robot dynamics assume motion is continuous, causing unrealistic model predictions for systems undergoing discontinuous impact and stiction behavior. In this work, we resolve this conflict with a smooth, implicit encoding of the structure inherent to contact-induced discontinuities. Our method, ContactNets, learns parameterizations of inter-body signed distance and contact-frame Jacobians, a representation that is compatible with many simulation, control, and planning environments for robotics. We furthermore circumvent the need to differentiate through stiff or non-smooth dynamics with a novel loss function inspired by the principles of complementarity and maximum dissipation. Our method can predict realistic impact, non-penetration, and stiction when trained on 60 seconds of real-world data., Comment: S.P. and M.H. contributed equally to this work; Accepted to CoRL 2020

We propose a control framework which can utilize tactile information by exploiting the complementarity structure of contact dynamics. Since many robotic tasks, like manipulation and locomotion, are fundamentally based in making and breaking contact with the environment, state-of-the-art control policies struggle to deal with the hybrid nature of multi-contact motion. Such controllers often rely heavily upon heuristics or, due to the combinatorial structure in the dynamics, are unsuitable for real-time control. Principled deployment of tactile sensors offers a promising mechanism for stable and robust control, but modern approaches often use this data in an ad hoc manner, for instance to guide guarded moves. This framework can close the loop on tactile sensors and it is non-combinatorial, enabling optimization algorithms to automatically synthesize provably stable control policies. We demonstrate this approach on multiple numerical examples, including quasi-static friction problems and a high dimensional problem with ten contacts. We also validate our results on an experimental setup and show the effectiveness of the proposed method on an underactuated multi-contact system., Comment: The final preprint, accepted to T-RO. arXiv admin note: text overlap with arXiv:1909.11221

While many robotic tasks, like manipulation and locomotion, are fundamentally based in making and breaking contact with the environment, state-of-the-art control policies struggle to deal with the hybrid nature of multi-contact motion. Such controllers often rely heavily upon heuristics or, due to the combinatoric structure in the dynamics, are unsuitable for real-time control. Principled deployment of tactile sensors offers a promising mechanism for stable and robust control, but modern approaches often use this data in an ad hoc manner, for instance to guide guarded moves. In this work, by exploiting the complementarity structure of contact dynamics, we propose a control framework which can close the loop on rich, tactile sensors. Critically, this framework is non-combinatoric, enabling optimization algorithms to automatically synthesize provably stable control policies. We demonstrate this approach on three different underactuated, multi-contact robotics problems., Comment: The work has been submitted to ICRA 2020

State-of-the-art approaches to legged locomotion are widely dependent on the use of models like the linear inverted pendulum (LIP) and the spring-loaded inverted pendulum (SLIP), popular because their simplicity enables a wide array of tools for planning, control, and analysis. However, they inevitably limit the ability to execute complex tasks or agile maneuvers. In this work, we aim to automatically synthesize models that remain low-dimensional but retain the capabilities of the high-dimensional system. For example, if one were to restore a small degree of complexity to LIP, SLIP, or a similar model, our approach discovers the form of that additional complexity which optimizes performance. In this paper, we define a class of reduced-order models and provide an algorithm for optimization within this class. To demonstrate our method, we optimize models for walking at a range of speeds and ground inclines, for both a five-link model and the Cassie bipedal robot., Comment: Submitted to ICRA 2020

Quasi-static models of robotic motion with frictional contact provide a computationally efficient framework for analysis and have been widely used for planning and control of non-prehensile manipulation. In this work, we present a novel quasi-static model of planar manipulation that directly maps commanded manipulator velocities to object motion. While quasi-static models have traditionally been unable to capture grasping and jamming behaviors, our approach solves this issue by explicitly modeling the limiting behavior of a velocity-controlled manipulator. We retain the precise modeling of surface contact pressure distributions and efficient computation of contact-rich behaviors of previous methods and additionally prove existence of solutions for any desired manipulator motion. We derive continuous and time-stepping formulations, both posed as tractable Linear Complementarity Problems (LCPs)., Comment: WAFR 2018

Many fundamental challenges in robotics, based in manipulation or locomotion, require making and breaking contact with the environment. To represent the complexity of frictional contact events, impulsive impact models are especially popular, as they often lead to mathematically and computationally tractable approaches. However, when two or more impacts occur simultaneously, the precise sequencing of impact forces is generally unknown, leading to the potential for multiple possible outcomes. This simultaneity is far from pathological, and occurs in many common robotics applications. In this work, we propose an approach for resolving simultaneous frictional impacts, represented as a differential inclusion. Solutions to our model, an extension to multiple contacts of Routh's method, naturally capture the set of potential post-impact velocities.We prove that solutions to the presented model must terminate. This is, to the best of our knowledge, the first such guarantee for set-valued outcomes to simultaneous frictional impacts., Comment: Robotics: Science and Systems 2019