arXiv subjects

Michael Posa

Publications and source records attributed to Michael Posa.

36 records · Page 2Linked to original sources

arXiv2023

Instance-Agnostic Geometry and Contact Dynamics Learning

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.

cs.CV↗

arXiv2023

Bipedal Walking on Constrained Footholds with MPC Footstep Control

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.

cs.RO↗

arXiv2023

Set-Valued Rigid Body Dynamics for Simultaneous, Inelastic, Frictional Impacts

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.

cs.RO↗

arXiv2023

Integrable Whole-body Orientation Coordinates for Legged Robots

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.

cs.RO↗

arXiv2022

Optimization-Based Control for Dynamic Legged Robots

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.

cs.RO↗

arXiv2022

Validating Robotics Simulators on Real-World Impacts

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.

cs.RO↗

arXiv2022

Generalization Bounded Implicit Learning of Nearly Discontinuous Functions

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.

cs.RO↗

arXiv2022

Real-Time Multi-Contact Model Predictive Control via ADMM

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.

cs.RO↗

arXiv2021

Learning Linear Complementarity Systems

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.

cs.LG↗

arXiv2021

Stabilization of Complementarity Systems via Contact-Aware Controllers

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.

cs.RO↗

arXiv2021

Impact Invariant Control with Applications to Bipedal 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.

cs.RO↗

arXiv2021

Fundamental Challenges in Deep Learning for Stiff Contact Dynamics

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.

cs.RO↗

arXiv2020

Stability Analysis of Complementarity Systems with Neural Network Controllers

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.

eess.SY↗

arXiv2020

ContactNets: Learning Discontinuous Contact Dynamics with Smooth, Implicit Representations

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.

cs.RO↗

arXiv2019

Contact-Aware Controller Design for Complementarity Systems

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.

cs.RO↗

arXiv2019

Optimal Reduced-order Modeling of Bipedal Locomotion

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.

cs.RO↗

arXiv2019

Modeling and Analysis of Non-unique Behaviors in Multiple Frictional Impacts

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.

cs.RO↗

arXiv2019

A Quasi-static Model and Simulation Approach for Pushing, Grasping, and Jamming

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).

cs.RO↗