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Zachary Manchester

Publications and source records attributed to Zachary Manchester.

At least 55 records · Page 3Linked to original sources
arXiv2024

Contingency-Aware Station-Keeping Control of Halo Orbits

We present an algorithm to perform fuel-optimal stationkeeping for spacecraft in unstable halo orbits with additional constraints to ensure safety in the event of a control failure. We formulate a convex trajectory-optimization problem to generate impulsive spacecraft maneuvers to loosely track a halo orbit using a receding-horizon controller. Our solution also provides a safe exit strategy in the event that propulsion is lost at any point in the mission. We validate our algorithm in simulations of the three-body Earth-Moon and Saturn-Enceladus systems, demonstrating both low total delta-v and a safe contingency plan throughout the mission.

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arXiv2024

A Convex Formulation of the Soft-Capture Problem

We present a fast trajectory optimization algorithm for the soft capture of uncooperative tumbling space objects. Our algorithm generates safe, dynamically feasible, and minimum-fuel trajectories for a six-degree-of-freedom servicing spacecraft to achieve soft capture (near-zero relative velocity at contact) between predefined locations on the servicer spacecraft and target body. We solve a convex problem by enforcing a convex relaxation of the field-of-view constraint, followed by a sequential convex program correcting the trajectory for collision avoidance. The optimization problems can be solved with a standard second-order cone programming solver, making the algorithm both fast and practical for implementation in flight software. We demonstrate the performance and robustness of our algorithm in simulation over a range of object tumble rates up to 10°/s.

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arXiv2023

Efficient Online Learning of Contact Force Models for Connector Insertion

Contact-rich manipulation tasks with stiff frictional elements like connector insertion are difficult to model with rigid-body simulators. In this work, we propose a new approach for modeling these environments by learning a quasi-static contact force model instead of a full simulator. Using a feature vector that contains information about the configuration and control, we find a linear mapping adequately captures the relationship between this feature vector and the sensed contact forces. A novel Linear Model Learning (LML) algorithm is used to solve for the globally optimal mapping in real time without any matrix inversions, resulting in an algorithm that runs in nearly constant time on a GPU as the model size increases. We validate the proposed approach for connector insertion both in simulation and hardware experiments, where the learned model is combined with an optimization-based controller to achieve smooth insertions in the presence of misalignments and uncertainty. Our website featuring videos, code, and more materials is available at https://model-based-plugging.github.io/.

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arXiv2023

ReLU-QP: A GPU-Accelerated Quadratic Programming Solver for Model-Predictive Control

We present ReLU-QP, a GPU-accelerated solver for quadratic programs (QPs) that is capable of solving high-dimensional control problems at real-time rates. ReLU-QP is derived by exactly reformulating the Alternating Direction Method of Multipliers (ADMM) algorithm for solving QPs as a deep, weight-tied neural network with rectified linear unit (ReLU) activations. This reformulation enables the deployment of ReLU-QP on GPUs using standard machine-learning toolboxes. We evaluate the performance of ReLU-QP across three model-predictive control (MPC) benchmarks: stabilizing random linear dynamical systems with control limits, balancing an Atlas humanoid robot on a single foot, and tracking whole-body reference trajectories on a quadruped equipped with a six-degree-of-freedom arm. These benchmarks indicate that ReLU-QP is competitive with state-of-the-art CPU-based solvers for small-to-medium-scale problems and offers order-of-magnitude speed improvements for larger-scale problems.

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arXiv2023

Variational Integrators and Graph-Based Solvers for Multibody Dynamics in Maximal Coordinates

Multibody dynamics simulators are an important tool in many fields, including learning and control for robotics. However, many existing dynamics simulators suffer from inaccuracies when dealing with constrained mechanical systems due to unsuitable integrators with bad energy behavior and problematic constraint violations, for example for contact interactions. Variational integrators are numerical discretization methods that can reduce physical inaccuracies when simulating mechanical systems, and formulating the dynamics in maximal coordinates allows for easy and numerically robust incorporation of constraints such as kinematic loops or contacts. Therefore, this article derives a variational integrator for mechanical systems with equality and inequality constraints in maximal coordinates. Additionally, efficient graph-based sparsity-exploiting algorithms for solving the integrator are provided and implemented as an open-source simulator. The evaluation of the simulator shows improved physical accuracy due to the variational integrator and the advantages of the sparse solvers. Comparisons to minimal-coordinate algorithms show improved numerical robustness and application examples of a walking robot and an exoskeleton with explicit constraints demonstrate the necessity and capabilities of maximal coordinates.

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arXiv2023

Direct Collocation for Quantum Optimal Control

We present an adaptation of direct collocation -- a trajectory optimization method commonly used in robotics and aerospace applications -- to quantum optimal control (QOC); we refer to this method as Pade Integrator COllocation (PICO). This approach supports general nonlinear constraints on the states and controls, takes advantage of state-of-the-art large-scale nonlinear programming solvers, and has superior convergence properties compared to standard approaches like GRAPE and CRAB. PICO also allows for the formulation of novel free-time and minimum-time control problems -- crucial for realizing high-performance quantum computers when the optimal pulse duration is not known a priori. We demonstrate PICO's performance both in simulation and on hardware with a 3D circuit cavity quantum electrodynamics system.

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arXiv2023

Learning Covariances for Estimation with Constrained Bilevel Optimization

We consider the problem of learning error covariance matrices for robotic state estimation. The convergence of a state estimator to the correct belief over the robot state is dependent on the proper tuning of noise models. During inference, these models are used to weigh different blocks of the Jacobian and error vector resulting from linearization and hence, additionally affect the stability and convergence of the non-linear system. We propose a gradient-based method to estimate well-conditioned covariance matrices by formulating the learning process as a constrained bilevel optimization problem over factor graphs. We evaluate our method against baselines across a range of simulated and real-world tasks and demonstrate that our technique converges to model estimates that lead to better solutions as evidenced by the improved tracking accuracy on unseen test trajectories.

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arXiv2023

SLoMo: A General System for Legged Robot Motion Imitation from Casual Videos

We present SLoMo: a first-of-its-kind framework for transferring skilled motions from casually captured "in the wild" video footage of humans and animals to legged robots. SLoMo works in three stages: 1) synthesize a physically plausible reconstructed key-point trajectory from monocular videos; 2) optimize a dynamically feasible reference trajectory for the robot offline that includes body and foot motion, as well as contact sequences that closely tracks the key points; 3) track the reference trajectory online using a general-purpose model-predictive controller on robot hardware. Traditional motion imitation for legged motor skills often requires expert animators, collaborative demonstrations, and/or expensive motion capture equipment, all of which limits scalability. Instead, SLoMo only relies on easy-to-obtain monocular video footage, readily available in online repositories such as YouTube. It converts videos into motion primitives that can be executed reliably by real-world robots. We demonstrate our approach by transferring the motions of cats, dogs, and humans to example robots including a quadruped (on hardware) and a humanoid (in simulation). To the best knowledge of the authors, this is the first attempt at a general-purpose motion transfer framework that imitates animal and human motions on legged robots directly from casual videos without artificial markers or labels.

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arXiv2023

Propulsion-Free Cross-Track Control of a LEO Small-Satellite Constellation with Differential Drag

In this work, we achieve propellantless control of both cross-track and along-track separation of a satellite formation by manipulating atmospheric drag. Increasing the differential drag of one satellite with respect to another directly introduces along-track separation, while cross-track separation can be achieved by taking advantage of higher-order terms in the Earth's gravitational field that are functions of altitude. We present an algorithm for solving an n-satellite formation flying problem based on linear programming. We demonstrate this algorithm in a receeding-horizon control scheme in the presence of disturbances and modeling errors in a high-fidelity closed-loop orbital dynamics simulation. Our results show that separation distances of hundreds of kilometers can be achieved by a small-satellite formation in low-Earth orbit over a few months.

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arXiv2023

Differentiable Collision Detection for a Set of Convex Primitives

Collision detection between objects is critical for simulation, control, and learning for robotic systems. However, existing collision detection routines are inherently non-differentiable, limiting their applications in gradient-based optimization tools. In this work, we propose DCOL: a fast and fully differentiable collision-detection framework that reasons about collisions between a set of composable and highly expressive convex primitive shapes. This is achieved by formulating the collision detection problem as a convex optimization problem that solves for the minimum uniform scaling applied to each primitive before they intersect. The optimization problem is fully differentiable with respect to the configurations of each primitive and is able to return a collision detection metric and contact points on each object, agnostic of interpenetration. We demonstrate the capabilities of DCOL on a range of robotics problems from trajectory optimization and contact physics, and have made an open-source implementation available.

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arXiv2023

Differentiable Physics Simulation of Dynamics-Augmented Neural Objects

We present a differentiable pipeline for simulating the motion of objects that represent their geometry as a continuous density field parameterized as a deep network. This includes Neural Radiance Fields (NeRFs), and other related models. From the density field, we estimate the dynamical properties of the object, including its mass, center of mass, and inertia matrix. We then introduce a differentiable contact model based on the density field for computing normal and friction forces resulting from collisions. This allows a robot to autonomously build object models that are visually and \emph{dynamically} accurate from still images and videos of objects in motion. The resulting Dynamics-Augmented Neural Objects (DANOs) are simulated with an existing differentiable simulation engine, Dojo, interacting with other standard simulation objects, such as spheres, planes, and robots specified as URDFs. A robot can use this simulation to optimize grasps and manipulation trajectories of neural objects, or to improve the neural object models through gradient-based real-to-simulation transfer. We demonstrate the pipeline to learn the coefficient of friction of a bar of soap from a real video of the soap sliding on a table. We also learn the coefficient of friction and mass of a Stanford bunny through interactions with a Panda robot arm from synthetic data, and we optimize trajectories in simulation for the Panda arm to push the bunny to a goal location.

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arXiv2023

Aquarium: A Fully Differentiable Fluid-Structure Interaction Solver for Robotics Applications

We present Aquarium, a differentiable fluid-structure interaction solver for robotics that offers stable simulation, accurately coupled fluid-robot physics in two dimensions, and full differentiability with respect to fluid and robot states and parameters. Aquarium achieves stable simulation with accurate flow physics by directly integrating over the incompressible Navier-Stokes equations using a fully implicit Crank-Nicolson scheme with a second-order finite-volume spatial discretization. The fluid and robot physics are coupled using the immersed-boundary method by formulating the no-slip condition as an equality constraint applied directly to the Navier-Stokes system. This choice of coupling allows the fluid-structure interaction to be posed and solved as a nonlinear optimization problem. This optimization-based formulation is then exploited using the implicit-function theorem to compute derivatives. Derivatives can then be passed to downstream gradient-based optimization or learning algorithms. We demonstrate Aquarium's ability to accurately simulate coupled fluid-robot physics with numerous 2D examples, including a cylinder in free stream and a soft robotic fish tail with hardware validation. We also demonstrate Aquarium's ability to provide analytical gradients by performing gradient-based shape-and-gait optimization of an oscillating diamond foil to maximize its generated thrust.

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arXiv2023

Data-Efficient Model Learning for Control with Jacobian-Regularized Dynamic-Mode Decomposition}

We present a data-efficient algorithm for learning models for model-predictive control (MPC). Our approach, Jacobian-Regularized Dynamic-Mode Decomposition (JDMD), offers improved sample efficiency over traditional Koopman approaches based on Dynamic-Mode Decomposition (DMD) by leveraging Jacobian information from an approximate prior model of the system, and improved tracking performance over traditional model-based MPC. We demonstrate JDMD's ability to quickly learn bilinear Koopman dynamics representations across several realistic examples in simulation, including a perching maneuver for a fixed-wing aircraft with an empirically derived high-fidelity physics model. In all cases, we show that the models learned by JDMD provide superior tracking and generalization performance within a model-predictive control framework, even in the presence of significant model mismatch, when compared to approximate prior models and models learned by standard Extended DMD (EDMD).

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arXiv2023

Direct Policy Optimization using Deterministic Sampling and Collocation

We present an approach for approximately solving discrete-time stochastic optimal-control problems by combining direct trajectory optimization, deterministic sampling, and policy optimization. Our feedback motion-planning algorithm uses a quasi-Newton method to simultaneously optimize a reference trajectory, a set of deterministically chosen sample trajectories, and a parameterized policy. We demonstrate that this approach exactly recovers LQR policies in the case of linear dynamics, quadratic objective, and Gaussian disturbances. We also demonstrate the algorithm on several nonlinear, underactuated robotic systems to highlight its performance and ability to handle control limits, safely avoid obstacles, and generate robust plans in the presence of unmodeled dynamics.

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arXiv2023

Trajectory Optimization with Optimization-Based Dynamics

We present a framework for bi-level trajectory optimization in which a system's dynamics are encoded as the solution to a constrained optimization problem and smooth gradients of this lower-level problem are passed to an upper-level trajectory optimizer. This optimization-based dynamics representation enables constraint handling, additional variables, and non-smooth behavior to be abstracted away from the upper-level optimizer, and allows classical unconstrained optimizers to synthesize trajectories for more complex systems. We provide an interior-point method for efficient evaluation of constrained dynamics and utilize implicit differentiation to compute smooth gradients of this representation. We demonstrate the framework by modeling systems from locomotion, aerospace, and manipulation domains including: acrobot with joint limits, cart-pole subject to Coulomb friction, Raibert hopper, rocket landing with thrust limits, and planar-push task with optimization-based dynamics and then optimize trajectories using iterative LQR.

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arXiv2023

CALIPSO: A Differentiable Solver for Trajectory Optimization with Conic and Complementarity Constraints

We present a new solver for non-convex trajectory optimization problems that is specialized for robotics applications. CALIPSO, or the Conic Augmented Lagrangian Interior-Point SOlver, combines several strategies for constrained numerical optimization to natively handle second-order cones and complementarity constraints. It reliably solves challenging motion-planning problems that include contact-implicit formulations of impacts and Coulomb friction and state-triggered constraints where general-purpose non-convex solvers like SNOPT and Ipopt fail to converge. Additionally, CALIPSO supports efficient differentiation of solutions with respect to problem data, enabling bi-level optimization applications like auto-tuning of feedback policies. Reliable convergence of the solver is demonstrated on a range of problems from manipulation, locomotion, and aerospace domains. An open-source implementation of this solver is available.

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arXiv2023

Fast Contact-Implicit Model-Predictive Control

We present a general approach for controlling robotic systems that make and break contact with their environments. Contact-implicit model predictive control (CI-MPC) generalizes linear MPC to contact-rich settings by utilizing a bi-level planning formulation with lower-level contact dynamics formulated as time-varying linear complementarity problems (LCPs) computed using strategic Taylor approximations about a reference trajectory. These dynamics enable the upper-level planning problem to reason about contact timing and forces, and generate entirely new contact-mode sequences online. To achieve reliable and fast numerical convergence, we devise a structure-exploiting interior-point solver for these LCP contact dynamics and a custom trajectory optimizer for the tracking problem. We demonstrate real-time solution rates for CI-MPC and the ability to generate and track non-periodic behaviours in hardware experiments on a quadrupedal robot. We also show that the controller is robust to model mismatch and can respond to disturbances by discovering and exploiting new contact modes across a variety of robotic systems in simulation, including a pushbot, planar hopper, planar quadruped, and planar biped.

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arXiv2023

Single-Level Differentiable Contact Simulation

We present a differentiable formulation of rigid-body contact dynamics for objects and robots represented as compositions of convex primitives. Existing optimization-based approaches simulating contact between convex primitives rely on a bilevel formulation that separates collision detection and contact simulation. These approaches are unreliable in realistic contact simulation scenarios because isolating the collision detection problem introduces contact location non-uniqueness. Our approach combines contact simulation and collision detection into a unified single-level optimization problem. This disambiguates the collision detection problem in a physics-informed manner. Compared to previous differentiable simulation approaches, our formulation features improved simulation robustness and a reduction in computational complexity by more than an order of magnitude. We illustrate the contact and collision differentiability on a robotic manipulation task requiring optimization-through-contact. We provide a numerically efficient implementation of our formulation in the Julia language called Silico.jl.

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