arXiv subjects

Zachary Manchester

Publications and source records attributed to Zachary Manchester.

At least 19 recordsLinked to original sources

arXiv2026

mjorbit: A Simulation Framework for Space Robotics

This paper presents a general framework for simulating multi-body space robots with contact. We bring efficient, large-scale robot simulation to in-space servicing, assembly, and manufacturing applications. First, we perform an empirical trade study of methods for coupling orbit propagation with existing robotics simulation frameworks. Next, we present mjorbit, a general, flexible, and performant framework built on the MuJoCo engine widely used in robotics, to which we add key spacecraft dynamics, actuators, and sensors. We provide a low-latency C++ CPU backend and a high-throughput GPU backend behind a simple Python API. We demonstrate mjorbit by solving several realistic on-orbit case studies with both model-predictive control and reinforcement learning. Open-source code and examples are available at: https://johnzhang3.github.io/mjorbit/

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arXiv2026

Hybrid Feedback Sampling for Sample-Efficient Model Predictive Control

Thanks to its parallelizability and flexibility, sampling-based Model Predictive Control (MPC) has become widely popular for controlling real-world robotic systems. However, for high-dimensional and open-loop unstable dynamical systems, the required number of samples to improve the control sequence will grow exponentially with the horizon, leading to poor sample efficiency and numerical instability. This paper investigates the instability of shooting methods in sampling-based MPC and shows that the optimal sampling proposal distribution can be realized by sampling with an optimized feedback policy. We refer to this algorithm as Feedback Sampling MPC (FS-MPC). FS-MPC involves a hybrid sampling design which balances local and global search based on the system stability and the available computation budget. Our theoretical analysis shows that our hybrid sampling approach achieves faster convergence than standard MPPI and better optimality than standard feedback sampling. Empirically, in diverse contact-rich control tasks like humanoid loco-manipulation and dexterous manipulation, we show that FS-MPC successfully tackles dynamically unstable tasks where standard sample-based approaches struggle, and strictly outperforms feedback policies alone. Finally, we validate our method on humanoid robot locomotion and manipulation tasks in the real world.

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arXiv2026

A Differentiable Interior-Point Method in Single Precision

Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit function theorem. However, the standard treatment of primal-dual complementarity makes the underlying linear systems increasingly ill-conditioned near the solution. While this ill-conditioning is often benign in double precision, it can be catastrophic in single precision, preventing interior-point methods from fully exploiting the accelerated hardware that underpins modern machine learning. This paper introduces a differentiable interior-point method designed for low-precision arithmetic. By using an alternative complementarity representation, we ensure that the underlying linear systems remain spectrally bounded -- even near the solution -- a property that is essential for computing accurate gradients and avoiding arithmetic exceptions. As a result, our method enables interior-point solvers to reliably solve and differentiate optimization problems in single precision that were previously confined to double precision. We demonstrate the approach through an ablation study against the standard interior-point formulation and applications in bilevel and end-to-end learning settings where differentiating through constrained optimization is essential. The source code is available at https://github.com/qpax-solver/qpax.

math.OC↗

arXiv2026

TinySDP: Real Time Semidefinite Optimization for Certifiable and Agile Edge Robotics

Semidefinite programming (SDP) provides a principled framework for convex relaxations of nonconvex geometric constraints in motion planning, yet existing solvers are too computationally expensive for real-time control, particularly on resource-constrained embedded systems. To address this gap, we introduce TinySDP, the first semidefinite programming solver designed for embedded systems, enabling real-time model-predictive control (MPC) on microcontrollers for problems with nonconvex obstacle constraints. Our approach integrates positive-semidefinite cone projections into a cached-Riccati-based ADMM solver, leveraging computational structure for embedded tractability. We pair this solver with an a posteriori rank-1 certificate that converts relaxed solutions into explicit geometric guarantees at each timestep. On challenging benchmarks, e.g., cul-de-sac and dynamic obstacle avoidance scenarios that induce failures in local methods, TinySDP achieves collision-free navigation with up to 73% shorter paths than state-of-the-art baselines. We validate our approach on a Crazyflie quadrotor, demonstrating that semidefinite constraints can be enforced at real-time rates for agile embedded robotics.

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arXiv2026

Planetary Exploration 3.0: A Roadmap for Software-Defined, Radically Adaptive Space Systems

The surface and subsurface of worlds beyond Mars remain largely unexplored. Yet these worlds hold keys to fundamental questions in planetary science - from potentially habitable subsurface oceans on icy moons to ancient records preserved in Kuiper Belt objects. NASA's success in Mars exploration was achieved through incrementalism: 22 progressively sophisticated missions over decades. This paradigm, which we call Planetary Exploration 2.0 (PE 2.0), is untenable for the outer Solar System, where cruise times of a decade or more make iterative missions infeasible. We propose Planetary Exploration 3.0 (PE 3.0): a paradigm in which unvisited worlds are explored by a single or a few missions with radically adaptive space systems. A PE 3.0 mission conducts both initial exploratory science and follow-on hypothesis-driven science based on its own in situ data returns, evolving spacecraft capabilities to work resiliently in previously unseen environments. The key enabler of PE 3.0 is software-defined space systems (SDSSs) - systems that can adapt their functions at all levels through software updates. This paper presents findings from a Keck Institute for Space Studies (KISS) workshop on PE 3.0, covering: (1) PE 3.0 systems engineering including science definition, architecture, design methods, and verification & validation; (2) software-defined space system technologies including reconfigurable hardware, multi-functionality, and modularity; (3) onboard intelligence including autonomous science, navigation, controls, and embodied AI; and (4) three PE 3.0 mission concepts: a Neptune/Triton smart flyby, an ocean world explorer, and an Oort cloud reconnaissance mission.

astro-ph.IM↗

arXiv2026

Complementarity by Construction: A Lie-Group Approach to Solving Quadratic Programs with Linear Complementarity Constraints

Many problems in robotics require reasoning over a mix of continuous dynamics and discrete events, such as making and breaking contact in manipulation and locomotion. These problems are locally well modeled by linear complementarity quadratic programs (LCQPs), an extension to QPs that introduce complementarity constraints. While very expressive, LCQPs are non-convex, and few solvers exist for computing good local solutions for use in planning pipelines. In this work, we observe that complementarity constraints form a Lie group under infinitesimal relaxation, and leverage this structure to perform on-manifold optimization. We introduce a retraction map that is numerically well behaved, and use it to parameterize the constraints so that they are satisfied by construction. The resulting solver avoids many of the classical issues with complementarity constraints. We provide an open-source solver, Marble, that is implemented in C++ with Julia and Python bindings. We demonstrate that Marble is competitive on a suite of benchmark problems, and solves a number of robotics problems where existing approaches fail to converge.

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arXiv2026

Sumo: Dynamic and Generalizable Whole-Body Loco-Manipulation

This paper presents a sim-to-real approach that enables legged robots to dynamically manipulate large and heavy objects with whole-body dexterity. Our key insight is that by performing test-time steering of a pre-trained whole-body control policy with a sample-based planner, we can enable these robots to solve a variety of dynamic loco-manipulation tasks. Interestingly, we find our method generalizes to a diverse set of objects and tasks with no additional tuning or training, and can be further enhanced by flexibly adjusting the cost function at test time. We demonstrate the capabilities of our approach through a variety of challenging loco-manipulation tasks on a Spot quadruped robot in the real world, including uprighting a tire heavier than the robot's nominal lifting capacity and dragging a crowd-control barrier larger and taller than the robot itself. Additionally, we show that the same approach can be generalized to humanoid loco-manipulation tasks, such as opening a door and pushing a table, in simulation. Project code and videos are available at https://sumo.rai-inst.com/.

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arXiv2026

Implicit Primal-Dual Interior-Point Methods for Quadratic Programming

This paper introduces a new method for solving quadratic programs using primal-dual interior-point methods. Instead of handling complementarity as an explicit equation in the Karush-Kuhn-Tucker (KKT) conditions, we ensure that complementarity is implicitly satisfied by construction. This is achieved by introducing an auxiliary variable and relating it to the duals and slacks via a retraction map. Specifically, we prove that the softplus function has favorable numerical properties compared to the commonly used exponential map. The resulting KKT system is guaranteed to be spectrally bounded, thereby eliminating the most pressing limitation of primal-dual methods: ill-conditioning near the solution. These attributes facilitate the solution of the underlying linear system, either by removing the need to compute factorizations at every iteration, enabling factorization-free approaches like indirect solvers, or allowing the solver to achieve high accuracy in low-precision arithmetic. Consequently, this novel perspective opens new opportunities for interior-point methods, especially for solving large-scale problems to high precision.

math.OC↗

arXiv2026

ADMM-based Continuous Trajectory Optimization in Graphs of Convex Sets

This paper presents a numerical solver for computing continuous trajectories in non-convex environments. Our approach relies on a customized implementation of the Alternating Direction Method of Multipliers (ADMM) built upon two key components: First, we parameterize trajectories as polynomials, allowing the primal update to be computed in closed form as a minimum-control-effort problem. Second, we introduce the concept of a spatio-temporal allocation graph based on a mixed-integer formulation and pose the slack update as a shortest-path search. The combination of these ingredients results in a solver with several distinct advantages over the state of the art. By jointly optimizing over both discrete spatial and continuous temporal domains, our method accesses a larger search space than existing decoupled approaches, enabling the discovery of superior trajectories. Additionally, the solver's structural robustness ensures reliable convergence from naive initializations, removing the bottleneck of complex warm starting in non-convex environments.

cs.RO↗

arXiv2026

Sound of Touch: Active Acoustic Tactile Sensing via String Vibrations

Distributed tactile sensing remains difficult to scale over large areas: dense sensor arrays increase wiring, cost, and fragility, while many alternatives provide limited coverage or miss fast interaction dynamics. We present Sound of Touch, an active acoustic tactile-sensing methodology that uses vibrating tensioned strings as sensing elements. The string is continuously excited electromagnetically, and a small number of pickups (contact microphones) observe spectral changes induced by contact. From short-duration audio signals, our system estimates contact location and normal force, and detects slip. To guide design and interpret the sensing mechanism, we derive a physics-based string-vibration simulator that predicts how contact position and force shift vibration modes. Experiments demonstrate millimeter-scale localization, reliable force estimation, and real-time slip detection. Our contributions are: (i) a lightweight, scalable string-based tactile sensing hardware concept for instrumenting extended robot surfaces; (ii) a physics-grounded simulation and analysis tool for contact-induced spectral shifts; and (iii) a real-time inference pipeline that maps vibration measurements to contact state.

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arXiv2025

How to Train Your Latent Control Barrier Function: Smooth Safety Filtering Under Hard-to-Model Constraints

Latent safety filters extend Hamilton-Jacobi (HJ) reachability to operate on latent state representations and dynamics learned directly from high-dimensional observations, enabling safe visuomotor control under hard-to-model constraints. However, existing methods implement "least-restrictive" filtering that discretely switch between nominal and safety policies, potentially undermining the task performance that makes modern visuomotor policies valuable. While reachability value functions can, in principle, be adapted to be control barrier functions (CBFs) for smooth optimization-based filtering, we theoretically and empirically show that current latent-space learning methods produce fundamentally incompatible value functions. We identify two sources of incompatibility: First, in HJ reachability, failures are encoded via a "margin function" in latent space, whose sign indicates whether or not a latent is in the constraint set. However, representing the margin function as a classifier yields saturated value functions that exhibit discontinuous jumps. We prove that the value function's Lipschitz constant scales linearly with the margin function's Lipschitz constant, revealing that smooth CBFs require smooth margins. Second, reinforcement learning (RL) approximations trained solely on safety policy data yield inaccurate value estimates for nominal policy actions, precisely where CBF filtering needs them. We propose the LatentCBF, which addresses both challenges through gradient penalties that lead to smooth margin functions without additional labeling, and a value-training procedure that mixes data from both nominal and safety policy distributions. Experiments on simulated benchmarks and hardware with a vision-based manipulation policy demonstrate that LatentCBF enables smooth safety filtering while doubling the task-completion rate over prior switching methods.

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arXiv2025

Convex Maneuver Planning for Spacecraft Collision Avoidance

Conjunction analysis and maneuver planning for spacecraft collision avoidance remains a manual and time-consuming process, typically involving repeated forward simulations of hand-designed maneuvers. With the growing density of satellites in low-Earth orbit (LEO), autonomy is becoming essential for efficiently evaluating and mitigating collisions. In this work, we present an algorithm to design low-thrust collision-avoidance maneuvers for short-term conjunction events. We first formulate the problem as a nonconvex quadratically-constrained quadratic program (QCQP), which we then relax into a convex semidefinite program (SDP) using Shor's relaxation. We demonstrate empirically that the relaxation is tight, which enables the recovery of globally optimal solutions to the original nonconvex problem. Our formulation produces a minimum-energy solution while ensuring a desired probability of collision at the time of closest approach. Finally, if the desired probability of collision cannot be satisfied, we relax this constraint into a penalty, yielding a minimum-risk solution. We validate our algorithm with a high-fidelity simulation of a satellite conjunction in low-Earth orbit with a simulated conjunction data message (CDM), demonstrating its effectiveness in reducing collision risk.

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arXiv2025

The Trajectory Bundle Method: Unifying Sequential-Convex Programming and Sampling-Based Trajectory Optimization

We present a unified framework for solving trajectory optimization problems in a derivative-free manner through the use of sequential convex programming. Traditionally, nonconvex optimization problems are solved by forming and solving a sequence of convex optimization problems, where the cost and constraint functions are approximated locally through Taylor series expansions. This presents a challenge for functions where differentiation is expensive or unavailable. In this work, we present a derivative-free approach to form these convex approximations by computing samples of the dynamics, cost, and constraint functions and letting the solver interpolate between them. Our framework includes sample-based trajectory optimization techniques like model-predictive path integral (MPPI) control as a special case and generalizes them to enable features like multiple shooting and general equality and inequality constraints that are traditionally associated with derivative-based sequential convex programming methods. The resulting framework is simple, flexible, and capable of solving a wide variety of practical motion planning and control problems.

math.OC↗

arXiv2025

The Surprising Effectiveness of Linear Models for Whole-Body Model-Predictive Control

When do locomotion controllers require reasoning about nonlinearities? In this work, we show that a whole-body model-predictive controller using a simple linear time-invariant approximation of the whole-body dynamics is able to execute basic locomotion tasks on complex legged robots. The formulation requires no online nonlinear dynamics evaluations or matrix inversions. We demonstrate walking, disturbance rejection, and even navigation to a goal position without a separate footstep planner on a quadrupedal robot. In addition, we demonstrate dynamic walking on a hydraulic humanoid, a robot with significant limb inertia, complex actuator dynamics, and large sim-to-real gap.

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arXiv2025

Universal Dynamics with Globally Controlled Analog Quantum Simulators

Analog quantum simulators with global control fields have emerged as powerful platforms for exploring complex quantum phenomena. Despite these advances, a fundamental theoretical question remains unresolved: to what extent can such systems realize universal quantum dynamics under global control? Here we establish a necessary and sufficient condition for universal quantum computation using only global pulse control, proving that a broad class of analog quantum simulators is, in fact, universal. We further extend this framework to fermionic and bosonic systems, including modern platforms such as ultracold atoms in optical superlattices. Moreover, we observe that analog simulators driven by random global pulses exhibit information scrambling comparable to random unitary circuits. In a dual-species neutral-atom array setup, the measurement outcomes anti-concentrate on a $\log N$ timescale despite the presence of only temporal randomness, opening opportunities for efficient randomness generation. To bridge theoretical possibility with experimental reality, we introduce \emph{direct quantum optimal control}, a control framework that enables the synthesis of complex effective Hamiltonians while incorporating realistic hardware constraints. Using this approach, we experimentally engineer three-body interactions outside the blockade regime and demonstrate topological dynamics on a Rydberg-atom array. Experimental measurements reveal dynamical signatures of symmetry-protected-topological edge modes, confirming both the expressivity and feasibility of our method. Our work opens a new avenue for quantum simulation beyond native hardware Hamiltonians, enabling the engineering of effective multi-body interactions and advancing the frontier of quantum information processing with globally-controlled analog platforms.

quant-ph↗

arXiv2025

Multi-IMU Sensor Fusion for Legged Robots

This paper presents a state-estimation solution for legged robots that uses a set of low-cost, compact, and lightweight sensors to achieve low-drift pose and velocity estimation under challenging locomotion conditions. The key idea is to leverage multiple inertial measurement units on different links of the robot to correct a major error source in standard proprioceptive odometry. We fuse the inertial sensor information and joint encoder measurements in an extended Kalman filter, then combine the velocity estimate from this filter with camera data in a factor-graph-based sliding-window estimator to form a visual-inertial-leg odometry method. We validate our state estimator through comprehensive theoretical analysis and hardware experiments performed using real-world robot data collected during a variety of challenging locomotion tasks. Our algorithm consistently achieves minimal position deviation, even in scenarios involving substantial ground impact, foot slippage, and sudden body rotations. A C++ implementation, along with a large-scale dataset, is available at https://github.com/ShuoYangRobotics/Cerberus2.0.

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arXiv2025

Realizing Robotic Swimming with Unified Fluid-Robot Multiphysics

Matching the swimming efficiency and agility of fish has remained an elusive goal in underwater robotics. Such locomotion capabilities rely on complex vortex interactions between the robot's body and the surrounding fluid. However, simulating these dynamics, which are governed by coupled ordinary and partial differential equations, is significantly more difficult than the multi-body dynamics of classical rigid robotic systems. We present a differentiable framework for simulating strongly coupled fluid-robot multiphysics as a unified optimization problem. The coupled manipulator and incompressible Navier-Stokes equations are derived together from a single Lagrangian using the principle of least action. We employ discrete variational mechanics to derive a stable, well-conditioned, and physically accurate scheme for jointly simulating articulated bodies and the surrounding fluid. We leverage the implicit function theorem to compute derivatives of the fully coupled dynamics. Using this simulator and its gradients, we realize undulating swimming gaits and optimize a highly dynamic C-start escape maneuver for a bioinspired eel robot. We validate both gaits on physical hardware, demonstrating successful sim-to-real transfer. Simulation code, hardware data, and schematics for the eel robot can be found here: https://unified-fluid-robot-multiphysics.github.io/

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arXiv2025

Whole-Body Model-Predictive Control of Legged Robots with MuJoCo

We demonstrate the surprising real-world effectiveness of a very simple approach to whole-body model-predictive control (MPC) of quadruped and humanoid robots: the iterative LQR (iLQR) algorithm with MuJoCo dynamics and finite-difference approximated derivatives. Building upon the previous success of model-based behavior synthesis and control of locomotion and manipulation tasks with MuJoCo in simulation, we show that these policies can easily generalize to the real world with few sim-to-real considerations. Our baseline method achieves real-time whole-body MPC on a variety of hardware experiments, including dynamic quadruped locomotion, quadruped walking on two legs, and full-sized humanoid bipedal locomotion. We hope this easy-to-reproduce hardware baseline lowers the barrier to entry for real-world whole-body MPC research and contributes to accelerating research velocity in the community. Our code and experiment videos will be available online at:https://johnzhang3.github.io/mujoco_ilqr

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