arXiv subjects

Zachary Manchester

Publications and source records attributed to Zachary Manchester.

At least 37 records · Page 2Linked to original sources

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.

cs.RO↗

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.

cs.RO↗

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.

cs.RO↗

arXiv2025

Dojo: A Differentiable Physics Engine for Robotics

We present Dojo, a differentiable physics engine for robotics that prioritizes stable simulation, accurate contact physics, and differentiability with respect to states, actions, and system parameters. Dojo models hard contact and friction with a nonlinear complementarity problem with second-order cone constraints. We introduce a custom primal-dual interior-point method to solve the second order cone program for stable forward simulation over a broad range of sample rates. We obtain smooth gradient approximations with this solver through the implicit function theorem, giving gradients that are useful for downstream trajectory optimization, policy optimization, and system identification applications. Specifically, we propose to use the central path parameter threshold in the interior point solver as a user-tunable design parameter. A high value gives a smooth approximation to contact dynamics with smooth gradients for optimization and learning, while a low value gives precise simulation rollouts with hard contact. We demonstrate Dojo's differentiability in trajectory optimization, policy learning, and system identification examples. We also benchmark Dojo against MuJoCo, PyBullet, Drake, and Brax on a variety of robot models, and study the stability and simulation quality over a range of sample frequencies and accuracy tolerances. Finally, we evaluate the sim-to-real gap in hardware experiments with a Ufactory xArm 6 robot. Dojo is an open source project implemented in Julia with Python bindings, with code available at https://github.com/dojo-sim/Dojo.jl.

cs.RO↗

arXiv2025

TinyMPC: Model-Predictive Control on Resource-Constrained Microcontrollers

Model-predictive control (MPC) is a powerful tool for controlling highly dynamic robotic systems subject to complex constraints. However, MPC is computationally demanding, and is often impractical to implement on small, resource-constrained robotic platforms. We present TinyMPC, a high-speed MPC solver with a low memory footprint targeting the microcontrollers common on small robots. Our approach is based on the alternating direction method of multipliers (ADMM) and leverages the structure of the MPC problem for efficiency. We demonstrate TinyMPC's effectiveness by benchmarking against the state-of-the-art solver OSQP, achieving nearly an order of magnitude speed increase, as well as through hardware experiments on a 27 gram quadrotor, demonstrating high-speed trajectory tracking and dynamic obstacle avoidance. TinyMPC is publicly available at https://tinympc.org.

cs.RO↗

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.

cs.RO↗

arXiv2025

A Universal Formulation for Path-Parametric Planning and Control

We present a unified framework for path-parametric planning and control. This formulation is universal as it standardizes the entire spectrum of path-parametric techniques -- from traditional path following to more recent contouring or progress-maximizing Model Predictive Control and Reinforcement Learning -- under a single framework. The ingredients underlying this universality are twofold: First, we present a compact and efficient technique capable of computing singularity-free, smooth and differentiable moving frames. Second, we derive a spatial path parameterization of the Cartesian coordinates for any arbitrary curve without prior assumptions on its parametric speed or moving frame, and that perfectly interplays with the aforementioned path parameterization method. The combination of these two ingredients leads to a planning and control framework that unites existing path-parametric techniques in literature.

cs.RO↗

arXiv2024

From Pixels to Torques with Linear Feedback

We demonstrate the effectiveness of simple observer-based linear feedback policies for "pixels-to-torques" control of robotic systems using only a robot-facing camera. Specifically, we show that the matrices of an image-based Luenberger observer (linear state estimator) for a "student" output-feedback policy can be learned from demonstration data provided by a "teacher" state-feedback policy via simple linear-least-squares regression. The resulting linear output-feedback controller maps directly from high-dimensional raw images to torques while being amenable to the rich set of analytical tools from linear systems theory, allowing us to enforce closed-loop stability constraints in the learning problem. We also investigate a nonlinear extension of the method via the Koopman embedding. Finally, we demonstrate the surprising effectiveness of linear pixels-to-torques policies on a cartpole system, both in simulation and on real hardware. The policy successfully executes both stabilizing and swing-up trajectory-tracking tasks using only camera feedback while subject to model mismatch, process and sensor noise, perturbations, and occlusions. Open-source code for all experiments can be found here: https://roboticexplorationlab.org/projects/linear_pixels_to_torques.html

cs.RO↗

arXiv2024

Wallbounce : Push wall to navigate with Contact-Implicit MPC

In this work, we introduce a framework that enables highly maneuverable locomotion using non-periodic contacts. This task is challenging for traditional optimization and planning methods to handle due to difficulties in specifying contact mode sequences in real-time. To address this, we use a bi-level contact-implicit planner and hybrid model predictive controller to draft and execute a motion plan. We investigate how this method allows us to plan arm contact events on the shmoobot, a smaller ballbot, which uses an inverse mouse-ball drive to achieve dynamic balancing with a low number of actuators. Through multiple experiments we show how the arms allow for acceleration, deceleration and dynamic obstacle avoidance that are not achievable with the mouse-ball drive alone. This demonstrates how a holistic approach to locomotion can increase the control authority of unique robot morpohologies without additional hardware by leveraging robot arms that are typically used only for manipulation. Project website: https://cmushmoobot.github.io/Wallbounce

cs.RO↗

arXiv2024

Optimal Attitude Control of Large Flexible Space Structures with Distributed Momentum Actuators

Recent spacecraft mission concepts propose larger payloads that have lighter, less rigid structures. For large lightweight structures, the natural frequencies of their vibration modes may fall within the attitude controller bandwidth, threatening the stability and settling time of the controller and compromising performance. This work tackles this issue by proposing an attitude control design paradigm of distributing momentum actuators throughout the structure to have more control authority over vibration modes. The issue of jitter disturbances introduced by these actuators is addressed by expanding the bandwidth of the attitude controller to suppress excess vibrations. Numerical simulation results show that, at the expense of more control action, a distributed configuration can achieve lower settling times and reduce structural deformation compared to a more standard centralized configuration.

astro-ph.IM↗

arXiv2024

PHODCOS: Pythagorean Hodograph-based Differentiable Coordinate System

This paper presents PHODCOS, an algorithm that assigns a moving coordinate system to a given curve. The parametric functions underlying the coordinate system, i.e., the path function, the moving frame and its angular velocity, are exact -- approximation free -- differentiable, and sufficiently continuous. This allows for computing a coordinate system for highly nonlinear curves, while remaining compliant with autonomous navigation algorithms that require first and second order gradient information. In addition, the coordinate system obtained by PHODCOS is fully defined by a finite number of coefficients, which may then be used to compute additional geometric properties of the curve, such as arc-length, curvature, torsion, etc. Therefore, PHODCOS presents an appealing paradigm to enhance the geometrical awareness of existing guidance and navigation on-orbit spacecraft maneuvers. The PHODCOS algorithm is presented alongside an analysis of its error and approximation order, and thus, it is guaranteed that the obtained coordinate system matches the given curve within a desired tolerance. To demonstrate the applicability of the coordinate system resulting from PHODCOS, we present numerical examples in the Near Rectilinear Halo Orbit (NRHO) for the Lunar Gateway.

cs.RO↗

arXiv2024

Robots with Attitude: Singularity-Free Quaternion-Based Model-Predictive Control for Agile Legged Robots

We present a model-predictive control (MPC) framework for legged robots that avoids the singularities associated with common three-parameter attitude representations like Euler angles during large-angle rotations. Our method parameterizes the robot's attitude with singularity-free unit quaternions and makes modifications to the iterative linear-quadratic regulator (iLQR) algorithm to deal with the resulting geometry. The derivation of our algorithm requires only elementary calculus and linear algebra, deliberately avoiding the abstraction and notation of Lie groups. We demonstrate the performance and computational efficiency of quaternion MPC in several experiments on quadruped and humanoid robots.

cs.RO↗

arXiv2024

Real-Time Whole-Body Control of Legged Robots with Model-Predictive Path Integral Control

This paper presents a system for enabling real-time synthesis of whole-body locomotion and manipulation policies for real-world legged robots. Motivated by recent advancements in robot simulation, we leverage the efficient parallelization capabilities of the MuJoCo simulator to achieve fast sampling over the robot state and action trajectories. Our results show surprisingly effective real-world locomotion and manipulation capabilities with a very simple control strategy. We demonstrate our approach on several hardware and simulation experiments: robust locomotion over flat and uneven terrains, climbing over a box whose height is comparable to the robot, and pushing a box to a goal position. To our knowledge, this is the first successful deployment of whole-body sampling-based MPC on real-world legged robot hardware. Experiment videos and code can be found at: https://whole-body-mppi.github.io/

cs.RO↗

arXiv2024

Differentiable Collision-Free Parametric Corridors

This paper presents a method to compute differentiable collision-free parametric corridors. In contrast to existing solutions that decompose the obstacle-free space into multiple convex sets, the continuous corridors computed by our method are smooth and differentiable, making them compatible with existing numerical techniques for learning and optimization. To achieve this, we represent the collision-free corridors as a path-parametric off-centered ellipse with a polynomial basis. We show that the problem of maximizing the volume of such corridors is convex, and can be efficiently solved. To assess the effectiveness of the proposed method, we examine its performance in a synthetic case study and subsequently evaluate its applicability in a real-world scenario from the KITTI dataset.

cs.RO↗

arXiv2024

Building a Better B-Dot: Fast Detumbling with Non-Monotonic Lyapunov Functions

Spacecraft detumbling with magnetic torque coils is an inherently underactuated control problem. Contemporary and classical magnetorquer detumbling methods do not adequately consider this underactuation, and suffer from poor performance as a result. These controllers can get stuck on an uncontrollable manifold, resulting in long detumbling times and high power consumption. This work presents a novel detumble controller based on a non-monotonic Lyapunov function that predicts the future magnetic field along the satellite's orbit and avoids uncontrollable configurations. In comparison to other controllers in the literature, our controller detumbles a satellite in significantly less time while also converging to lower overall angular momentum. We provide a derivation and proof of convergence for our controller as well as Monte-Carlo simulation results demonstrating its performance in representative use cases.

eess.SY↗

arXiv2024

On the Differentiability of the Primal-Dual Interior-Point Method

Primal-Dual Interior-Point methods are capable of solving constrained convex optimization problems to tight tolerances in a fast and robust manner. The derivatives of the primal-dual solution with respect to the problem matrices can be computed using the implicit function theorem, enabling efficient differentiation of these optimizers for a fraction of the cost of the total solution time. In the presence of active inequality constraints, this technique is only capable of providing discontinuous subgradients that present a challenge to algorithms that rely on the smoothness of these derivatives. This paper presents a technique for relaxing primal-dual solutions with a logarithmic barrier to provide smooth derivatives near active inequality constraints, with the ability to specify a uniform and consistent amount of smoothing. We pair this with an efficient primal-dual interior-point algorithm for solving an always-feasible $\ell_1$-penalized variant of a convex quadratic program, eliminating the issues surrounding learning potentially infeasible problems. This parallelizable and smoothly differentiable solver is demonstrated on a range of robotics tasks where smoothing is important. An open source implementation in JAX is available at github.com/kevin-tracy/qpax.

math.OC↗

arXiv2024

From Variance to Veracity: Unbundling and Mitigating Gradient Variance in Differentiable Bundle Adjustment Layers

Various pose estimation and tracking problems in robotics can be decomposed into a correspondence estimation problem (often computed using a deep network) followed by a weighted least squares optimization problem to solve for the poses. Recent work has shown that coupling the two problems by iteratively refining one conditioned on the other's output yields SOTA results across domains. However, training these models has proved challenging, requiring a litany of tricks to stabilize and speed up training. In this work, we take the visual odometry problem as an example and identify three plausible causes: (1) flow loss interference, (2) linearization errors in the bundle adjustment (BA) layer, and (3) dependence of weight gradients on the BA residual. We show how these issues result in noisy and higher variance gradients, potentially leading to a slow down in training and instabilities. We then propose a simple, yet effective solution to reduce the gradient variance by using the weights predicted by the network in the inner optimization loop to weight the correspondence objective in the training problem. This helps the training objective `focus' on the more important points, thereby reducing the variance and mitigating the influence of outliers. We show that the resulting method leads to faster training and can be more flexibly trained in varying training setups without sacrificing performance. In particular we show $2$--$2.5\times$ training speedups over a baseline visual odometry model we modify.

cs.CV↗