Zachary Manchester

Simon Le Cleac'h, Hong-Xing Yu, Michelle Guo et al. · stanford

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.

Ishaan Mahajan, Khai Nguyen, Sam Schoedel et al. · cmu

Model-predictive control (MPC) is a state-of-the-art control method for constrained robotic systems, yet deployment on resource-limited hardware remains difficult. This challenge is magnified by expressive conic constraints, which offer greater modeling power but require significantly more computation than linear alternatives. To address this challenge, we extend recent work developing fast, structure-exploiting, cached solvers for embedded applications based on the Alternating Direction Method of Multipliers (ADMM) to provide support for second-order cones, as well as C++ code generation from Python, MATLAB, and Julia. Microcontroller benchmarks show that our solver provides up to a two-order-of-magnitude speedup, ranging from 10.6x to 142.7x, over state-of-the-art embedded solvers on QP and SOCP problems, and enables us to fit order-of-magnitude larger problems in memory. We validate our solver's deployed performance through simulation and hardware experiments, including trajectory tracking with conic constraints on a 27g Crazyflie quadrotor. Our open-source code is available at https://tinympc.org.

Jeong Hun Lee, Junzhe Hu, Sofia Kwok et al.

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/

Arun L. Bishop, Micah I. Reich, Zachary Manchester

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.

Masahiro Ono, Daniel Selva, Morgan L. Cable et al.

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.

Ishaan Mahajan, Jon Arrizabalaga, Andrea Grillo et al.

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.

Jon Arrizabalaga, Zachary Manchester

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.

Lukas Pries, Jon Arrizabalaga, Zachary Manchester et al.

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.

Kunal Menda, Jayesh K. Gupta, Zachary Manchester et al.

Model-based paradigms for decision-making and control are becoming ubiquitous in robotics. They rely on the ability to efficiently learn a model of the system from data. Structured Mechanical Models (SMMs) are a data-efficient black-box parameterization of mechanical systems, typically fit to data by minimizing the error between predicted and observed accelerations or next states. In this work, we propose a methodology for fitting SMMs to data by minimizing the discrete Euler-Lagrange residual. To study our methodology, we fit models to joint-angle time-series from undamped and damped double-pendulums, studying the quality of learned models fit to data with and without observation noise. Experiments show that our methodology learns models that are better in accuracy to those of the conventional schemes for fitting SMMs. We identify use cases in which our method is a more appropriate methodology. Source code for reproducing the experiments is available at https://github.com/sisl/delsmm.

Simon Le Cleac'h, Mac Schwager, Zachary Manchester

Existing game-theoretic planning methods assume that the robot knows the objective functions of the other agents a priori while, in practical scenarios, this is rarely the case. This paper introduces LUCIDGames, an inverse optimal control algorithm that is able to estimate the other agents' objective functions in real time, and incorporate those estimates online into a receding-horizon game-theoretic planner. LUCIDGames solves the inverse optimal control problem by recasting it in a recursive parameter-estimation framework. LUCIDGames uses an unscented Kalman filter (UKF) to iteratively update a Bayesian estimate of the other agents' cost function parameters, improving that estimate online as more data is gathered from the other agents' observed trajectories. The planner then takes account of the uncertainty in the Bayesian parameter estimates of other agents by planning a trajectory for the robot subject to uncertainty ellipse constraints. The algorithm assumes no explicit communication or coordination between the robot and the other agents in the environment. An MPC implementation of LUCIDGames demonstrates real-time performance on complex autonomous driving scenarios with an update frequency of 40 Hz. Empirical results demonstrate that LUCIDGames improves the robot's performance over existing game-theoretic and traditional MPC planning approaches. Our implementation of LUCIDGames is available at https://github.com/RoboticExplorationLab/LUCIDGames.jl.

Kunal Menda, Jean de Becdelièvre, Jayesh K. Gupta et al.

System identification is a key step for model-based control, estimator design, and output prediction. This work considers the offline identification of partially observed nonlinear systems. We empirically show that the certainty-equivalent approximation to expectation-maximization can be a reliable and scalable approach for high-dimensional deterministic systems, which are common in robotics. We formulate certainty-equivalent expectation-maximization as block coordinate-ascent, and provide an efficient implementation. The algorithm is tested on a simulated system of coupled Lorenz attractors, demonstrating its ability to identify high-dimensional systems that can be intractable for particle-based approaches. Our approach is also used to identify the dynamics of an aerobatic helicopter. By augmenting the state with unobserved fluid states, a model is learned that predicts the acceleration of the helicopter better than state-of-the-art approaches. The codebase for this work is available at https://github.com/sisl/CEEM.

Hong-Ye Hu, Abigail McClain Gomez, Liyuan Chen et al.

Analog quantum simulators with global control fields have emerged as powerful platforms for exploring complex quantum phenomena. Recent breakthroughs, such as the coherent control of thousands of atoms, highlight the growing potential for quantum applications at scale. 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. Crucially, to connect the theoretical possibility with experimental reality, we introduce a new control technique into the experiment - direct quantum optimal control. This method enables the synthesis of complex effective Hamiltonians and allows us to incorporate realistic hardware constraints. To show its practical power, we experimentally engineer three-body interactions outside the blockade regime and demonstrate topological dynamics on a Rydberg atom array. Using the new control framework, we overcome key experimental challenges, including hardware limitations and atom position fluctuations in the non-blockade regime, by identifying smooth, short-duration pulses that achieve high-fidelity dynamics. Experimental measurements reveal dynamical signatures of symmetry-protected-topological edge modes, confirming both the expressivity and feasibility of our approach. 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.

John Z. Zhang, Maks Sorokin, Jan Brüdigam et al.

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 \href{https://sumo.rai-inst.com/}{https://sumo.rai-inst.com/}.

Kensuke Nakamura, Arun L. Bishop, Steven Man et al.

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.

Swaminathan Gurumurthy, Karnik Ram, Bingqing Chen et al.

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.

Swaminathan Gurumurthy, Shaojie Bai, Zachary Manchester et al.

Many tasks in deep learning involve optimizing over the \emph{inputs} to a network to minimize or maximize some objective; examples include optimization over latent spaces in a generative model to match a target image, or adversarially perturbing an input to worsen classifier performance. Performing such optimization, however, is traditionally quite costly, as it involves a complete forward and backward pass through the network for each gradient step. In a separate line of work, a recent thread of research has developed the deep equilibrium (DEQ) model, a class of models that foregoes traditional network depth and instead computes the output of a network by finding the fixed point of a single nonlinear layer. In this paper, we show that there is a natural synergy between these two settings. Although, naively using DEQs for these optimization problems is expensive (owing to the time needed to compute a fixed point for each gradient step), we can leverage the fact that gradient-based optimization can \emph{itself} be cast as a fixed point iteration to substantially improve the overall speed. That is, we \emph{simultaneously} both solve for the DEQ fixed point \emph{and} optimize over network inputs, all within a single ``augmented'' DEQ model that jointly encodes both the original network and the optimization process. Indeed, the procedure is fast enough that it allows us to efficiently \emph{train} DEQ models for tasks traditionally relying on an ``inner'' optimization loop. We demonstrate this strategy on various tasks such as training generative models while optimizing over latent codes, training models for inverse problems like denoising and inpainting, adversarial training and gradient based meta-learning.

Taylor A. Howell, Simon Le Cleac'h, Sumeet Singh et al.

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.

Simon Le Cleac'h, Taylor Howell, Shuo Yang et al.

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.

Simon Le Cleac'h, Mac Schwager, Zachary Manchester

Dynamic games are an effective paradigm for dealing with the control of multiple interacting actors. This paper introduces ALGAMES (Augmented Lagrangian GAME-theoretic Solver), a solver that handles trajectory-optimization problems with multiple actors and general nonlinear state and input constraints. Its novelty resides in satisfying the first-order optimality conditions with a quasi-Newton root-finding algorithm and rigorously enforcing constraints using an augmented Lagrangian method. We evaluate our solver in the context of autonomous driving on scenarios with a strong level of interactions between the vehicles. We assess the robustness of the solver using Monte Carlo simulations. It is able to reliably solve complex problems like ramp merging with three vehicles three times faster than a state-of-the-art DDP-based approach. A model-predictive control (MPC) implementation of the algorithm, running at more than 60 Hz, demonstrates ALGAMES' ability to mitigate the "frozen robot" problem on complex autonomous driving scenarios like merging onto a crowded highway.

Remy Derollez, Simon Le Cleac'h, Zachary Manchester

Managing uncertainty is a fundamental and critical issue in spacecraft entry guidance. This paper presents a novel approach for uncertainty propagation during entry, descent and landing that relies on a new sum-of-squares robust verification technique. Unlike risk-based and probabilistic approaches, our technique does not rely on any probabilistic assumptions. It uses a set-based description to bound uncertainties and disturbances like vehicle and atmospheric parameters and winds. The approach leverages a recently developed sampling-based version of sum-of-squares programming to compute regions of finite time invariance, commonly referred to as "invariant funnels". We apply this approach to a three-degree-of-freedom entry vehicle model and test it using a Mars Science Laboratory reference trajectory. We compute tight approximations of robust invariant funnels that are guaranteed to reach a goal region with increased landing accuracy while respecting realistic thermal constraints.

Taylor A. Howell, Chunjiang Fu, Zachary Manchester

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.

Jayesh K. Gupta, Kunal Menda, Zachary Manchester et al.

Model-based methods are the dominant paradigm for controlling robotic systems, though their efficacy depends heavily on the accuracy of the model used. Deep neural networks have been used to learn models of robot dynamics from data, but they suffer from data-inefficiency and the difficulty to incorporate prior knowledge. We introduce Structured Mechanical Models, a flexible model class for mechanical systems that are data-efficient, easily amenable to prior knowledge, and easily usable with model-based control techniques. The goal of this work is to demonstrate the benefits of using Structured Mechanical Models in lieu of black-box neural networks when modeling robot dynamics. We demonstrate that they generalize better from limited data and yield more reliable model-based controllers on a variety of simulated robotic domains.

Jan Brüdigam, Zachary Manchester

Most dynamic simulation tools parameterize the configuration of multi-body robotic systems using minimal coordinates, also called generalized or joint coordinates. However, maximal-coordinate approaches have several advantages over minimal-coordinate parameterizations, including native handling of closed kinematic loops and nonholonomic constraints. This paper describes a linear-time variational integrator that is formulated in maximal coordinates. Due to its variational formulation, the algorithm does not suffer from constraint drift and has favorable energy and momentum conservation properties. A sparse matrix factorization technique allows the dynamics of a loop-free articulated mechanism with $n$ links to be computed in $O(n)$ (linear) time. Additional constraints that introduce loops can also be handled by the algorithm without incurring much computational overhead. Experimental results show that our approach offers speed competitive with state-of-the-art minimal-coordinate algorithms while outperforming them in several scenarios, especially when dealing with closed loops and configuration singularities.

Simon Le Cleac'h, Mac Schwager, Zachary Manchester

Dynamic games are an effective paradigm for dealing with the control of multiple interacting actors. This paper introduces ALGAMES (Augmented Lagrangian GAME-theoretic Solver), a solver that handles trajectory optimization problems with multiple actors and general nonlinear state and input constraints. Its novelty resides in satisfying the first order optimality conditions with a quasi-Newton root-finding algorithm and rigorously enforcing constraints using an augmented Lagrangian formulation. We evaluate our solver in the context of autonomous driving on scenarios with a strong level of interactions between the vehicles. We assess the robustness of the solver using Monte Carlo simulations. It is able to reliably solve complex problems like ramp merging with three vehicles three times faster than a state-of-the-art DDP-based approach. A model predictive control (MPC) implementation of the algorithm demonstrates real-time performance on complex autonomous driving scenarios with an update frequency higher than 60 Hz.

Benoit Landry, Joseph Lorenzetti, Zachary Manchester et al.

Many robotics applications, from object manipulation to locomotion, require planning methods that are capable of handling the dynamics of contact. Trajectory optimization has been shown to be a viable approach that can be made to support contact dynamics. However, the current state-of-the art methods remain slow and are often difficult to get to converge. In this work, we leverage recent advances in bilevel optimization to design an algorithm capable of efficiently generating trajectories that involve making and breaking contact. We demonstrate our method's efficiency by outperforming an alternative state-of-the-art method on two benchmark problems. We moreover demonstrate the method's ability to design a simple periodic gait for a quadruped with 15 degrees of freedom and four contact points.

Jayesh K. Gupta, Kunal Menda, Zachary Manchester et al.

Learning accurate dynamics models is necessary for optimal, compliant control of robotic systems. Current approaches to white-box modeling using analytic parameterizations, or black-box modeling using neural networks, can suffer from high bias or high variance. We address the need for a flexible, gray-box model of mechanical systems that can seamlessly incorporate prior knowledge where it is available, and train expressive function approximators where it is not. We propose to parameterize a mechanical system using neural networks to model its Lagrangian and the generalized forces that act on it. We test our method on a simulated, actuated double pendulum. We show that our method outperforms a naive, black-box model in terms of data-efficiency, as well as performance in model-based reinforcement learning. We also conduct a systematic study of our method's ability to incorporate available prior knowledge about the system to improve data efficiency.

Benoit Landry, Zachary Manchester, Marco Pavone

Many problems in modern robotics can be addressed by modeling them as bilevel optimization problems. In this work, we leverage augmented Lagrangian methods and recent advances in automatic differentiation to develop a general-purpose nonlinear optimization solver that is well suited to bilevel optimization. We then demonstrate the validity and scalability of our algorithm with two representative robotic problems, namely robust control and parameter estimation for a system involving contact. We stress the general nature of the algorithm and its potential relevance to many other problems in robotics.

Neel Doshi, Kaushik Jayaram, Benjamin Goldberg et al.

Planning locomotion trajectories for legged microrobots is challenging because of their complex morphology, high frequency passive dynamics, and discontinuous contact interactions with their environment. Consequently, such research is often driven by time-consuming experimental methods. As an alternative, we present a framework for systematically modeling, planning, and controlling legged microrobots. We develop a three-dimensional dynamic model of a 1.5 gram quadrupedal microrobot with complexity (e.g., number of degrees of freedom) similar to larger-scale legged robots. We then adapt a recently developed variational contact-implicit trajectory optimization method to generate feasible whole-body locomotion plans for this microrobot, and we demonstrate that these plans can be tracked with simple joint-space controllers. We plan and execute periodic gaits at multiple stride frequencies and on various surfaces. These gaits achieve high per-cycle velocities, including a maximum of 10.87 mm/cycle, which is 15% faster than previously measured velocities for this microrobot. Furthermore, we plan and execute a vertical jump of 9.96 mm, which is 78% of the microrobot's center-of-mass height. To the best of our knowledge, this is the first end-to-end demonstration of planning and tracking whole-body dynamic locomotion on a millimeter-scale legged microrobot.