Aaron M. Johnson

Ilyass Taouil, Michal Ciebelski, Shafeef Omar et al.

We present MotionDisco, a framework that discovers contact-rich, long-horizon humanoid loco-manipulation motions from scratch, without relying on teleoperation or motion retargeting from human demonstrations. This is challenging because the space of possible contact interactions grows combinatorially with the task horizon and the number of objects in the scene. MotionDisco enables rapid discovery of novel motions by coupling a large language model (LLM) guided evolutionary search over sequences of interactions with an efficient sequential kinodynamic trajectory optimizer and pruning strategy, enabling the rapid discovery of novel skills. Through extensive ablation studies, we show that our LLM-guided search discovers successful whole-body trajectories across several challenging long-horizon tasks. Finally, by training reinforcement learning tracking policies on the discovered trajectories, we transfer the motions to a real humanoid robot. This is the first work to discover and deploy long-horizon humanoid loco-manipulation skills entirely through automated evolutionary search. Supplementary videos of the experiments are available at: https://youtu.be/DHiVz34QYlw.

Naomi Oke, Aja Carter, Ben Gu et al.

Scaling the design of robots up or down remains a fundamental challenge. While biological systems follow well-established isometric and allometric scaling laws relating mass, stride frequency, velocity, and torque, it is unclear how these relationships translate to robotic systems. In this paper, we generate similar allometric scaling laws for bipedal robots across three orders of magnitude in leg length. First, we conduct a review of legged robots from the literature and extract empirical relationships between leg length (L), body length, mass, and speed. These data show that robot mass scales more closely to L^2, in contrast to the L^3 scaling predicted by isometric scaling. We then perform controlled simulation studies in Drake using three variants of real quasi-passive, hip-actuated walkers with different foot geometries and control strategies. We evaluate the performance of each design scaled with leg length, L. Across all robots, walking velocity follows the expected L^(1/2) trend from dynamic similarity. Minimum required torque scales more closely with m*L than the isometric model of m*L^2. Foot geometry scaled proportionally with L^1. These results provide new insight into how robot designs allometrically scale to different sizes, and how that scaling is different from isometric or biological scaling laws.

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.

J. Joe Payne, Nathan J. Kong, Aaron M. Johnson

In this paper we present a method for updating robotic state belief through contact with uncertain surfaces and apply this update to a Kalman filter for more accurate state estimation. Examining how guard surface uncertainty affects the time spent in each mode, we derive a guard saltation matrix - which maps perturbations prior to hybrid events to perturbations after - accounting for additional variation in the resulting state. Additionally, we propose the use of parameterized reset functions - capturing how unknown parameters change how states are mapped from one mode to the next - the Jacobian of which accounts for the additional uncertainty in the resulting state. The accuracy of these mappings is shown by simulating sampled distributions through uncertain transition events and comparing the resulting covariances. Finally, we integrate these additional terms into the "uncertainty aware Salted Kalman Filter", uaSKF, and show a peak reduction in average estimation error by 24-60% on a variety of test conditions and systems.

James Zhu, Nathan J. Kong, George Council et al.

Many controllers for legged robotic systems leverage open- or closed-loop control at discrete hybrid events to enhance stability. These controllers appear in several well studied phenomena such as the Raibert stepping controller, paddle juggling and swing leg retraction. This work introduces hybrid event shaping (HES): a generalized method for analyzing and producing stable hybrid event controllers. HES utilizes the saltation matrix, which gives a closed-form equation for the effect that hybrid events have on stability. We also introduce shape parameters, which are higher order terms that can be tuned completely independently from the system dynamics to promote stability. Optimization methods are used to produce values of these parameters that optimize a stability measure. Hybrid event shaping captures previously developed control methods while also producing new optimally stable trajectories without the need for continuous-domain feedback.

Nathan J. Kong, George Council, Aaron M. Johnson

Trajectory optimization is a popular strategy for planning trajectories for robotic systems. However, many robotic tasks require changing contact conditions, which is difficult due to the hybrid nature of the dynamics. The optimal sequence and timing of these modes are typically not known ahead of time. In this work, we extend the Iterative Linear Quadratic Regulator (iLQR) method to a class of piecewise smooth hybrid dynamical systems by allowing for changing hybrid modes in the forward pass, using the saltation matrix to update the gradient information in the backwards pass, and using a reference extension to account for mode mismatch. We demonstrate these changes on a variety of hybrid systems and compare the different strategies for computing the gradients.

Nathan J. Kong, J. Joe Payne, George Council et al.

Many state estimation and control algorithms require knowledge of how probability distributions propagate through dynamical systems. However, despite hybrid dynamical systems becoming increasingly important in many fields, there has been little work on utilizing the knowledge of how probability distributions map through hybrid transitions. Here, we make use of a propagation law that employs the saltation matrix (a first-order update to the sensitivity equation) to create the Salted Kalman Filter (SKF), a natural extension of the Kalman Filter and Extended Kalman Filter to hybrid dynamical systems. Away from hybrid events, the SKF is a standard Kalman filter. When a hybrid event occurs, the saltation matrix plays an analogous role as that of the system dynamics, subsequently inducing a discrete modification to both the prediction and update steps. The SKF outperforms a naive variational update - the Jacobian of the reset map - by having a reduced mean squared error in state estimation, especially immediately after a hybrid transition event. Compared a hybrid particle filter, the particle filter outperforms the SKF in mean squared error only when a large number of particles are used, likely due to a more accurate accounting of the split distribution near a hybrid transition.

Wooshik Kim, Catherine Pavlov, Aaron M. Johnson

Autonomy for robots interacting with sand will enable a wide range of beneficial behaviors, from earth moving for construction and farming vehicles to navigating rough terrain for Mars rovers. The goal of this work is to shape sand into desired forms. Unlike other common autonomous tasks of achieving desired state of a robot, achieving a desired shape of a continuously deformable environment like sand is a much more challenging task. The state of robot can be described with a couple of states-x, y, z, roll, pitch, yaw-but the desired shape of sand can not be described with just a few values. Sand is an aggregation of billions of small particles. After simplifying the model of sand and tool interaction by looking only at the surface of the heightmap, we can formulate the problems into something that is still high dimensional (hundreds to thousands of state dimensions) but much more solvable. We show how this problem can be formulated into a graph search problem and solve it with the A-star algorithm and report preliminary results on using deep reinforcement learning methods like Deep Q-Network and Deep Deterministic Policy Gradient.

Matt Martone, Catherine Pavlov, Adam Zeloof et al.

Modern climbing robots have risen to great heights, but mechanisms meant to scale cliffs often locomote slowly and over-cautiously on level ground. Here we introduce T-RHex, an iteration on the classic cockroach-inspired hexapod that has been augmented with microspine feet for climbing. T-RHex is a mechanically intelligent platform capable of efficient locomotion on ground with added climbing abilities. The legs integrate the compliance required for the microspines with the compliance required for locomotion in order to simplify the design and reduce mass. The microspine fabrication is simplified by embedding the spines during an additive manufacturing process. We present results that show that the addition of microspines to the T-RHex platform greatly increases the maximum slope that the robot is able to statically hang on (up to a 45 degree overhang) and ascend (up to 55 degrees) without sacrificing ground mobility.

Amir Patel, Stacey Shield, Saif Kazi et al.

In this paper we propose a method to improve the accuracy of trajectory optimization for dynamic robots with intermittent contact by using orthogonal collocation. Until recently, most trajectory optimization methods for systems with contacts employ mode-scheduling, which requires an a priori knowledge of the contact order and thus cannot produce complex or non-intuitive behaviors. Contact-implicit trajectory optimization methods offer a solution to this by allowing the optimization to make or break contacts as needed, but thus far have suffered from poor accuracy. Here, we combine methods from direct collocation using higher order orthogonal polynomials with contact-implicit optimization to generate trajectories with significantly improved accuracy. The key insight is to increase the order of the polynomial representation while maintaining the assumption that impact occurs over the duration of one finite element.

Gilwoo Lee, Zita Marinho, Aaron M. Johnson et al.

This paper introduces a novel system identification and tracking method for PieceWise Smooth (PWS) nonlinear stochastic hybrid systems. We are able to correctly identify and track challenging problems with diverse dynamics and low dimensional transitions. We exploit the composite structure system to learn a simpler model on each component/mode. We use Gaussian Process Regression techniques to learn smooth, nonlinear manifolds across mode transitions, guard-regions, and make multi-step ahead predictions on each mode dynamics. We combine a PWS non-linear model with a particle filter to effectively track multi-modal transitions. We further use synthetic oversampling techniques to address the challenge of detecting mode transition which is sparse compared to mode dynamics. This work provides an effective form of model learning in a complex hybrid system, which can be useful for future integration in a reinforcement learning setting. We compare multi-step prediction and tracking performance against traditional dynamical system tracking methods, such as EKF and Switching Gaussian Processes, and show that this framework performs significantly better, being able to correctly track complex dynamics with sparse transitions.

Thomas Libby, Aaron M. Johnson, Evan Chang-Siu et al.

This paper develops a comparative framework for the design of actuated inertial appendages for planar, aerial reorientation. We define the Inertial Reorientation template, the simplest model of this behavior, and leverage its linear dynamics to reveal the design constraints linking a task with the body designs capable of completing it. As practicable inertial appendage designs lead to morphology that is generally more complex, we advance a notion of "anchoring" whereby a judicious choice of physical design in concert with an appropriate control policy yields a system whose closed loop dynamics are sufficiently captured by the template as to permit all further design to take place in its far simpler parameter space. This approach is effective and accurate over the diverse design spaces afforded by existing platforms, enabling performance comparison through the shared task space. We analyze examples from the literature and find advantages to each body type, but conclude that tails provide the highest potential performance for reasonable designs. Thus motivated, we build a physical example by retrofitting a tail to a RHex robot and present empirical evidence of its efficacy.

Aaron M. Johnson, Samuel A. Burden, Daniel E. Koditschek

Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs individually. In concert, it is well known that the interaction of such idealized approximations can lead to conflicting and even paradoxical results. As robotics modeling moves from the consideration of isolated behaviors to the analysis of tasks requiring their composition, a mathematically tractable framework for building models that combine these simple approximations yet achieve reliable results is overdue. In this paper we present a formal hybrid dynamical system model that introduces suitably restricted compositions of these familiar abstractions with the guarantee of consistency analogous to global existence and uniqueness in classical dynamical systems. The hybrid system developed here provides a discontinuous but self-consistent approximation to the continuous (though possibly very stiff and fast) dynamics of a physical robot undergoing intermittent impacts. The modeling choices sacrifice some quantitative numerical efficiencies while maintaining qualitatively correct and analytically tractable results with consistency guarantees promoting their use in formal reasoning about mechanism, feedback control, and behavior design in robots that make and break contact with their environment.