Aaron M. Johnson

In this paper, we enable new mobility and manipulation modes for wheeled planetary exploration rovers through the use of terramechanics modeling and field experiments. Useful modes of wheel-based soil manipulation and examples of rovers driving with degraded mobility systems are first demonstrated in lunar and Martian analog environments. We show a full-scale rover use its wheels to dig trenches up to 10.6 cm deep, dig holes to estimate soil characteristics, and modify terrain to make it accessible to a smaller robot. We also measure the impact of actuator failure on a rover in lunar simulant. Here, we show the slip doubled on moderate slopes for a damaged drive motor, which would exceed the rover’s operational limits for slip, motivating the need for driving strategies that mitigate mobility loss. We then develop an optimization framework which uses a recently developed terramechanics model to automatically generate both open and closed-loop driving strategies for planetary rovers performing terrain manipulation or operating in a degraded state with no need for hand tuning of behaviors. Finally, we demonstrate the generated driving strategies for soil manipulation and mobility compensation on a rover in a controlled lab setting, where we show that 1) mobility is maintained while manipulating soil; and 2) mobility is regained while experiencing failure of steer and drive actuators.

Miniaturizing legged robot platforms is challenging due to hardware limitations that constrain the number, power density, and precision of actuators at that size. By leveraging design principles of quasi-passive walking robots at any scale, stable locomotion and steering can be achieved with simple mechanisms and open-loop control. Here, we present the design and control of “Zippy”, the smallest self-contained bipedal walking robot at only 3.6 cm tall. Zippy has rounded feet, a single motor without feedback control, and is capable of turning, skipping, and ascending steps. At its fastest pace, the robot achieves a forward walking speed of 25 cm/s, which is 10 leg lengths per second, the fastest biped robot of any size by that metric. This work explores the design and performance of the robot and compares it to similar dynamic walking robots at larger scales.

Map-based LiDAR localization, while widely used in autonomous systems, faces significant challenges in degraded environments due to the lack of distinct geometric features. This paper introduces SuperLoc, a robust LiDAR localization package that addresses key limitations in existing methods. SuperLoc features a novel predictive alignment risk assessment technique, enabling early detection and mitigation of potential failures before optimization. This approach significantly improves performance in challenging scenarios such as corridors, tunnels, and caves. Unlike existing degeneracy mitigation algorithms that rely on post-optimization analysis and heuristic thresholds, SuperLoc evaluates the localizability of raw sensor measurements. Experimental results demonstrate significant performance improvements over state-of-the-art methods across various degraded environments. Our approach achieves a 54% increase in accuracy and exhibits better robustness. To facilitate further research, we release our implementation along with datasets from eight challenging scenarios.

Miniaturizing legged robot platforms is challenging due to hardware limitations that constrain the number, power density, and precision of actuators at that size. By leveraging design principles of quasi-passive walking robots at any scale, stable locomotion and steering can be achieved with simple mechanisms and open-loop control. Here, we present the design and control of "Zippy", the smallest self-contained bipedal walking robot at only 3.6 cm tall. Zippy has rounded feet, a single motor without feedback control, and is capable of turning, skipping, and ascending steps. At its fastest pace, the robot achieves a forward walking speed of 25 cm/s, which is 10 leg lengths per second, the fastest biped robot of any size by that metric. This work explores the design and performance of the robot and compares it to similar dynamic walking robots at larger scales.

In this letter we present Hybrid iterative Linear Quadratic Estimation (HiLQE), an optimization based offline state estimation algorithm for hybrid dynamical systems. We utilize the saltation matrix, a first order approximation of the variational update through an event driven hybrid transition, to calculate gradient information through hybrid events in the backward pass of an iterative linear quadratic optimization over state estimates. This enables accurate computation of the value function approximation at each timestep. Additionally, the forward pass in the iterative algorithm is augmented with hybrid dynamics in the rollout. A reference extension method is used to account for varying impact times when comparing states for the feedback gain in noise calculation. The proposed method is demonstrated on an ASLIP hopper system with position measurements. In comparison to the Salted Kalman Filter (SKF), the algorithm presented here achieves a maximum of 63.55% reduction in estimation error magnitude over all state dimensions near impact events.

As bipedal robots become more and more popular in commercial and industrial settings, the ability to control them with a high degree of reliability is critical. To that end, this paper considers how to accurately estimate which feet are currently in contact with the ground so as to avoid improper control actions that could jeopardize the stability of the robot. Additionally, modern algorithms for estimating the position and orientation of a robot's base frame rely heavily on such contact mode estimates. Dedicated contact sensors on the feet can be used to estimate this contact mode, but these sensors are prone to noise, time delays, damage/yielding from repeated impacts with the ground, and are not available on every robot. To overcome these limitations, we propose a momentum observer based method for contact mode estimation that does not rely on such contact sensors. Often, momentum observers assume that the robot's base frame can be treated as an inertial frame. However, since many humanoids' legs represent a significant portion of the overall mass, the proposed method instead utilizes multiple simultaneous dynamic models. Each of these models assumes a different contact condition. A given contact assumption is then used to constrain the full dynamics in order to avoid assuming that either the body is an inertial frame or that a fully accurate estimate of body velocity is known. The (dis)agreement between each model's estimates and measurements is used to determine which contact mode is most likely using a Markov-style fusion method. The proposed method produces contact detection accuracy of up to 98.44% with a low noise simulation and 77.12% when utilizing data collect on the Sarcos Guardian XO robot (a hybrid humanoid/exoskeleton).

Map-based LiDAR localization, while widely used in autonomous systems, faces significant challenges in degraded environments due to lacking distinct geometric features. This paper introduces SuperLoc, a robust LiDAR localization package that addresses key limitations in existing methods. SuperLoc features a novel predictive alignment risk assessment technique, enabling early detection and mitigation of potential failures before optimization. This approach significantly improves performance in challenging scenarios such as corridors, tunnels, and caves. Unlike existing degeneracy mitigation algorithms that rely on post-optimization analysis and heuristic thresholds, SuperLoc evaluates the localizability of raw sensor measurements. Experimental results demonstrate significant performance improvements over state-of-the-art methods across various degraded environments. Our approach achieves a 54% increase in accuracy and exhibits the highest robustness. To facilitate further research, we release our implementation along with datasets from eight challenging scenarios

This work introduces a novel paradigm for solving optimal control problems for hybrid dynamical systems under uncertainties. Robotic systems having contact with the environment can be modeled as hybrid systems. Controller design for hybrid systems under disturbances is complicated by the discontinuous jump dynamics, mode changes with inconsistent state dimensions, and variations in jumping timing and states caused by noise. We formulate this problem into a stochastic control problem with hybrid transition constraints and propose the Hybrid Path Integral (H-PI) framework to obtain the optimal controller. Despite random mode changes across stochastic path samples, we show that the ratio between hybrid path distributions with varying drift terms remains analogous to the smooth path distributions. We then show that the optimal controller can be obtained by evaluating a path integral with hybrid constraints. Importance sampling for path distributions with hybrid dynamics constraints is introduced to reduce the variance of the path integral evaluation, where we leverage the recently developed Hybrid iterative-Linear-Quadratic-Regulator (H-iLQR) controller to induce a hybrid path distribution proposal with low variance. The proposed method is validated through numerical experiments on various hybrid systems and extensive ablation studies. All the sampling processes are conducted in parallel on a Graphics Processing Unit (GPU).

In this paper we present Hybrid iterative Linear Quadratic Estimation (HiLQE), an optimization based offline state estimation algorithm for hybrid dynamical systems. We utilize the saltation matrix, a first order approximation of the variational update through an event driven hybrid transition, to calculate gradient information through hybrid events in the backward pass of an iterative linear quadratic optimization over state estimates. This enables accurate computation of the value function approximation at each timestep. Additionally, the forward pass in the iterative algorithm is augmented with hybrid dynamics in the rollout. A reference extension method is used to account for varying impact times when comparing states for the feedback gain in noise calculation. The proposed method is demonstrated on an ASLIP hopper system with position measurements. In comparison to the Salted Kalman Filter (SKF), the algorithm presented here achieves a maximum of 63.55% reduction in estimation error magnitude over all state dimensions near impact events.

This work addresses the problem of optimally steering the state covariance of a linear stochastic system from an initial to a target, subject to hybrid transitions. The nonlinear and discontinuous jump dynamics complicate the control design for hybrid systems. Under uncertainties, stochastic jump timing and state variations further intensify this challenge. This work aims to regulate the hybrid system's state trajectory to stay close to a nominal deterministic one, despite uncertainties and noises. We address this problem by directly controlling state covariances around a mean trajectory, and this problem is termed the Hybrid Covariance Steering (H-CS) problem. The jump dynamics are approximated to the first order by leveraging the Saltation Matrix. When the jump dynamics are nonsingular, we derive an analytical closed-form solution to the H-CS problem. For general jump dynamics with possible singularity and changes in the state dimensions, we reformulate the problem into a convex optimization over path distributions by leveraging Schrodinger's Bridge duality to the smooth covariance control problem. The covariance propagation at hybrid events is enforced as equality constraints to handle singularity issues. The proposed convex framework scales linearly with the number of jump events, ensuring efficient, optimal solutions. This work thus provides a computationally efficient solution to the general H-CS problem. Numerical experiments are conducted to validate the proposed method.

At the 10- by 10-Foot Supersonic Wind Tunnel at the NASA Glenn Research Center, a future full test section characterization generated an ideal opportunity to design and build new characterization hardware to improve the understanding of the flow field, including flow quality, uniformity, and uncertainty in primary variables of interest. An array of flow sensing probes, referred to as the Characterization Array, was designed and built to replace 1960’s-era test section characterization hardware. Many references exist to guide wind tunnel characterization practitioners in the design of new hardware to properly measure various aspects of the flow within their wind tunnel facilities. Although reliable sources of information, these references tend to be over 30 years old and are not exhaustive. In scenarios where design decisions needed to be validated, computational simulations of the flow field around the characterization hardware were used. Decisions regarding probe location, probe spacing, and performance of various probes were justified using computational fluid dynamic simulations and rules-of-thumb from the legacy resources available in literature. This paper is intended to serve as an example of the benefits from integrating CFD into the design of wind tunnel hardware, particularly hardware for wind tunnel characterization.

Dynamic and agile locomotion in legged robots enables them to overcome obstacles and navigate complex and unstructured terrain. However, the leg mechanisms and actuators needed for versatile locomotion are much more challenging to manufacture and integrate in sub‐gram scale robots. Herein, Picotaur, a 15.4 mg hexapedal robot with legs that enable various locomotion tasks such as turning, climbing 3D‐printed stairs, and pushing loads for the first time at these size scales, is presented. 3D printing with two‐photon polymerization enables the manufacture of electrostatically driven 2 degrees of freedom legs on a robot body made from a flexible printed circuit board. Based on simple control inputs, Picotaur can achieve alternating tripod gaits, reaching speeds up to 57 mm (7.2 body lengths) per second, as well as pronking gaits to tackle a wider variety of terrain. This approach to manufacturing and controlling legged robots at smaller scales provides a path forward toward robots that can be used for practical applications ranging from inspection to exploration and rival the performance of insects at similar size scales.

Prior research has investigated the benefits and costs of double-anonymous review (DAR, also known as double-blind review) in comparison to single-anonymous review (SAR) and open review (OR). Several review papers have attempted to compile experimental results in peer review research both broadly and in engineering and computer science. This document summarizes prior research in peer review that may inform decisions about the format of peer review in the field of robotics and makes some recommendations for potential next steps for robotics publication.

Hybrid dynamical systems, i.e., systems that have both continuous and discrete states, are ubiquitous in engineering but are difficult to work with due to their discontinuous transitions. For example, a robot leg is able to exert very little control effort, while it is in the air compared to when it is on the ground. When the leg hits the ground, the penetrating velocity instantaneously collapses to zero. These instantaneous changes in dynamics and discontinuities (or jumps) in state make standard smooth tools for planning, estimation, control, and learning difficult for hybrid systems. One of the key tools for accounting for these jumps is called the saltation matrix. The saltation matrix is the sensitivity update when a hybrid jump occurs and has been used in a variety of fields, including robotics, power circuits, and computational neuroscience. This article presents an intuitive derivation of the saltation matrix and discusses what it captures, where it has been used in the past, how it is used for linear and quadratic forms, how it is computed for rigid body systems with unilateral constraints, and some of the structural properties of the saltation matrix in these cases.

Good site characterization is essential for the selection of remediation alternatives for impacted soils. The value of site characterization is critically dependent on the quality and quantity of the data collected. Current methods for characterizing impacted soils rely on expensive manual sample collection and off-site analysis. However, recent advances in terrestrial robotics and artificial intelligence offer a potentially revolutionary set of tools and methods that will help to autonomously explore natural environments, select sample locations with the highest value of information, extract samples, and analyze the data in real-time without exposing humans to potentially hazardous conditions. A fundamental challenge to realizing this potential is determining how to design an autonomous system for a given investigation with many, and often conflicting design criteria. This work presents a novel design methodology to navigate these criteria. Specifically, this methodology breaks the system into four components – sensing, sampling, mobility, and autonomy – and connects design variables to the investigation objectives and constraints. These connections are established for each component through a survey of existing technology, discussion of key technical challenges, and highlighting conditions where generality can promote multi-application deployment. An illustrative example of this design process is presented for the development and deployment of a robotic platform characterizing salt-impacted oil & gas reserve pits. After calibration, the relationship between the in situ robot chloride measurements and laboratory-based chloride measurements had a good linear relationship (R2-value = 0.861) and statistical significance (p-value = 0.003).

This paper presents a scalable multi-robot motion planning algorithm called Conflict-Based Model Predictive Control (CB-MPC). Inspired by Conflict-Based Search (CBS), the planner leverages a modified high-level conflict tree to efficiently resolve robot-robot conflicts in the continuous space, while reasoning about each agent’s kinematic and dynamic constraints and actuation limits using MPC as the low-level planner. We show that tracking high-level multi-robot plans with a vanilla MPC controller is insufficient, and results in unexpected collisions in tight navigation scenarios under realistic execution. Compared to other variations of multi-robot MPC like joint, prioritized, and distributed, we demonstrate that CB-MPC improves the executability and success rate, allows for closer robot-robot interactions, and scales better with higher numbers of robots without compromising the solution quality across a variety of environments.

Autonomous off-road driving is challenging as unsafe actions may lead to catastrophic damage. As such, developing controllers in simulation is often desirable. However, robot dynamics in unstructured off-road environments can be highly complex and difficult to simulate accurately. Domain randomization addresses this problem by randomizing simulation dynamics to train policies that are robust towards modeling errors. While these policies are robust across a range of dynamics, they are sub-optimal for any particular system dynamics. We introduce a novel model-based reinforcement learning approach that aims to balance robustness with adaptability. We train a System Identification Transformer (SIT) and an Adaptive Dynamics Model (ADM) under a variety of simulated dynamics. The SIT uses attention mechanisms to distill target system state-transition observations into a context vector, which provides an abstraction for the target dynamics. Conditioned on this, the ADM probabilistically models the system’s dynamics. Online, we use a Risk-Aware Model Predictive Path Integral controller to safely control the robot under its current understanding of dynamics. We demonstrate in simulation and in the real world that this approach enables safer behaviors upon initialization and becomes less conservative (i.e. faster) as its understanding of the target system dynamics improves with more observations. In particular, our approach results in an approximately 41% improvement in lap-time over the non-adaptive baseline while remaining safe across different environments.

In order to perform highly dynamic and agile maneuvers, legged robots typically spend time in underactuated domains (e.g. with feet off the ground) where the system has limited command of its acceleration and a constrained amount of time before transitioning to a new domain (e.g. foot touchdown). Meanwhile, these transitions can instantaneously change the system’s state, possibly causing perturbations to be mapped arbitrarily far away from the target trajectory. These properties make it difficult for local feedback controllers to effectively recover from disturbances as the system evolves through underactuated domains and hybrid impact events. To address this, we utilize the fundamental solution matrix that characterizes the evolution of perturbations through a hybrid trajectory and its 2-norm, which represents the worst-case growth of perturbations. In this paper, the worst-case perturbation analysis is used to explicitly reason about the tracking performance of a hybrid trajectory and is incorporated in an iLQR framework to optimize a trajectory while taking into account the closed-loop convergence of the trajectory under an LQR tracking controller. The generated convergent trajectories recover more effectively from perturbations, are more robust to large disturbances, and use less feedback control effort than trajectories generated with traditional methods.

This work introduces a formulation of model predictive control (MPC), which adaptively reasons about the complexity of the model while maintaining feasibility and stability guarantees. Existing approaches often handle computational complexity by shortening prediction horizons or simplifying models, both of which can result in instability. Inspired by related approaches in behavioral economics, motion planning, and biomechanics, our method solves MPC problems with a simple model for dynamics and constraints over regions of the horizon where such a model is feasible and a complex model where it is not. The approach leverages an interleaving of planning and execution to iteratively identify these regions, which can be safely simplified if they satisfy an exact template/anchor relationship. We show that this method does not compromise the stability and feasibility properties of the system, and measures performance in simulation experiments on a quadrupedal robot executing agile behaviors over terrains of interest. We find that this adaptive method enables more agile motion (55% increase in top speed) and expands the range of executable tasks compared with fixed-complexity implementations.

We present the design and experimental results of the first 1-DOF, hip-actuated bipedal robot. While passive dynamic walking is simple by nature, many existing bipeds inspired by this form of walking are complex in control, mechanical design, or both. Our design using only two rigid bodies connected by a single motor aims to enable exploration of walking at smaller sizes where more complex designs cannot be constructed. The walker, “Mugatu”, is self-contained and autonomous, open-loop stable over a range of input parameters, able to stop and start from standing, and able to control its heading left and right. We analyze the mechanical design and distill down a set of design rules that enable these behaviors. Experimental evaluations measure speed, energy consumption, and steering.

Autonomous off-road driving is challenging as risky actions taken by the robot may lead to catastrophic damage. As such, developing controllers in simulation is often desirable as it provides a safer and more economical alternative. However, accurately modeling robot dynamics is difficult due to the complex robot dynamics and terrain interactions in unstructured environments. Domain randomization addresses this problem by randomizing simulation dynamics parameters, however this approach sacrifices performance for robustness leading to policies that are sub-optimal for any target dynamics. We introduce a novel model-based reinforcement learning approach that aims to balance robustness with adaptability. Our approach trains a System Identification Transformer (SIT) and an Adaptive Dynamics Model (ADM) under a variety of simulated dynamics. The SIT uses attention mechanisms to distill state-transition observations from the target system into a context vector, which provides an abstraction for its target dynamics. Conditioned on this, the ADM probabilistically models the system's dynamics. Online, we use a Risk-Aware Model Predictive Path Integral controller (MPPI) to safely control the robot under its current understanding of the dynamics. We demonstrate in simulation as well as in multiple real-world environments that this approach enables safer behaviors upon initialization and becomes less conservative (i.e. faster) as its understanding of the target system dynamics improves with more observations. In particular, our approach results in an approximately 41% improvement in lap-time over the non-adaptive baseline while remaining safe across different environments.

Legged robots leverage ground contacts and the reaction forces they provide to achieve agile locomotion. However, uncertainty coupled with contact discontinuities can lead to failure, especially in real-world environments with unexpected height variations such as rocky hills or curbs. To enable dynamic traversal of extreme terrain, this work introduces 1) a proprioception-based gait planner for estimating unknown hybrid events due to elevation changes and responding by modifying contact schedules and planned footholds online, and 2) a two-degree-of-freedom tail for improving contact-independent control and a corresponding decoupled control scheme for better versatility and efficiency. Simulation results show that the gait planner significantly improves stability under unforeseen terrain height changes compared to methods that assume fixed contact schedules and footholds. Further, tests have shown that the tail is particularly effective at maintaining stability when encountering a terrain change with an initial angular disturbance. The results show that these approaches work synergistically to stabilize locomotion with elevation changes up to 1.5 times the leg length and tilted initial states.

Trajectory optimization problems for legged robots are commonly formulated with fixed contact schedules. These multi-phase Hybrid Trajectory Optimization (HTO) methods result in locally optimal trajectories, but the result depends heavily upon the predefined contact mode sequence. Contact-Implicit Optimization (CIO) offers a potential solution to this issue by allowing the contact mode to be determined throughout the trajectory by the optimization solver. However, CIO suffers from long solve times and convergence issues. This work combines the benefits of these two methods into one algorithm: Staged Contact Optimization (SCO). SCO tightens constraints on contact in stages, eventually fixing them to allow robust and fast convergence to a feasible solution. Results on a planar biped and spatial quadruped demonstrate speed and optimality improvements over CIO and HTO. These properties make SCO well suited for offline trajectory generation or as an effective tool for exploring the dynamic capabilities of a robot.

Entanglements like vines and branches in natural settings or cords and pipes in human spaces prevent mobile robots from accessing many environments. Legged robots should be effective in these settings, and more so than wheeled or tracked platforms, but naive controllers quickly become entangled and stuck. In this paper we present a method for proprioception aimed specifically at the task of sensing entanglements of a robot's legs as well as a reaction strategy to disentangle legs during their swing phase as they advance to their next foothold. We demonstrate our proprioception and reaction strategy enables traversal of entanglements of many stiffnesses and geometries succeeding in 14 out of 16 trials in laboratory tests, as well as a natural outdoor environment.

Model predictive control (MPC) is a popular strategy for controlling robots but is difficult for systems with contact due to the complex nature of hybrid dynamics. To implement MPC for systems with contact, dynamic models are often simplified or contact sequences fixed in time in order to plan trajectories efficiently. In this work, we propose the hybrid iterative linear quadratic regulator (iLQR) (HiLQR), which extends iLQR to a class of piecewisesmooth hybrid dynamical systems with state jumps. This is accomplished by, first, allowing for changing hybrid modes in the forward pass, second, using the saltation matrix to update the gradient information in the backwards pass, and third, 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. We further show how HiLQR can work in an MPC fashion (HiLQR MPC) by, first, modifying how the cost function is computed when contact modes do not align, second, utilizing parallelizations when simulating rigid body dynamics, and third, using efficient analytical derivative computations of the rigid body dynamics. The result is a system that can modify the contact sequence of the reference behavior and plan whole body motions cohesively—which is crucial when dealing with large perturbations. HiLQR MPC is tested on two systems: first, the hybrid cost modification is validated on a simple actuated bouncing ball hybrid system. Then, HiLQR MPC is compared against methods that utilize centroidal dynamic assumptions on a quadruped robot (Unitree A1). HiLQR MPC outperforms the centroidal methods in both simulation and hardware tests.

Robots operating in close proximity to humans rely heavily on human trust to successfully complete their tasks. But what are the real outcomes when this trust is violated? Self-defense law provides a framework for analyzing tangible failure scenarios that can inform the design of robots and their algorithms. Studying self-defense is particularly important for ground robots since they operate within public environments, where they can pose a legitimate threat to the safety of nearby humans. Moreover, even if ground robots can guarantee human safety, the perception of a physical threat is sufficient to justify human self-defense against robots. In this paper, we synthesize works in law, engineering, and social science to present four actionable recommendations for how the robotics community can craft robots to mitigate the likelihood of self-defense situations arising. We establish how current U.S. self-defense law can justify a human protecting themselves against a robot, discuss the current literature on human attitudes toward robots, and analyze methods that have been produced to allow robots to operate close to humans. Finally, we present hypothetical scenarios that underscore how current robot navigation methods can fail to sufficiently consider self-defense concerns and the need for the recommendations to guide improvements in the field.

We present the design and experimental results of the first 1-DOF, hip-actuated bipedal robot. While passive dynamic walking is simple by nature, many existing bipeds inspired by this form of walking are complex in control, mechanical design, or both. Our design using only two rigid bodies connected by a single motor aims to enable exploration of walking at smaller sizes where more complex designs cannot be constructed. The walker, "Mugatu", is self-contained and autonomous, open-loop stable over a range of input parameters, able to stop and start from standing, and able to control its heading left and right. We analyze the mechanical design and distill down a set of design rules that enable these behaviors. Experimental evaluations measure speed, energy consumption, and steering.

This paper presents a novel and efficient collision checking approach called Updating and Collision Check Skipping Quad-tree (USQ) for multi-robot motion planning. USQ extends the standard quad-tree data structure through a time-efficient update mechanism, which significantly reduces the total number of collision checks and the collision checking time. In addition, it handles transitions at the quad-tree quadrant boundaries based on worst-case trajectories of agents. These extensions make quad-trees suitable for efficient collision checking in multi-robot motion planning of large robot teams. We evaluate the efficiency of USQ in comparison with Regenerating Quad-tree (RQ) from scratch at each timestep and naive pairwise collision checking across a variety of randomized environments. The results indicate that USQ significantly reduces the number of collision checks and the collision checking time compared to other baselines for different numbers of robots and map sizes. In a 50-robot experiment, USQ accurately detected all collisions, outperforming RQ which has longer run-times and/or misses up to 25% of collisions.

Hybrid dynamical systems, i.e. systems that have both continuous and discrete states, are ubiquitous in engineering, but are difficult to work with due to their discontinuous transitions. For example, a robot leg is able to exert very little control effort while it is in the air compared to when it is on the ground. When the leg hits the ground, the penetrating velocity instantaneously collapses to zero. These instantaneous changes in dynamics and discontinuities (or jumps) in state make standard smooth tools for planning, estimation, control, and learning difficult for hybrid systems. One of the key tools for accounting for these jumps is called the saltation matrix. The saltation matrix is the sensitivity update when a hybrid jump occurs and has been used in a variety of fields including robotics, power circuits, and computational neuroscience. This paper presents an intuitive derivation of the saltation matrix and discusses what it captures, where it has been used in the past, how it is used for linear and quadratic forms, how it is computed for rigid body systems with unilateral constraints, and some of the structural properties of the saltation matrix in these cases.

View Video Presentation: https://doi.org/10.2514/6.2023-4367.vid Within the past decade, a measurement uncertainty analysis (MUA) team was assembled at the NASA Glenn Research Center to assist the wind tunnel characterization team with quantification of uncertainty estimates for variables of interest in wind tunnels and test cells across the center. The initial analysis performed by the team was conducted on the 8- by 6-Foot Supersonic Wind Tunnel using results from the 1996/97 full calibration test entry. These MUA results were published in 2016 which included recommendations for methods to improve the uncertainty estimates for various variables of interest, such as changes to regression models, tunnel operation philosophy, and instrumentation choices. The wind tunnel characterization team utilized the proposed methods in 2019 during a full characterization test entry. Following publication of the 2019 test section characterization results, the MUA team pursued an update to the uncertainty estimates for the facility, which validated previous recommendations and revealed significantly reduced systematic uncertainties across most variables of interest. Inclusion of within-test repeat points in the 2019 test entry allowed for higher fidelity estimates of random uncertainty to be generated, as well. This collaboration between the facility, wind tunnel characterization, and MUA teams serves as an example of the data quality benefits that can be achieved through rigorous analysis of the sources of uncertainty in a ground-test facility.

Trajectory optimization problems for legged robots are commonly formulated with fixed contact schedules. These multi-phase Hybrid Trajectory Optimization (HTO) methods result in locally optimal trajectories, but the result depends heavily upon the predefined contact mode sequence. Contact-Implicit Optimization (CIO) offers a potential solution to this issue by allowing the contact mode to be determined throughout the trajectory by the optimization solver. However, CIO suffers from long solve times and convergence issues. This work combines the benefits of these two methods into one algorithm: Staged Contact Optimization (SCO). SCO tightens constraints on contact in stages, eventually fixing them to allow robust and fast convergence to a feasible solution. Results on a planar biped and spatial quadruped demonstrate speed and optimality improvements over CIO and HTO. These properties make SCO well suited for offline trajectory generation or as an effective tool for exploring the dynamic capabilities of a robot.

Entanglements like vines and branches in natural settings or cords and pipes in human spaces prevent mobile robots from accessing many environments. Legged robots should be effective in these settings, and more so than wheeled or tracked platforms, but naive controllers quickly become entangled and stuck. In this paper we present a method for proprioception aimed specifically at the task of sensing entanglements of a robot's legs as well as a reaction strategy to disentangle legs during their swing phase as they advance to their next foothold. We demonstrate our proprioception and reaction strategy enables traversal of entanglements of many stiffnesses and geometries succeeding in 14 out of 16 trials in laboratory tests, as well as a natural outdoor environment.

Robots operating in close proximity to humans rely heavily on human trust to successfully complete their tasks. But what are the real outcomes when this trust is violated? Self-defense law provides a framework for analyzing tangible failure scenarios that can inform the design of robots and their algorithms. Studying self-defense is particularly important for ground robots since they operate within public environments, where they can pose a legitimate threat to the safety of nearby humans. Moreover, even if ground robots can guarantee human safety, the perception of a physical threat is sufficient to justify human self-defense against robots. In this paper, we synthesize works in law, engineering, and social science to present four actionable recommendations for how the robotics community can craft robots to mitigate the likelihood of self-defense situations arising. We establish how current U.S. self-defense law can justify a human protecting themselves against a robot, discuss the current literature on human attitudes toward robots, and analyze methods that have been produced to allow robots to operate close to humans. Finally, we present hypothetical scenarios that underscore how current robot navigation methods can fail to sufficiently consider self-defense concerns and the need for the recommendations to guide improvements in the field.

In order to perform highly dynamic and agile maneuvers, legged robots typically spend time in underactuated domains (e.g. with feet off the ground) where the system has limited command of its acceleration and a constrained amount of time before transitioning to a new domain (e.g. foot touchdown). Meanwhile, these transitions can instantaneously change the system's state, possibly causing perturbations to be mapped arbitrarily far away from the target trajectory. These properties make it difficult for local feedback controllers to effectively recover from disturbances as the system evolves through underactuated domains and hybrid impact events. To address this, we utilize the fundamental solution matrix that characterizes the evolution of perturbations through a hybrid trajectory and its 2-norm, which represents the worst-case growth of perturbations. In this paper, the worst-case perturbation analysis is used to explicitly reason about the tracking performance of a hybrid trajectory and is incorporated in an iLQR framework to optimize a trajectory while taking into account the closed-loop convergence of the trajectory under an LQR tracking controller. The generated convergent trajectories recover more effectively from perturbations, are more robust to large disturbances, and use less feedback control effort than trajectories generated with traditional methods.

Legged robots leverage ground contacts and the reaction forces they provide to achieve agile locomotion. However, uncertainty coupled with contact discontinuities can lead to failure, especially in real-world environments with unexpected height variations such as rocky hills or curbs. To enable dynamic traversal of extreme terrain, this work introduces 1) a proprioception-based gait planner for estimating unknown hybrid events due to elevation changes and responding by modifying contact schedules and planned footholds online, and 2) a two-degree-of-freedom tail for improving contact-independent control and a corresponding decoupled control scheme for better versatility and efficiency. Simulation results show that the gait planner significantly improves stability under unforeseen terrain height changes compared to methods that assume fixed contact schedules and footholds. Further, tests have shown that the tail is particularly effective at maintaining stability when encountering a terrain change with an initial angular disturbance. The results show that these approaches work synergistically to stabilize locomotion with elevation changes up to 1.5 times the leg length and tilted initial states.

This paper presents a scalable multi-robot motion planning algorithm called Conflict-Based Model Predictive Control (CB-MPC). Inspired by Conflict-Based Search (CBS), the planner leverages a similar high-level conflict tree to efficiently resolve robot-robot conflicts in the continuous space, while reasoning about each agent's kinematic and dynamic constraints and actuation limits using MPC as the low-level planner. We show that tracking high-level multi-robot plans with a vanilla MPC controller is insufficient, and results in unexpected collisions in tight navigation scenarios. Compared to other variations of multi-robot MPC like joint, prioritized, and distributed, we demonstrate that CB-MPC improves the executability and success rate, allows for closer robot-robot interactions, and reduces the computational cost significantly without compromising the solution quality across a variety of environments. Furthermore, we show that CB-MPC combined with a high-level path planner can effectively substitute computationally expensive full-horizon multi-robot kinodynamic planners.