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.

Climbing robots can investigate scientifically valuable sites that conventional rovers cannot access due to steep terrain features. Robots equipped with microspine grippers are particularly well-suited to ascending rocky cliff faces, but most existing designs are either large and slow or limited to relatively flat surfaces such as walls. We present a novel free-climbing robot to bridge this gap through innovations in gripper design and force control. Fully passive grippers and wrist joints allow secure grasping while reducing mass and complexity. Forces are distributed among the robot’s grippers using an optimization-based control strategy to minimize the risk of unexpected detachment. The robot prototype has demonstrated vertical climbing on both flat cinder block walls and uneven rock surfaces in full Earth gravity.

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.

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.

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.

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.

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.

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.

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.

We present simplified 2D dynamic models of the 3D, passive dynamic inspired walking gait of a physical quasi-passive walking robot. Quasi-passive walkers are robots that integrate passive walking principles and some form of actuation. Our ultimate goal is to better understand the dynamics of actuated walking in order to create miniature, untethered, bipedal walking robots. At these smaller scales there is limited space and power available, and so in this work we leverage the passive dynamics of walking to reduce the burden on the actuators and controllers. Prior quasi-passive walkers are much larger than our intended scale, have more complicated mechanical designs, and require more precise feedback control and/or learning algorithms. By leveraging the passive 3D dynamics, carefully designing the spherical feet, and changing the actuation scheme, we are able to produce a very simple 3D bipedal walking model that has a total of 5 rigid bodies and a single actuator per leg. Additionally, the model requires no feedback as each actuator is controlled by an open-loop sinusoidal profile. We validate this model in 2D simulations in which we measure the stability properties while varying the leg length/amplitude ratio, the frequency of actuation, and the spherical foot profile. These results are also validated experimentally on a 3D walking robot (15cm leg length) that implements the modeled walking dynamics. Finally, we experimentally investigate the ability to control the heading of the robot by changing the open-loop control parameters of the robot.

Methods for state estimation that rely on visual information are challenging on legged robots due to rapid changes in the viewing angle of onboard cameras. In this work, we show that by leveraging structure in the way that the robot locomotes, the accuracy of visual-inertial SLAM in these challenging scenarios can be increased. We present a method that takes advantage of the underlying periodic predictability often present in the motion of legged robots to improve the performance of the feature tracking module within a visual-inertial SLAM system. Our method performs multi-session SLAM on a single robot, where each session is responsible for mapping during a distinct portion of the robot's gait cycle. Our method produces lower absolute trajectory error than several state-of-the-art methods for visual-inertial SLAM in both a simulated environment and on data collected on a quadrupedal robot executing dynamic gaits. On real-world bounding gaits, our median trajectory error was less than 35% of the error of the next best estimate provided by state-of-the-art methods.

We present TartanDrive, a large scale dataset for learning dynamics models for off-road driving. We collected a dataset of roughly 200,000 off-road driving interactions on a modified Yamaha Viking ATV with seven unique sensing modalities in diverse terrains. To the authors' knowledge, this is the largest real-world multi-modal off-road driving dataset, both in terms of number of interactions and sensing modalities. We also benchmark several state-of-the-art methods for model-based reinforcement learning from high-dimensional observations on this dataset. We find that extending these models to multi-modality leads to significant performance on off-road dynamics prediction, especially in more challenging terrains. We also identify some shortcomings with current neural network architectures for the off-road driving task. Our dataset is available at https://github.com/castacks/tartan_drive.

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 designing 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.

Microspine grippers allow robots to ascend steep rocky slopes and cliff faces, enabling scientific exploration of exposed strata on Earth and other solar system bodies. Historically, the Shape Deposition Manufacturing (SDM) process has been used to fabricate multi-material suspensions for load-sharing among multiple microspines. We instead apply the Hybrid Deposition Manufacturing (HDM) process to microspine fabrication, and we further propose a novel 3D-printed microspine suspension design that can be manufactured via Fused Deposition Manufacturing (FDM) alone, using a single flexible material with an embedded fishhook. We use a model of microspine stiffness that allows designers to compensate for order-of-magnitude changes in material tensile modulus by adjusting geometric parameters of the design. The stiffness model and the FDM microspine design are validated through tensile testing, and mechanical properties of the HDM and FDM designs are compared against a standard SDM microspine design. We demonstrate that the FDM process can produce microspines with equivalent normal and axial stiffness and superior maximum load and fatigue response to SDM microspines, and discuss additional advantages of the FDM process for rapid prototyping and broader accessibility.

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 novel 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 parame-terized reset functions - capturing how unknown parameters change how states are mapped from one mode to the next - the Jacobian of which accounts for 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.

Many agile legged animals employ lightweight, furry tails to regulate orientation during running, leaping, and turning. Most robots attempting the same tasks either lack a tail or employ one with high inertia, which can induce impractical payload and energy costs. Inspired by nature's solution to this tradeoff, we explore the use of aerodynamic drag tails in reorientation tasks. In this article, we present a model of the aerodynamic drag and from this derive a metric that allows for direct comparison between aerodynamic and inertial tails. Motivated by this model, we construct a tail to maximize this effectiveness while minimizing inertia. We demonstrate the utility of this tail for two dynamic behaviors executed on a quadrupedal robot. First, in aerial reorientation the robot achieves a 90°rotation within one body length of fall at the same performance as an inertial tail but with just 37% of the normalized inertia. Second, the forward acceleration of the robot is improved by 12% despite increasing the system mass by 10% over a tailless version. These results show that aerodynamic drag can provide significant control authority for a robot while decreasing the payload and energy cost.

This work presents a motion planning algorithm for legged robots capable of constructing long-horizon dynamic plans in real-time. Many existing methods use models that prohibit flight phases or even require static stability, while those that permit these dynamics often plan over short horizons or take minutes to compute. The algorithm presented here resolves these issues through a reduced-order dynamical model that handles motion primitives with stance and flight phases and supports an RRT-Connect framework for rapid exploration. Kinematic and dynamic constraint approximations are computed efficiently and validated with a whole-body trajectory optimization. The algorithm is tested over challenging terrain requiring long planning horizons and dynamic motions in seconds - an order of magnitude faster than existing methods. The speed and global nature of the planner offer a new level of autonomy for legged robot applications.

Localizing contacts and collisions is an important aspect of failure detection and recovery for robots and can aid perception and exploration of the environment. Contrary to state-of-the-art methods that rely on forces and torques measured on the robot, this paper proposes a kinematic method for proprioceptive contact localization on compliant robots using velocity measurements. The method is validated on two planar robots, the quadrupedal Minitaur and the two-fingered Direct Drive (DD) Hand which are compliant due to inherent transparency from direct drive actuation. Comparisons to other state-of-the-art proprioceptive methods are shown in simulation. Preliminary results on further extensions to complex geometry (through numerical methods) and spatial robots (with a particle filter) are discussed.

Planetary exploration rovers are expensive, weight constrained, and cannot be serviced once deployed. Here, we explore one way to increase their capabilities while avoiding the cost, mass, and complexity leading to these issues. We propose to re-use the large wheel actuators for trenching and other digging operations, which will enable a range of missions such as sampling deeper layers of soil. We present a new, closed-form model of the soil displaced by an angled, spinning wheel to analyze the trenching potential of a driving strategy and inform the control of the wheel. The model is demonstrated with single wheel experiments under different driving conditions. The model suggests: that a deep trench does not require large tractive efforts; that the shape of the trench can be controlled; and that a rear wheel has a lower risk of entrapment when trenching than a front wheel. Ultimately this model could be used in a nonprehensile manipulation planning or learning algorithm to enable autonomous trenching.

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 to permit all further designs 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 a 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.

This paper explores the design space of simple legged robots capable of leaping culminating in new behaviors for the Penn Jerboa, an underactuated, dynamically dexterous robot. Using a combination of formal reasoning and physical intuition, we analyze and test successively more capable leaping behaviors through successively more complicated body mechanics. The final version of this machine studied here bounds up a ledge 1.5 times its hip height and crosses a gap 2 times its body length, exceeding in this last regard the mark set by the far more mature RHex hexapod. Theoretical contributions include a non-existence proof of a useful class of leaps for a stripped-down initial version of the new machine, setting in motion the sequence of improvements leading to the final resulting performance. Conceptual contributions include a growing understanding of the Ground Reaction Complex as an effective abstraction for classifying and generating transitional contact behaviors in robotics.

As dynamic robot behaviors become more capable and well understood, the need arises for a wide variety of equally capable and systematically applicable transitions between them. We use a hybrid systems framework to characterize the dynamic transitions of a planar “legged” rigid body from rest on level ground to a fully aerial state. The various contact conditions fit together to form a topologically regular structure, the “ground reaction complex”. The body's actuated dynamics excite multifarious transitions between the cells of this complex, whose regular adjacency relations index naturally the resulting “leaps” (path sequences through the cells from rest to free flight). We exhibit on a RHex robot some of the most interesting “words” formed by these achievable path sequences, documenting unprecedented levels of performance and new application possibilities that illustrate the value of understanding and expressing this vocabulary systematically.

On challenging, uneven terrain a legged robot's open loop posture will almost inevitably be inefficient, due to uncoordinated support of gravitational loads with coupled internal torques. By reasoning about certain structural properties governing the infinitesimal kinematics of the closed chains arising from a typical stance, we have developed a computationally trivial self-manipulation behavior that can minimize both internal and external torques absent any terrain information. The key to this behavior is a change of basis in torque space that approximates the partially decoupled nature of the two types of disturbances. The new coordinates reveal how to use actuator current measurements as proprioceptive sensors for the approximate gradients of both the internal and external task potential fields, without recourse to further modeling. The behavior is derived using a manipulation framework informed by the dual relationship between a legged robot and a multifingered hand. We implement the reactive posture controller resulting from simple online descent along these proprioceptively sensed gradients on the X-RHex robot to document the significant savings in standing power.

We present a framework for detecting, identifying, and recovering within stride from faults and other leg contact disturbances encountered by a walking hexapedal robot. Detection is achieved by means of a software contact-event sensor with no additional sensing hardware beyond the commercial actuators' standard shaft encoders. A simple finite state machine identifies disturbances as due either to an expected ground contact, a missing ground contact indicating leg fault, or an unexpected “wall” contact. Recovery proceeds as necessary by means of a recently developed topological gait transition coordinator. We demonstrate the efficacy of this system by presenting preliminary data arising from two reactive behaviors - wall avoidance and leg-break recovery. We believe that extensions of this framework will enable reactive behaviors allowing the robot to function with guarded autonomy under widely varying terrain and self-health conditions.

Many factors such as size, power, and weight constrain the design of modular snake robots. Meeting these constraints requires implementing a complex mechanical and electrical architecture. Here we present our solution, which involves the construction of sixteen aluminum modules and creation of the Super Servo, a modified hobby servo. To create the Super Servo, we have replaced the electronics in a hobby servo, adding such components as sensors to monitor current and temperature, a communications bus, and a programmable microcontroller. Any robust solution must also protect components from hazardous environments such as sand and brush. To resolve this problem we insert the robots into skins that cover their surface. Functions such as climbing the inside and outside of a pipe add a new dimension of interaction. Thus we attach a compliant, high-friction material to every module, which assists in tasks that require gripping. This combination of the mechanical and electrical architectures results in a robust and versatile robot.