This paper presents the addition of two models for added mass to the fluid-field spring-loaded inverted pendulum (FF-SLIP) Model for legged swimming. The relative ability of these models to capture the increased fluid forces due to virtual mass displacement is evaluated using a two-legged swimming robot, Tadpole. We show that a simple addition to our reduced-order model can predict fluid-leg interaction forces while remaining computationally efficient.

The seafloor is a complex environment and it is challenging to conduct detailed mapping, soil composition sampling, and habitat characterization missions in this benthic region. As a step toward overcoming these challenges, we present a quadruped robot capable of walking on the seafloor and maneuvering via midfluid swimming. SELQIE, the Seafloor Environment Legged Quadruped Intelligent Explorer, is capable of walking underwater at speeds up to$0.2 ~\mathrm{m} / \mathrm{s}$, swimming at over$0.16 ~\mathrm{m} / \mathrm{s}$, and transitioning between modes. We also introduce a path planning algorithm that can account for both swimming and walking gaits to efficiently navigate around or over obstacles, and demonstrate the robot executing such a multi-modal trajectory.

For effective operation in challenging outdoor environments, mobile unmanned robots face stiff and competing demands including payload capacity, driving speed, range, as well as the ability to traverse rough terrain. To address these issues we introduce the hybrid wheel-leg quadrupedal robot WaLTER. WaLTER utilizes a unique combination of continuously rotating distal leg joints, actuated wheels, and a roll body DOF to efficiently drive on flat ground and effectively tumble over stairs and difficult, broken terrain. We developed an intuitive teleoperation scheme and employed deep reinforcement learning as proof of concept control techniques for the novel morphology. To test its capabilities, we constructed a multi-body simulation in MuJoCo and a 2.1 kg physical prototype for experimentation on traversability and energy economy. Our testing demonstrated the ability to traverse rougher terrain relative to larger-wheeled counterparts and reliable stair-climbing while maintaining a 4 km range on a 24.4 Wh battery (COT: 1.21).

Legged animals have developed a variety of modes of locomotion to adapt to the diverse and unknown terrain challenges posed in the natural world. Legged robots, however, have been largely limited to specializing in one domain, with few that have endeavored to bridge the gap between two. In this work we present the Scansorial, Terrestrial, and Aquatic Robot Quadruped (STARQ), a novel legged robot capable of bridging three different domains with three modes of locomotion: walking, climbing, and swimming. In this study we describe model-based design techniques as well as design innovations that have made multimodal locomotion possible including waterproof hips for 2-DOF high torque legs, legs capable of effective power transmission in three modes, and bi-directionally compliant feet for walking and attaching to vertical surfaces. To demonstrate the robot's capabilities we present locomotion test data including speed and cost of transport in each of these domains. We also demonstrate the capability to transition from walking to swimming in a natural environment.

In this paper we present swimming and modeling for Trident, a three-link lamprey inspired robot that is able to climb on flat smooth walls. We explore two gaits proposed to work for linear swimming, and three gaits for turning maneuvers. We compare the experimental results obtained from these swimming experiments with two different reduced order fluid interaction models, one a previously published potential flow model, and the other a slender cylinder model we developed. We find that depending on the the parameters of swimming chosen, we are able to move forward, backward and sideways with a peak speed of 2.5 cm/s. We identify the conditions when these models apply and aspects that will require additional complexity.

This paper describes the development of a single reduced-order dynamic model that captures running on land, running while submerged, and for the first time swimming on the surface of water. By capturing the effect of fluid forces on both the body and the leg, the Spring-Loaded Inverted Pendulum (SLIP) model is extended to operate in amphibious and aquatic regimes. Three distinct stable motion patterns, or dog-paddle type gaits are identified when swimming at the air-water interface. The model shows that, for surfaces swimming, alteration of the leg stroke frequency and length produces gaits that are either smooth and efficient or are vertically oscillatory and exhibit rapid disturbance rejection. Furthermore, when the model is examined at the physical parameter values corresponding to dogs (specifically Labrador Retrievers), the animal-based control parameters demonstrate nearly optimal performance.

As we build our legged robots smaller and cheaper, stable and agile control without expensive inertial sensors becomes increasingly important. We seek to enable versatile dynamic behaviors on robots with limited modes of state feedback, specifically proprioceptive-only sensing. This work uses model-based trajectory optimization methods to design open-loop stable motion primitives. We specifically design running gaits for a single-legged planar robot, and can generate motion primitives in under 3 seconds, approaching online-capable speeds. A direct-collocation-formulated optimization generated axial force profiles for the direct-drive robot to achieve desired running speed and apex height. When implemented in hardware, these trajectories produced open-loop stable running. Further, the measured running achieved the desired speed within 10% of the speed specified for the optimization in spite of having no control loop actively measuring or controlling running speed. Additionally, we examine the shape of the optimized force profile and observe features that may be applicable to open-loop stable running in general.

Robots encounter many risks that threaten the success of practical locomotion tasks. Legs break, electrical components overheat, and feet can unexpectedly slip. When all risks cannot be completely avoided, how does a robot decide its best action? We present a method for planning robot motions by reasoning about risk-of-failure probabilities instead of applying cost-penalty functions or inflexible path constraints. This work develops a risk-constrained formulation that can be straightforwardly included in existing motion planning optimizations. The risk constraints scale tractably with many risk sources, and in some cases, only add linear constraints to the optimization problem and are therefore compatible with model-predictive control techniques. We present a toy "Puck World" proof-of-concept example and a practical implementation on a planar monopod robot that runs at 3.2 m/s when permitted to take high-risk maneuvers. We believe this risk approach can be used to optimize robot behaviors under numerous conflicting task pressures and model risk-conscious behaviors in animals.

Although they take many forms, legged robots rely upon springs to achieve high speed, dynamic locomotion. In this paper we examine the effect of adding parallel springs to robots that rely on virtual compliance. Specifically, we consider the trade-off between energetic efficiency and leg versatility that comes while using Parallel Elastic Actuators (PEAs). To do this, we vary the ratio of physical to virtual compliance for legged systems using a) a modified SLIP model, b) a single legged hopping robot, and c) a multibody simulation of the quadruped robot LLAMA. In each case we show that having a small physical compliance significantly improves the efficiency while also maintaining the robot's versatility.

This paper describes the design, control and initial experimental results of the quadruped robot LLAMA. Designed to operate in a human-scale world, this 67kg-class, all-electric robot is capable of rapid motion over a variety of terrains. Thanks to a unique leg configuration and custom high-torque, low gear-ratio motors, it can move omnidirectionally at speeds over 1 m/s. A hierarchical reactive control scheme allows for robust and efficient motion even under variable payloads. This paper describes the structure of the controller and outlines simulation results that probe the performance envelope of the robot suggesting payload capacities up to one third of its body weight. Initial testing shows robust motion over loose debris and a variety of ground slopes. Videos of the robot may be seen at https://tinyurl.com/llama-robot.

Autonomous navigation through unstructured terrains has been most effectively demonstrated by animals, who utilize a large set of locomotive styles to move through their native habitats. While legged robots have recently demonstrated several of these locomotion modalities (such as walking, running, jumping, and climbing vertical walls), motion planners have yet to be able to leverage these unique mobility characteristics. In this article, we outline some of the specific motion planning challenges faced when attempting to plan for legged systems with dynamic gaits, with specific instances of these demonstrated by the dynamic climbing platform TAILS. Using a unique implementation of sampling-based model predictive optimization, we demonstrate the ability to motion plan around obstacles on vertical walls and experimentally demonstrate this on TAILS by navigating through traditionally difficult narrow gap problems.

Energy-efficient navigation is an important technology for mobile robots because of its potential to increase the operation time of the robot. In particular, when coupled with a dynamic legged quadruped, the need for energy savings is made more apparent as payloads are limited. Due to the complexity in modeling motion and power models of these robots, a new approach is necessary to effectively motion plan for these complex robots. We accomplish this by using Sampling-Based Model Predictive optimization (SBMPO) which was extended for use on the LLAMA quadrupedal platform in simulation. SBMPO allows for direct generation of trajectories while using a heuristic-based search to speed up computations. This approach is shown to effectively motion plan while optimizing for energy consumption and maintaining the natural dynamics of the robot in a simulated environment.

Many running animals, unlike their robotic counterparts, have distinct morphologies and functional roles for their front and rear legs. In this paper we present a new control approach for a 5kg autonomous dynamic quadruped that explicitly encodes separate roles for each contralateral pair of legs. This controller utilizes a functional dynamic decomposition similar to Raibert's three part control law, but focuses on fore-aft leg specialization to regulate the robot's performance. The velocity of this controller, which exceeds 5 body lengths per sec, is compared with an improved trajectory-based controller and shown to be significantly more robust to changes in environment.

The design process for leg morphology has taken much of its inspiration from the manipulator community, including the concept of maximizing the workspace of a design. In this paper, we define the concept of Effective Dynamic Workspace, which examines the subset of the overall workspace capable of achieving the desired template dynamics. With this new design tool, the leg configuration of a new multi-modal platform BOBCAT is examined and refined. With the refined design, BOBCAT is able to achieve speeds of 2m/s while running and 0.17m/s while climbing a vertical wall.

In this paper, we examine the reduced order pendular dynamic climbing model with the addition of attachment windows based on prescribed body roll. With this model and on the new dynamic climbing platform, TAILS, we demonstrate dynamic downward climbing as well as identify distinct dynamic gaits within downward climbing. This, combined with the application of an asymmetric configuration of the rear legs enables strafing motions and thus dynamic maneuverability on walls in the vertical domain.

While numerous gaits in the horizontal regime (e.g. walking or running) have been defined for legged systems on level ground, no dynamically grounded definitions have been developed for dynamic vertical running. Gaits have clear implications to robotic control strategy, efficiency, and stability. However, while several climbing robotic systems have been described as achieving `running', the question of whether distinct dynamic gaits exist and what classifies these gaits has not been rigorously explored. In this paper, by applying definitions developed in the horizontal regime, we show evidence of three distinct gaits as well as discuss the implications of these gaits on the development of dynamic climbing systems.

Robots are often used to perform similar tasks on vastly different scales. When utilizing traditional design approaches, this typically requires a full redesign and optimization at each specified size, a costly and time intensive process. In this work, we propose an alternative approach based on the principle of dynamic similarity. With this method, an initial design may be conceived at any size and scaled to any other without needing to re-optimize either physical or control variables. In the following study, we derive a generalized scaling method for this application that not only preserves system performance, but also affords flexibility in the scaling process. The preservation of dynamic similarity is validated in simulation. We further explore the application for robot-to-robot scaling, flexibility afforded by an additional free parameter, and the implications of scaling on both power requirements and structural loading. With these insights, we provide an improved methodology for the efficient and cost-effective development of scaled robotic systems.

For efficient and safe locomotion the gaits of legged robots should vary with the type of terrain. Hence, terrain surface classification is an important problem for this class of mobile robots. Prior research has developed approaches to proprioceptive terrain classification for both wheeled and limbed robots that use sensor measurements dependent upon the dynamics of the robot, which ultimately requires the classification system to be trained at a large number of operating conditions (e.g., vehicle speeds and loads). This research develops an approach to terrain identification based on pressure images generated through direct surface contact using a robot skin constructed around a high-resolution pressure sensing array. Terrain signatures for classification are formulated from the magnitude frequency responses of the pressure images. The methodology is used to train and test a classifier using dynamically measured pressure images from a one-legged hopping robot. Experimental tests yield high classification accuracies, which are independent with respect to changing robot dynamics (i.e., different leg gaits). The findings of this paper suggest the methodology can be extended to autonomous field robots, providing the robot with crucial information about the environment that can be used to aid stability over rough terrains and enhance motion planning over varying terrains.

Dynamic climbing robots have shown vertical speeds that approach those of the fastest climbing animals, but to date, no work has been conducted on directional control or maneuverability while climbing for these platforms. Directional control in animals during high-speed terrestrial running utilizes altered leg kinematics and leg specialization, however, little work has been done to classify biological strategies for maneuverability in the scansorial regime. To gain insight on how alterations of leg kinematics effect maneuverability during high-speed climbing, we propose three methods for directional control and implement them on a high-speed, dynamic climbing robotic platform. These methods alter the leg kinematics of the platform through asymmetrically changing the foot placement, center of mass, and leg length. We show that heading angles of up to 37° off of vertical are possible while only decreasing the vertical ascension rate by 20%.

As the use of mobile robots expands to more diverse and challenging environments, improved mobility methods are required to provide these platforms with the ability to reliably negotiate these terrains. In this paper, we investigate SCARAB, a quadrupedal platform designed to rapidly traverse level, vertical, and inclined surfaces. This study extends previous work in which SCARAB's climbing performance was analyzed to demonstrate its ability to run effectively on level ground. We detail several modifications made to the platform to improve its capacity to both climb and run. This updated platform was used to investigate the influence of leg configuration and leg phasing on running performance and shows that SCARAB is able to run at speeds upward of 40cms-1. Furthermore, analysis of the dynamic characteristics shows similarity between those of the robot and the Lateral Leg Spring model, particularly for configurations that produce the highest running speeds. These results make SCARAB the first platform to effectively demonstrate horizontal plane dynamics quantitatively similar to this model, as well as the first to utilize two distinct dynamical locomotion modalities.

The ability of biological locomotors to rapidly and stably traverse unstructured environments has inspired the development of numerous legged robotic platforms. While strides have been made in negotiating terrains cluttered with obstacles, dealing with surface property variations has received less consideration. This work presents a leg stiffness control strategy that estimates the surface compliance and adjusts the leg stiffness in order to maintain a nominal locomotion behavior while allowing for stable transitions between surfaces of up to three orders of magnitude differences in ground compliance. Implementation of this technique with high-bandwidth variable stiffness actuators that are currently being developed will expand the range of legged robotic platforms to environments with sudden and significant changes in terrain characteristics.

Some of the unique properties associated with running with curved legs or feet (as opposed to point-contact feet) are examined in this work, including the rolling contact motion, the change of the leg's effective stiffness and rest length, the shift of the effective flexion point along the leg, and the compliant-vaulting motions over its tiptoe during stance. To examine these factors, a novel torque-driven reduced-order dynamical model with a clock-based control scheme and with a simple motor model is developed (named as torque-driven and damped half-circle-leg model (TD-HCL)). The controller parameters are optimized for running efficiency and forward speed using a direct search method, and the results are compared to those of other existing dynamical models such as the torque-driven and damped spring-loaded-inverted-pendulum (TD-SLIP) model, the torque-driven and damped two-segment-leg (TD-TSL) model, and the TD-SLIP with a rolling foot (TD-SLIP-RF) model. The results show that running with rolling is more efficient and more stable than running with legs that involve pin joint contact model. This work begins to explain why autonomous robots using curved legs run efficiently and robustly. New curved legs are designed and manufactured in order to validate these results.

Biomechanical studies suggest that animals' abilities to tune their effective leg compliance in response to changing terrain conditions plays an important role in their agile, robust locomotion. However, despite growing interest in leg compliance within the robotics literature, little experimental work has been reported on tunable passive leg compliance in running machines. In this paper we present an empirical study into the role of leg compliance using a composite tunable leg design implemented on our dynamic hexapod, EduBot, with gaits optimized for running speed using a range of leg stiffnesses, on two different surface stiffnesses, and with two different payload configurations (0 kg and 0.91 kg). We found that leg stiffness, surface compliance, and payload had a significant impact on the robot's final optimized speed and efficiency. These results document the value and efficacy of what we believe is the first autonomous dynamic legged robot capable of runtime leg stiffness adjustment.

The present work investigates the effect of rolling contact during stance phase in running by relating the variation of foot curvature radii to running efficiency, stability and forward speed. Both a conservative reduced-order running model and one with a simple motor and friction model are used to simulate running with a rolling foot. We find that having a larger foot radius implies smoother peak vertical ground reaction forces. Increased foot radius also yields, up to a point, a larger region of stable gaits for the conservative system, and more stable, fast, and efficient gaits for the actuated version. These results motivate the design of a new set of legs to test these findings on a dynamic running platform.

This paper describes the development of a horizontal-plane dynamic running robot based on a reduced order locomotion model, the Lateral-Leg Spring (LLS) model. Contributions include the development of a scaled, actuated, distributed mass simulation of the model, control approaches to compensate for physical and motor limitations, and the design and fabrication of bipedal running robot that instantiates the horizontal plane dynamics of the LLS model.

Humans and animals adapt their leg impedance during running for both internal(e.g. loading) and external(e.g. surface) changes. In this paper we examine the relationship between leg stiffness and the speed and stability of dynamic legged locomotion. We utilize a torque-driven reduced-order model of running based on a successful family of running robots to show how optimal clock-driven controllers can interact with variably compliant limbs to adapt to changing operating conditions. We show that the leg stiffness adaptation gives, in general, better results than simply optimizing the gait controller and nearly as good as the co-optimization of controller and leg stiffness.

Traditional legged runners and climbers have relied heavily on gait generators in the form of internal clocks or reference trajectories. In contrast, here we present physical experiments with a fast, dynamical, vertical wall climbing robot accompanying a stability proof for the controller that generates it without any need for an additional internal clock or reference signal. Specifically, we show that this ¿self-exciting¿ controller does indeed generate an ¿almost¿ globally asymptotically stable limit cycle: the attractor basin is as large as topologically possible and includes all the state space excluding a set with empty interior. We offer an empirical comparison of the resulting climbing behavior to that achieved by a more conventional clock-generated gait trajectory tracker. The new, self-exciting gait generator exhibits a marked improvement in vertical climbing speed, in fact setting a new benchmark in dynamic climbing by achieving a vertical speed of 1.5 body lengths per second.

Legged robots are by nature strongly non-linear, high-dimensional systems whose full complexity permits neither tractable mathematical analysis nor comprehensive numerical study. In consequence, a growing body of literature interrogates simplified "template" (Full and Koditschek, 1999; Ghigliazza et al., 2005) models - to date almost exclusively confined to sagittal- or horizontal-plane motion - with the aim of gaining insight into the design or control of the far messier reality. In this paper we introduce a simple bounding-in-place ("BIP") model as a candidate frontal plane template for straight-ahead level ground running and explore its use in formulating hypotheses about whether and why rolling motion is important in legged locomotion. Numerical study of left-right compliance asymmetry in the BIP model suggests that compliance ratios yielding lowest steady state roll suffer far longer disturbance recovery transients than those promoting greater steady state roll. We offer preliminary experimental data obtained from video motion capture data of the frontal plane disturbance recovery patterns of a RHex-like hexapod suggesting a correspondence to the conclusions of the numerical study.

The design of legged robots has long drawn on nature for inspiration. However, few of these robots exhibit the speed and robustness seen in even the simplest of animals. The paper presents the design and fabrication of a class of six-legged running robots based on biologically inspired functional principles. We first describe findings in biological research that motivate our robots' design, leg configuration, and control structure. We then describe an emerging layered-manufacturing technology that allows us to fabricate the robots with passive mechanical properties like those found in nature. Finally, we present preliminary tests over different terrains and conditions which show speed and robustness approaching the performance of small animals.