A Novel Lockable Spring-loaded Prismatic Spine to Support Agile Quadrupedal Locomotion

This paper introduces a way to systematically investigate the effect of compliant prismatic spines in quadrupedal robot locomotion. We develop a novel spring-loaded lockable spine module, together with a new Spinal Compliance-Integrated Quadruped (SCIQ) platform for both empirical and numerical research. Individual spine tests reveal beneficial spinal characteristics like a degressive spring, and validate the efficacy of a proposed compact locking/unlocking mechanism for the spine. Benchmark vertical jumping and landing tests with our robot show comparable jumping performance between the rigid and compliant spines. An observed advantage of the compliant spine module is that it can alleviate more challenging landing conditions by absorbing impact energy and dissipating the remainder via feet slipping through much in cat-like stretching fashion.Comment: To appear in 2023 IEEE IRO

Online Planning for Autonomous Running Jumps Over Obstacles in High-Speed Quadrupeds

This paper presents a new framework for the generation of high-speed running jumps to clear terrain obstacles in quadrupedal robots. Our methods enable the quadruped to autonomously jump over obstacles up to 40 cm in height within a single control framework. Specifically, we propose new control system components, layered on top of a low-level running controller, which actively modify the approach and select stance force profiles as required to clear a sensed obstacle. The approach controller enables the quadruped to end in a preferable state relative to the obstacle just before the jump. This multi-step gait planning is formulated as a multiple-horizon model predictive control problem and solved at each step through quadratic programming. Ground reaction force profiles to execute the running jump are selected through constrained nonlinear optimization on a simplified model of the robot that possesses polynomial dynamics. Exploiting the simplified structure of these dynamics, the presented method greatly accelerates the computation of otherwise costly function and constraint evaluations that are required during optimization. With these considerations, the new algorithms allow for online planning that is critical for reliable response to unexpected situations. Experimental results, for a stand-alone quadruped with on-board power and computation, show the viability of this approach, and represent important steps towards broader dynamic maneuverability in experimental machines.United States. Defense Advanced Research Projects Agency. Maximum Mobility and Manipulation (M3) ProgramKorean Agency for Defense Development (Contract UD1400731D

Quadrupedal robots with stiff and compliant actuation

In the broader context of quadrupedal locomotion, this overview article introduces and compares two platforms that are similar in structure, size, and morphology, yet differ greatly in their concept of actuation. The first, ALoF, is a classically stiff actuated robot that is controlled kinematically, while the second, StarlETH, uses a soft actuation scheme based on highly compliant series elastic actuators. We show how this conceptual difference influences design and control of the robots, compare the hardware of the two systems, and show exemplary their advantages in different applications. © Oldenbourg Wissenschaftsverlag

LeggedWalking on Inclined Surfaces

The main contribution of this MS Thesis is centered around taking steps towards successful multi-modal demonstrations using Northeastern's legged-aerial robot, Husky Carbon. This work discusses the challenges involved in achieving multi-modal locomotion such as trotting-hovering and thruster-assisted incline walking and reports progress made towards overcoming these challenges. Animals like birds use a combination of legged and aerial mobility, as seen in Chukars' wing-assisted incline running (WAIR), to achieve multi-modal locomotion. Chukars use forces generated by their flapping wings to manipulate ground contact forces and traverse steep slopes and overhangs. Husky's design takes inspiration from birds such as Chukars. This MS thesis presentation outlines the mechanical and electrical details of Husky's legged and aerial units. The thesis presents simulated incline walking using a high-fidelity model of the Husky Carbon over steep slopes of up to 45 degrees.Comment: Masters thesi

Understanding the motions of the cheetah tail using robotics

The cheetah is capable of incredible feats of manoeuvrability. But, what is interesting about these manoeuvres is that they involve rapid swinging of the animal's lengthy tail. Despite this, very little is understood about the cheetah tail and its motion, with the common view being that it is "heavy" and possibly used as a "counter balance" or as a "rudder". In this dissertation, this subject is investigated by exploring the motions of the cheetah tail by means of mathematic al models, feedback control and novel robot platforms. Particularly, the motion in the roll axis is first investigated and it is determined that it assists stability of high speed turns. This is validated by modelling and experimental testing on a novel tailed robot, Dima I. Inspired by cheetah video observations, the tail motion in the pitch axis during rapid acceleration and braking manoeuvres is also investigated. Once again modelling and experimental testing on a tailed robot are performed and the tail is shown to stabilise rapid acceleration manoeuvres. Video observations also indicate the tail movement in the shape of a cone: a combination of pitching and yawing. Understanding this motion is done by setting up an optimization problem. Here, the optimal motion was found to be to a cone which results in a continuous torque on the body during a turn while galloping. A novel two degree of freedom tailed robot, Dima II, was then developed to experimentally validate the effect of this motion. Lastly, measurement of the cheetah tail inertia was performed during a routine necropsy where it was found to have lower inertia than assumed. However, the tail has thick, long fur that was tested in a wind tunnel. Here it was found that the furry tail is capable of producing significant drag forces without a weight penalty. Subsequently, mathematical models incorporating the aerodynamics of the tail were developed and these were used to demonstrate its effectiveness during manoeuvres

Using learning algorithms to develop dynamic gaits for legged robots

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2006.Includes bibliographical references (p. 129-134).As more legged robots have begun to be developed for their obvious advantages in overall maneuverability and mobility over rough terrain and difficult obstacles, their shortcomings over flat terrain have become more apparent. These robots plod along at extremely low speeds even when the ground is flat and level due to the fact that virtually all legged robots use a very stable, very slow walking gait to move, regardless of whether the ground is flat or rough. The simplest way of solving this problem is to use the same method as legged animals: simply change the gait from a walk to a faster more dynamic gait in order to increase the robot's speed. It would be extremely useful if legged robots were capable of moving across flat ground at high velocities while still retaining their ability to cross extremely rough or broken ground. Unfortunately, dynamic gaits are quite difficult to program by hand and only minimal research has been done on them. This thesis evaluates the use of two different types of learning algorithms (a genetic algorithm and a modified gradient-climbing reinforcement learning algorithm) as applied to the problem of developing dynamic gaits for a simulation of the Sony Aibo robot.(cont.) The two algorithms are tested using a random starting population and a high-fitness starting population and the results from both tests are compared. The research focuses on three different types of dynamic gaits: the trot, the canter, and the gallop. The efficiencies of the learned gaits are compared to each other in order to try to determine the best type of high-speed gait for use on the Aibo robot. Problems with the design of the Aibo robot as related to performing dynamic gaits are also identified and solutions are proposed.by Brian Schaaf.S.M

Investigation of an Articulated Spine in a Quadruped Robotic System.

This research quantitatively analyzes a multi-body dynamics quadrupedal model with an articulated spine to evaluate the effects of speed and stride frequency on the energy requirements of the system. The articulated model consists of six planar, rigid bodies with a single joint in the middle of the torso. All joints are frictionless and mass is equally distributed in the limbs and torso. A model with the mid-torso joint removed, denoted as the rigid model, is used as a baseline comparison. Impulsive forces and torques are used to instantaneously reset the velocities at the phase transitions, allowing for ballistic trajectories during flight phases. Active torques at the haunch and shoulder joints are used during the stance phases to increase the model robustness. Simulations were conducted over effective high-speed gaits from 6.0 - 9.0 m/s. Stride frequencies were varied for both models. An evolutionary algorithm was employed to find plausible gaits based on biologically realistic constraints and bounds. The objective function for the optimization was cost of transport. Results show a decreasing cost of transport as speed increases for the articulated model with an optimal stride frequency of 3 s$^{-1}$ and an increasing cost of transport with increasing speed for the rigid model at an optimal stride frequency of 1.4 s$^{-1}$, with a crossover in the cost of transport between the two models occurring at 7.0 m/s. The rigid model favors low speeds and stride frequencies at the cost of a large impulsive vertical force, driving the system through a long, gathered flight phase used to cover the long distances at the low stride frequencies. The articulated model prefers higher speeds and stride frequencies at the cost of a large impulsive torque in the back joint, akin to the contraction of abdomen muscles, preventing the collapse of the back. Thus, it is demonstrated that the inclusion of back articulation enables a more energetically efficient high-speed gait than a rigid back system, as seen in biological systems. Detailed analysis is provided to identify the mechanics associated with the optimal gaits of both the rigid and the articulated systems to support this claim.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89831/1/bhaueise_1.pd

Actuation-Aware Simplified Dynamic Models for Robotic Legged Locomotion

In recent years, we witnessed an ever increasing number of successful hardware implementations of motion planners for legged robots. If one common property is to be identified among these real-world applications, that is the ability of online planning. Online planning is forgiving, in the sense that it allows to relentlessly compensate for external disturbances of whatever form they might be, ranging from unmodeled dynamics to external pushes or unexpected obstacles and, at the same time, follow user commands. Initially replanning was restricted only to heuristic-based planners that exploit the low computational effort of simplified dynamic models. Such models deliberately only capture the main dynamics of the system, thus leaving to the controllers the issue of anchoring the desired trajectory to the whole body model of the robot. In recent years, however, we have seen a number of new approaches attempting to increase the accuracy of the dynamic formulation without trading-off the computational efficiency of simplified models. In this dissertation, as an example of successful hardware implementation of heuristics and simplified model-based locomotion, I describe the framework that I developed for the generation of an omni-directional bounding gait for the HyQ quadruped robot. By analyzing the stable limit cycles for the sagittal dynamics and the Center of Pressure (CoP) for the lateral stabilization, the described locomotion framework is able to achieve a stable bounding while adapting to terrains of mild roughness and to sudden changes of the user desired linear and angular velocities. The next topic reported and second contribution of this dissertation is my effort to formulate more descriptive simplified dynamic models, without trading off their computational efficiency, in order to extend the navigation capabilities of legged robots to complex geometry environments. With this in mind, I investigated the possibility of incorporating feasibility constraints in these template models and, in particular, I focused on the joint torques limits which are usually neglected at the planning stage. In this direction, the third contribution discussed in this thesis is the formulation of the so called actuation wrench polytope (AWP), defined as the set of feasible wrenches that an articulated robot can perform given its actuation limits. Interesected with the contact wrench cone (CWC), this yields a new 6D polytope that we name feasible wrench polytope (FWP), defined as the set of all wrenches that a legged robot can realize given its actuation capabilities and the friction constraints. Results are reported where, thanks to efficient computational geometry algorithms and to appropriate approximations, the FWP is employed for a one-step receding horizon optimization of center of mass trajectory and phase durations given a predefined step sequence on rough terrains. For the sake of reachable workspace augmentation, I then decided to trade off the generality of the FWP formulation for a suboptimal scenario in which a quasi-static motion is assumed. This led to the definition of the, so called, local/instantaneous actuation region and of the global actuation/feasible region. They both can be seen as different variants of 2D linear subspaces orthogonal to gravity where the robot is guaranteed to place its own center of mass while being able to carry its own body weight given its actuation capabilities. These areas can be intersected with the well known frictional support region, resulting in a 2D linear feasible region, thus providing an intuitive tool that enables the concurrent online optimization of actuation consistent CoM trajectories and target foothold locations on rough terrains