Work minimization accounts for footfall phasing in slow quadrupedal gaits

Quadrupeds, like most bipeds, tend to walk with an even left/right footfall timing. However, the phasing between hind and forelimbs shows considerable variation. Here, we account for this variation by modeling and explaining the influence of hind-fore limb phasing on mechanical work requirements. These mechanics account for the different strategies used by: (1) slow animals (a group including crocodile, tortoise, hippopotamus and some babies); (2) normal medium to large mammals; and (3) (with an appropriate minus sign) sloths undertaking suspended locomotion across a range of speeds. While the unusual hind-fore phasing of primates does not match global work minimizing predictions, it does approach an only slightly more costly local minimum. Phases predicted to be particularly costly have not been reported in nature

Analytic Model for Quadruped Locomotion Task-Space Planning

Despite the extensive presence of the legged locomotion in animals, it is extremely challenging to be reproduced with robots. Legged locomotion is an dynamic task which benefits from a planning that takes advantage of the gravitational pull on the system. However, the computational cost of such optimization rapidly increases with the complexity of kinematic structures, rendering impossible real-time deployment in unstructured environments. This paper proposes a simplified method that can generate desired centre of mass and feet trajectory for quadrupeds. The model describes a quadruped as two bipeds connected via their centres of mass, and it is based on the extension of an algebraic bipedal model that uses the topology of the gravitational attractor to describe bipedal locomotion strategies. The results show that the model generates trajectories that agrees with previous studies. The model will be deployed in the future as seed solution for whole-body trajectory optimization in the attempt to reduce the computational cost and obtain real-time planning of complex action in challenging environments.Comment: Accepted to be Published in 2019, 41th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Berlin German

Exploring Passive Dynamics in Legged Locomotion

A common observation among legged animals is that they move their limbs differently as they change their speed. The observed distinct patterns of limb movement are usually referred to as different gaits. Experiments with humans and mammals have shown that switching between different gaits as locomotion speed changes, enables energetically more economical locomotion. However, it still remains unclear why animals with very different morphologies use similar gaits, where these gaits come from, and how they are related. This dissertation approaches these questions by exploring the natural passive dynamic motions of a range of simplified mechanical models of legged locomotion. Recent research has shown that a simple bipedal model with compliant legs and a single set of parameters can match ground reaction forces of both human walking and running. As first contribution of this dissertation, this concept is extended to quadrupeds. A unified model is developed to reproduce many quadrupedal gaits by only varying the initial states of a motion. In addition, the model parameters are optimized to match the experimental data of real horses, as measured by an instrumented treadmill. It is shown that the proposed model is able to not only create similar kinematic motion trajectories, but can also explain the ground reaction forces of real horses moving with different gaits. In order to reveal the mechanical contribution to gaits, the simplistic bipedal and quadrupedal models are then augmented to have passive swing leg motions by including torsional springs at the hip joints. Through a numerical continuation of periodic motions, this work shows that a wide range of gaits emerges from a simple bouncing-in-place motion starting with different footfall patterns. For both, bipedal and quadrupedal models, these gaits arise along one-dimensional manifolds of solutions with varying total energy. Through breaking temporal and spatial symmetries of the periodic motions, these manifolds bifurcate into distinct branches with various footfall sequences. That is, passive gaits are obtained as different oscillatory motions of a single mechanical system with a single set of parameters. By reproducing a variety of gaits as a manifestation of the passive dynamics of unified models, this work provides insights into the underlying dynamics of legged locomotion and may help design of more economical controllers for legged machines.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147585/1/ganzheny_1.pd

Master of Science

thesisThis research studies the passive dynamics of an under-actuated trotting quadruped. The goal of this project is to perform three-dimensional (3D) dynamic simulations of a trotting quadruped robot to find proper leg configurations and stiffness range, in order to achieve stable trotting gait. First, a 3D simulation framework that includes all the six degrees of freedom of the body is introduced. Directionally compliant legs together with different leg configurations are employed to achieve passive stability. Compliant legs passively support the body during stance phase and during flight phase a motor is used to retract the legs. Leg configurations in the robot's sagittal and frontal plane are introduced. Numerical experiments are conducted to search the design space of the leg, focusing on increasing the passive stability of the robot. Increased stability is defined as decreased pitching, rolling, and yawing motion of the robot. The results indicate that optimized leg parameters can guarantee passive stable trotting with reduced roll, pitch, and yaw. Studies suggest that a quadruped robot with compliant legs is dynamically stable while trotting. Results indicate that the robot based on a biological model (i.e., caudal inclination of humeri and cranial inclination of femora) has the best performance. Stiff springs at hips and shoulders, soft spring at knees and elbows, and stiff springs at ankles and wrists are recommended. The results of this project provide a conceptual framework for understanding the movements of a trotting quadruped

Passive Quadrupedal Gait Synchronization for Extra Robotic Legs Using a Dynamically Coupled Double Rimless Wheel Model

The Extra Robotic Legs (XRL) system is a robotic augmentation worn by a human operator consisting of two articulated robot legs that walk with the operator and help bear a heavy backpack payload. It is desirable for the Human- XRL quadruped system to walk with the rear legs lead the front by 25% of the gait period, minimizing the energy lost from foot impacts while maximizing balance stability. Unlike quadrupedal robots, the XRL cannot command the human’s limbs to coordinate quadrupedal locomotion. Using a pair of Rimless Wheel models, it is shown that the systems coupled with a spring and damper converge to the desired 25% phase difference. A Poincar´e return map was generated using numerical simulation to examine the convergence properties to different coupler design parameters, and initial conditions. The Dynamically Coupled Double Rimless Wheel system was physically realized with a spring and dashpot chosen from the theoretical results, and initial experiments indicate that the desired synchronization properties may be achieved within several steps using this set of passive components alone

Legged Robots

International audienc

Don't break a leg: Running birds from quail to ostrich prioritise leg safety and economy in uneven terrain

Cursorial ground birds are paragons of bipedal running that span a 500-fold mass range from quail to ostrich. Here we investigate the task-level control priorities of cursorial birds by analysing how they negotiate single-step obstacles that create a conflict between body stability (attenuating deviations in body motion) and consistent leg force–length dynamics (for economy and leg safety). We also test the hypothesis that control priorities shift between body stability and leg safety with increasing body size, reflecting use of active control to overcome size-related challenges. Weight-support demands lead to a shift towards straighter legs and stiffer steady gait with increasing body size, but it remains unknown whether non-steady locomotor priorities diverge with size. We found that all measured species used a consistent obstacle negotiation strategy, involving unsteady body dynamics to minimise fluctuations in leg posture and loading across multiple steps, not directly prioritising body stability. Peak leg forces remained remarkably consistent across obstacle terrain, within 0.35 body weights of level running for obstacle heights from 0.1 to 0.5 times leg length. All species used similar stance leg actuation patterns, involving asymmetric force–length trajectories and posture-dependent actuation to add or remove energy depending on landing conditions. We present a simple stance leg model that explains key features of avian bipedal locomotion, and suggests economy as a key priority on both level and uneven terrain. We suggest that running ground birds target the closely coupled priorities of economy and leg safety as the direct imperatives of control, with adequate stability achieved through appropriately tuned intrinsic dynamics