Adaptive Control of Quadruped Locomotion Through Variable Compliance of Revolute Spiral Feet

In this article we present a novel mechanical design of a robot leg that possesses active and variable passive compliance properties. The hip and knee joints provide active compliance, while the variable passive compliance comes from the spiral foot spring, mounted on the ankle joint, which changes its stiffness by rotating and changing contact angle with the ground. The stiffness of the foot for various contact angles was identified experimentally by using the strength tester measurement system. The method for damping coefficient identification, based on the observation of energy losses during the stance phase of leg hopping motion, is described and used to obtain the foot damping model. The adaptation of spiral foot stiffness to varying ground stiffness is achieved by extracting a leg contact time from a feedback signal provided by a flex sensor mounted on the foot. The experiments on a single leg and quadruped platforms have confirmed that the presented spiral foot design provides stiffness adaptability, partial recovery of the energy from the previous hop and restriction of stance contact time, which are all necessary conditions to obtain more efficient quadruped locomotion.

Feedback control as a framework for understanding tradeoffs in biology

Control theory arose from a need to control synthetic systems. From regulating steam engines to tuning radios to devices capable of autonomous movement, it provided a formal mathematical basis for understanding the role of feedback in the stability (or change) of dynamical systems. It provides a framework for understanding any system with regulation via feedback, including biological ones such as regulatory gene networks, cellular metabolic systems, sensorimotor dynamics of moving animals, and even ecological or evolutionary dynamics of organisms and populations. Here, we focus on four case studies of the sensorimotor dynamics of animals, each of which involves the application of principles from control theory to probe stability and feedback in an organism's response to perturbations. We use examples from aquatic (two behaviors performed by electric fish), terrestrial (following of walls by cockroaches), and aerial environments (flight control by moths) to highlight how one can use control theory to understand the way feedback mechanisms interact with the physical dynamics of animals to determine their stability and response to sensory inputs and perturbations. Each case study is cast as a control problem with sensory input, neural processing, and motor dynamics, the output of which feeds back to the sensory inputs. Collectively, the interaction of these systems in a closed loop determines the behavior of the entire system.

Force and flow at the onset of drag in plowed granular media

We study the transient drag force FD on a localized intruder in a granular medium composed of spherical glass particles. A flat plate is translated horizontally from rest through the granular medium to observe how FD varies as a function of the medium's initial volume fraction, ϕ. The force response of the granular material differs above and below the granular critical state, ϕc, the volume fraction which corresponds to the onset of grain dilatancy. For ϕ<ϕc FD increases monotonically with displacement and is independent of drag velocity for the range of velocities examined (<10 cm/s). For ϕ>ϕc, FD rapidly rises to a maximum and then decreases over further displacement. The maximum force for ϕ>ϕc increases with increasing drag velocity. In quasi-two-dimensional drag experiments, we use granular particle image velocimetry (PIV) to measure time resolved strain fields associated with the horizontal motion of a plate started from rest. PIV experiments show that the maxima in FD for ϕ>ϕc are associated with maxima in the spatially averaged shear strain field. For ϕ>ϕc the shear strain occurs in a narrow region in front of the plate, a shear band. For ϕ<ϕc the shear strain is not localized, the shear band fluctuates in space and time, and the average shear increases monotonically with displacement. Laser speckle measurements made at the granular surface ahead of the plate reveal that for ϕ<ϕc particles are in motion far from the intruder and shearing region. For ϕ>ϕc, surface particles move only during the formation of the shear band, coincident with the maxima in FD, after which the particles remain immobile until the sheared region reaches the measurement region.

Towards terrain interaction prediction for bioinspired planetary exploration rovers

Deployment of a small legged vehicle to extend the reach of future planetary exploration missions is an attractive possibility but little is known about the behaviour of a walking rover on deformable planetary terrain. This paper applies ideas from the developing study of granular materials together with a detailed characterization of the sinkage process to propose and validate a combined model of terrain interaction based on an understanding of the physics and micro mechanics at the granular level. Whilst the model reflects the complexity of interactions expected from a walking rover, common themes emerge which enable the model to be streamlined to the extent that a simple mathematical representation is possible without resorting to numerical methods. Bespoke testing and analysis tools are described which reveal some unexpected conclusions and point the way towards intelligent control and foot geometry techniques to improve thrust generation.

Burrowing behaviour of robotic bivalves with synthetic morphologies

Several bivalve species burrow into sandy sediments to reach their living position. There are many hypotheses concerning the functional morphology of the bivalve shell for burrowing. Observational studies are limited and often qualitative and should be complemented by a synthetic approach mimicking the burrowing process using a robotic emulation. In this paper we present a simple mechatronic set-up to mimic the burrowing behaviour of bivalves. As environment we used water and quartz sand contained in a glass tank. Bivalve shells were mathematically modelled on the computer and then materialized using a 3D printer. The burrowing motion of the shells was induced by two external linear motors. Preliminary experiments did not expose any artefacts introduced to the burrowing process by the set-up. We tested effects of shell size, shape and surface sculpturing on the burrowing performance. Neither the typical bivalve shape nor surface sculpture did have a clear positive effect on burrowing depth in the performed experiments. We argue that the presented method is a valid and promising approach to investigate the functional morphology of bivalve shells and should be improved and extended in future studies. In contrast to the observation of living bivalves, our approach offers complete control over the parameters defining shell morphology and motion pattern. The technical set-up allows the systematic variation of all parameters to quantify their effects. The major drawback of the built set-up was that the reliability and significance of the results was limited by the lack of an optimal technique to standardize the sediment state before experiments.

Foot–terrain interaction mechanics for legged robots: Modeling and experimental validation

Contact mechanics plays an important role in the design, performance analysis, simulation, and control of legged robots. The Hunt–Crossley model and the Coulomb friction model are often used as black-box models with limited consideration of the properties of the terrain and the feet. This paper analyzes the foot–terrain interaction based on the knowledge of terramechanics and reveals the relationship between the parameters of the conventional models and the terramechanics models. The proposed models are derived in three categories: deformable foot on hard terrain, hard foot on deformable terrain, and deformable foot on deformable terrain. A novel model of tangential forces as the function of displacement is proposed on the basis of an in-depth understanding of the terrain properties. Methods for identifying the model parameters are also developed. Extensive foot–soil interaction experiments have been carried out, and the experimental results validate the high fidelity of the derived models.

Depth-dependent resistance of granular media to vertical penetration

We measure the quasistatic friction force acting on intruders moving downwards into a granular medium. By utilizing different intruder geometries, we demonstrate that the force acts locally normal to the intruder surface. By altering the hydrostatic loading of grain contacts by a sub-fluidizing airflow through the bed, we demonstrate that the relevant frictional contacts are loaded by gravity rather than by the motion of the intruder itself. Lastly, by measuring the final penetration depth versus airspeed and using an earlier result for inertial drag, we demonstrate that the same quasistatic friction force acts during impact. Altogether this force is set by a friction coefficient, hydrostatic pressure, projectile size and shape, and a dimensionless proportionality constant. The latter is the same in nearly all experiments, and is surprisingly greater than one.

Ground fluidization promotes rapid running of a lightweight robot

We study the locomotor mechanics of a small, lightweight robot (DynaRoACH, 10 cm, 25 g) which can move on a granular substrate of 3 mm diameter glass particles at speeds up to 5 body length/s, approaching the performance of certain desert-dwelling animals. To reveal how the robot achieves this performance, we used high-speed imaging to capture its kinematics, and developed a numerical multi-body simulation of the robot coupled to an experimentally validated simulation of the granular medium. Average speeds measured in experiment and simulation agreed well, and increased nonlinearly with stride frequency, reflecting a change in propulsion mode. At low frequencies, the robot used a quasi-static “rotary walking” mode, in which the substrate yielded as legs penetrated and then solidified once vertical force balance was achieved. At high frequencies the robot propelled itself using the speed-dependent fluid-like inertial response of the material. The simulation allows variation of parameters which are inconvenient to modify in experiment, and thus gives insight into how substrate and robot properties change performance. Our study reveals how lightweight animals can achieve high performance on granular substrates; such insights can advance the design and control of robots in deformable terrains.

Flipper-driven terrestrial locomotion of a sea turtle-inspired robot

To discover principles of flipper-based terrestrial locomotion we study the mechanics of a hatchling sea turtle-inspired robot, FlipperBot (FBot), during quasi-static movement on granular media. FBot implements a symmetric gait using two servo-motor-driven front limbs with flat-plate flippers and either freely rotating or fixed wrist joints. For a range of gaits, FBot moves with a constant step length. However, for gaits with sufficiently shallow flipper penetration or sufficiently large stroke, per step displacement decreases with each successive step resulting in failure (zero forward displacement) within a few steps. For the fixed wrist, failure occurs when FBot interacts with ground disturbed during previous steps, and measurements reveal that flipper generated forces decrease as per step displacement decreases. The biologically inspired free wrist is less prone to failure, but slip-induced failure can still occur if FBot pitches forward and drives its leading edge into the substrate. In the constant step length regime, kinematic and force-based models accurately predict FBot's motion for free and fixed wrist configurations, respectively. When combined with independent force measurements, models and experiments provide insight into how disturbed ground leads to locomotory failure and help explain differences in hatchling sea turtle performance.