Push recovery with stepping strategy based on time-projection control

In this paper, we present a simple control framework for on-line push recovery with dynamic stepping properties. Due to relatively heavy legs in our robot, we need to take swing dynamics into account and thus use a linear model called 3LP which is composed of three pendulums to simulate swing and torso dynamics. Based on 3LP equations, we formulate discrete LQR controllers and use a particular time-projection method to adjust the next footstep location on-line during the motion continuously. This adjustment, which is found based on both pelvis and swing foot tracking errors, naturally takes the swing dynamics into account. Suggested adjustments are added to the Cartesian 3LP gaits and converted to joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies also ensure enough ground clearance in perturbed walking conditions. The proposed structure is robust, yet uses very simple state estimation and basic position tracking. We rely on the physical series elastic actuators to absorb impacts while introducing simple laws to compensate their tracking bias. Extensive experiments demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness due to relatively soft springs in the ankles and avoiding any Zero Moment Point (ZMP) control in our proposed architecture.Comment: 20 pages journal pape

The Design and Realization of a Sensitive Walking Platform

Legged locomotion provides robots with the capability of adapting to different terrain conditions. General complex terrain traversal methodologies solely rely on proprioception which readily leads to instability under dynamical situations. Biological legged locomotion utilizes somatosensory feedback to sense the real-time interaction of the feet with ground to enhance stability. Nevertheless, limited attention has been given to sensing the feet-terrain interaction in robotics. This project introduces a paradigm shift in robotic walking called sensitive walking realized through the development of a compliant bipedal platform. Sensitive walking extends upon the success of sensitive manipulation which utilizes tactile feedback to localize an object to grasp, determine an appropriate manipulation configuration, and constantly adapts to maintain grasp stability. Based on the same concepts of sensitive manipulation, sensitive walking utilizes podotactile feedback to enhance real-time walking stability by effectively adapting to variations in the terrain. Adapting legged robotic platforms to sensitive walking is not as simple as attaching any tactile sensor to the feet of a robot. The sensors and the limbs need to have specific characteristics that support the implementation of the algorithms and allow the biped to safely come in contact with the terrain and detect the interaction forces. The challenges in handling the synergy of hardware and sensor design, and fabrication in a podotactile-based sensitive walking robot are addressed. The bipedal platform provides contact compliance through 12 series elastic actuators and contains 190 highly flexible tactile sensors capable of sensing forces at any incident angle. Sensitive walking algorithms are provided to handle multi-legged locomotion challenges including stairs and irregular terrain

Frontal plane roll-over analysis of prosthetic feet

In prosthetic walking mediolateral balance is compromised due to the lack of active ankle control, by moments of force, in the prosthetic limb. Active control is reduced to the hip strategy, and passive mechanical stability depends on the curvature of the prosthetic foot under load. Mediolateral roll-over curvatures of prosthetic feet are largely unknown. In this study we determined the mediolateral roll-over characteristics of various prosthetic feet and foot-shoe combinations. Characteristics were determined by means of an inverted pendulum-like apparatus. The relationship between the centre of pressure (CoP) and the shank angle was measured and converted to roll-over shape and effective radius of curvature. Further, hysteresis (i.e., lagging in CoP displacement due to material compliance or slip) at vertical shank angle was determined from the hysteresis curve. Passive mechanical stability varied widely, though all measured foot-shoe combinations were relatively compliant. Mediolateral motion of the CoP ranged between 4 mm and 40 mm, thereby remaining well within each foot's physical width. Derived roll-over radii of curvature are also small, with an average of 102 mm. Hysteresis ranges between 20% and 115% of total CoP displacement and becomes more pronounced when adding a shoe. This may be due to slipping of the foot core in its cosmetic cover, or the foot in the shoe. Slip may be disadvantageous for balance control by limiting mediolateral travel of the CoP. It may therefore be clinically relevant to eliminate mediolateral slip in prosthetic foot design

Compliant Joints Increase the Energy Efficiency of Bipedal Robot

6International audienceThe energetic effects of knee locking and addition of linear elastic members to different joints of a seven-link fully actuated planar bipedal robot were studied. The focus was on the reduction of energy consumption during walking. An impactless walking gait was studied and the energetic cost of walking was determined without joint stiffness and knee locking as a baseline for comparison. The gait trajectory was then optimized by adding spring to different joints, energetic cost of walk was then calculated at different walking speeds. Support knee was then mechanically locked and gait was optimized to find the cost of walking. The energetic cost of walking determined for the above two cases was then compared to the baseline cost. It was observed that addition of torsional springs at both knees can reduce the walking cost up to 62% at lower speeds and both hips up to 35% at high walking speeds with spring stiffness as an optimization parameter for both cases. Mechanically locking the support knee can reduce the cost of walking up to 84% at slow walking speeds with gait and knee locking angle optimized

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

Development of a Hybrid Powered 2D Biped Walking Machine Designed for Rough Terrain Locomotion

Biped robots hold promise as terrestrial explorers because they require a single discrete foothold to place their next step. However, biped robots are multi-input multi-output dynamically unstable machines. This makes walking on rough terrain difficult at best. Progress has been made with non-periodic rough terrain like stairs or inclines with fully active walking machines. Terrain that requires the walker to change its gait pattern from a standard walk is still problematic. Most walking machines have difficulty detecting or responding to the small perturbations induced by this type of terrain. These small perturbations can lead to unstable gait cycles and possibly a fall. The Intelligent Systems and Automation Lab at the University of Kansas has built a three legged 2D biped walking machine to be used as a test stand for studying rough terrain walking. The specific aim of this research is to investigate how biped walkers can best maintain walking stability when acted upon by small perturbations caused by periodic rough terrain. The first walking machine prototype, referred to as Jaywalker has two main custom actuation systems. The first is the hip ratchet system. It allows the walker to have either a passive or active hip swing. The second is the hybrid parallel ankle actuator. This new actuator uses a pneumatic ram and stepper motor in parallel to produce an easily controlled high torque output. In open loop control it has less than a 1° tracking error and 0.065 RPM velocity error compared to a standard stepper motor. Step testing was conducted using the Jaywalker, with a passive hip, to determine if a walker with significant leg mass could walk without full body actuation. The results of testing show the Jaywalker is ultimately not capable of walking with a passive hip. However, the walking motion is fine until the terminal stance phase. At this point the legs fall quickly towards the ground as the knee extends the shank. This quick step phenomenon is caused by increased speeds and forces about the leg and hip caused by the extension of the shank. This issue can be overcome by fully actuating the hip, or by adding counterbalances to the legs about the hip