Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics

Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most studies of simple walking and running models have focused on the basins of attraction of passive limit-cycles and the notion of self-stability. We instead emphasize the importance of stepping beyond basins of attraction. We show an approach based on viability theory to quantify robust sets in state-action space. These sets are valid for the family of all robust control policies, which allows us to quantify the robustness inherent to the natural dynamics before designing the control policy or specifying a control objective. We illustrate our formulation using spring-mass models, simple low dimensional models of running systems. We then show an example application by optimizing robustness of a simulated planar monoped, using a gradient-free optimization scheme. Both case studies result in a nonlinear effective stiffness providing more robustness.Comment: 15 pages. This work has been accepted to IEEE Transactions on Robotics (2019

Effective Viscous Damping Enables Morphological Computation in Legged Locomotion

Muscle models and animal observations suggest that physical damping is beneficial for stabilization. Still, only a few implementations of mechanical damping exist in compliant robotic legged locomotion. It remains unclear how physical damping can be exploited for locomotion tasks, while its advantages as sensor-free, adaptive force- and negative work-producing actuators are promising. In a simplified numerical leg model, we studied the energy dissipation from viscous and Coulomb damping during vertical drops with ground-level perturbations. A parallel spring-damper is engaged between touch-down and mid-stance, and its damper auto-disengages during mid-stance and takeoff. Our simulations indicate that an adjustable and viscous damper is desired. In hardware we explored effective viscous damping and adjustability and quantified the dissipated energy. We tested two mechanical, leg-mounted damping mechanisms; a commercial hydraulic damper, and a custom-made pneumatic damper. The pneumatic damper exploits a rolling diaphragm with an adjustable orifice, minimizing Coulomb damping effects while permitting adjustable resistance. Experimental results show that the leg-mounted, hydraulic damper exhibits the most effective viscous damping. Adjusting the orifice setting did not result in substantial changes of dissipated energy per drop, unlike adjusting damping parameters in the numerical model. Consequently, we also emphasize the importance of characterizing physical dampers during real legged impacts to evaluate their effectiveness for compliant legged locomotion

Adaptive, fast walking in a biped robot under neuronal control and learning

Human walking is a dynamic, partly self-stabilizing process relying on the interaction of the biomechanical design with its neuronal control. The coordination of this process is a very difficult problem, and it has been suggested that it involves a hierarchy of levels, where the lower ones, e.g., interactions between muscles and the spinal cord, are largely autonomous, and where higher level control (e.g., cortical) arises only pointwise, as needed. This requires an architecture of several nested, sensori–motor loops where the walking process provides feedback signals to the walker's sensory systems, which can be used to coordinate its movements. To complicate the situation, at a maximal walking speed of more than four leg-lengths per second, the cycle period available to coordinate all these loops is rather short. In this study we present a planar biped robot, which uses the design principle of nested loops to combine the self-stabilizing properties of its biomechanical design with several levels of neuronal control. Specifically, we show how to adapt control by including online learning mechanisms based on simulated synaptic plasticity. This robot can walk with a high speed (> 3.0 leg length/s), self-adapting to minor disturbances, and reacting in a robust way to abruptly induced gait changes. At the same time, it can learn walking on different terrains, requiring only few learning experiences. This study shows that the tight coupling of physical with neuronal control, guided by sensory feedback from the walking pattern itself, combined with synaptic learning may be a way forward to better understand and solve coordination problems in other complex motor tasks

Combining series elastic actuation and magneto-rheological damping for the control of agile locomotion

All-terrain robot locomotion is an active topic of research. Search and rescue maneuvers and exploratory missions could benefit from robots with the abilities of real animals. However, technological barriers exist to ultimately achieving the actuation system, which is able to meet the exigent requirements of these robots. This paper describes the locomotioncontrol of a leg prototype, designed and developed to make a quadruped walk dynamically while exhibiting compliant interaction with the environment. The actuation system of the leg is based on the hybrid use of series elasticity and magneto-rheological dampers, which provide variable compliance for natural-looking motion and improved interaction with the ground. The locomotioncontrol architecture has been proposed to exploit natural leg dynamics in order to improve energy efficiency. Results show that the controller achieves a significant reduction in energy consumption during the leg swing phase thanks to the exploitation of inherent leg dynamics. Added to this, experiments with the real leg prototype show that the combined use of series elasticity and magneto-rheologicaldamping at the knee provide a 20 % reduction in the energy wasted in braking the knee during its extension in the leg stance phase

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

Kinematic primitives for walking and trotting gaits of a quadruped robot with compliant legs

In this work we research the role of body dynamics in the complexity of kinematic patterns in a quadruped robot with compliant legs. Two gait patterns, lateral sequence walk and trot, along with leg length control patterns of different complexity were implemented in a modular, feed-forward locomotion controller. The controller was tested on a small, quadruped robot with compliant, segmented leg design, and led to self-stable and self-stabilizing robot locomotion. In-air stepping and on-ground locomotion leg kinematics were recorded, and the number and shapes of motion primitives accounting for 95% of the variance of kinematic leg data were extracted. This revealed that kinematic patterns resulting from feed-forward control had a lower complexity (in-air stepping, 2 to 3 primitives) than kinematic patterns from on-ground locomotion (4 primitives), although both experiments applied identical motor patterns. The complexity of on-ground kinematic patterns had increased, through ground contact and mechanical entrainment. The complexity of observed kinematic on-ground data matches those reported from level-ground locomotion data of legged animals. Results indicate that a very low complexity of modular, rhythmic, feed-forward motor control is sufficient for level-ground locomotion in combination with passive compliant legged hardware

On the Biomimetic Design of Agile-Robot Legs

The development of functional legged robots has encountered its limits in human-made actuation technology. This paper describes research on the biomimetic design of legs for agile quadrupeds. A biomimetic leg concept that extracts key principles from horse legs which are responsible for the agile and powerful locomotion of these animals is presented. The proposed biomimetic leg model defines the effective leg length, leg kinematics, limb mass distribution, actuator power, and elastic energy recovery as determinants of agile locomotion, and values for these five key elements are given. The transfer of the extracted principles to technological instantiations is analyzed in detail, considering the availability of current materials, structures and actuators. A real leg prototype has been developed following the biomimetic leg concept proposed. The actuation system is based on the hybrid use of series elasticity and magneto-rheological dampers which provides variable compliance for natural motion. From the experimental evaluation of this prototype, conclusions on the current technological barriers to achieve real functional legged robots to walk dynamically in agile locomotion are presented

Thrust control, stabilization and energetics of a quadruped running robot

In order to achieve powered autonomous running robots it is essential to develop efficient actuator systems, especially for generating the radial thrust in the legs. In addition, the control of the radial thrust of the legs can be a simple, effective method for stabilizing the body pitch in a running gait. This paper presents the mechanical systems, models and control strategies employed to generate and control leg thrust in the KOLT quadruped running robot. An analytical model of the electro-pneumatic leg thrusting system is presented and analyzed to evaluate its performance and to facilitate the design of control strategies. Several experiments have been conducted to estimate the energy losses and determine their origins as well as to compute the energetic efficiency of the actuation system. Two thrust control methods are also proposed and tested experimentally. The closed loop method regulates thrust through the control of the hip liftoff speed, a conceptually simple control strategy that stabilizes the body pitch in pronk and trot gaits without the need for central feedback, even on irregular terrain. The open-loop control method regulates the energy added in each hop based on the model of the actuator system. The efficacy of these models and techniques is tested in several planar trot and pronk experiments, and the results are analyzed focusing on the body stabilization, the power consumption and the energetic efficiency. © SAGE Publications 2008 Los Angeles

Empirical validation of a spined sagittal-plane quadrupedal model

We document empirically stable bounding using an actively powered spine on the Inu quadrupedal robot, and propose a reduced-order model to capture the dynamics associated with this additional, actuated spine degree of freedom. This model is sufficiently accurate as to roughly describe the robots mass center trajectory during a bounding limit cycle, thus making it a potential option for low dimensional representations of spine actuation in steady-state legged locomotion