Control of Planar Spring–Mass Running Through Virtual Tuning of Radial Leg Damping (original) (raw)
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Bioinspiration & Biomimetics, 2013
We proposed three swing leg control policies for spring-mass running robots, inspired by experimental data from our recent collaborative work on ground running birds. Previous investigations suggest that animals may prioritize injury avoidance and/or efficiency as their objective function during running rather than maintaining limit-cycle stability. Therefore, in this study we targeted structural capacity (maximum leg force to avoid damage) and efficiency as the main goals for our control policies, since these objective functions are crucial to reduce motor size and structure weight. Each proposed policy controls the leg angle as a function of time during flight phase such that its objective function during the subsequent stance phase is regulated. The three objective functions that are regulated in the control policies are (i) the leg peak force, (ii) the axial impulse, and (iii) the leg actuator work. It should be noted that each control policy regulates one single objective function. Surprisingly, all three swing leg control policies result in nearly identical subsequent stance phase dynamics. This implies that the implementation of any of the proposed control policies would satisfy both goals (damage avoidance and efficiency) at once. Furthermore, all three control policies require a surprisingly simple leg angle adjustment: leg retraction with constant angular acceleration.
Robust and efficient walking with spring-like legs
Bioinspiration & Biomimetics, 2010
The development of bipedal walking robots is inspired by human walking. A way of implementing walking could be performed by mimicking human leg dynamics. A fundamental model, representing human leg dynamics during walking and running, is the bipedal spring-mass model which is the basis for this paper. The aim of this study is the identification of leg parameters leading to a compromise between robustness and energy efficiency in walking. It is found that, compared to asymmetric walking, symmetric walking with flatter angles of attack reveals such a compromise. With increasing leg stiffness, energy efficiency increases continuously. However, robustness is the maximum at moderate leg stiffness and decreases slightly with increasing stiffness. Hence, an adjustable leg compliance would be preferred, which is adaptable to the environment. If the ground is even, a high leg stiffness leads to energy efficient walking. However, if external perturbations are expected, e.g. when the robot walks on uneven terrain, the leg should be softer and the angle of attack flatter. In the case of underactuated robots with constant physical springs, the leg stiffness should be larger than k = 14 in order to use the most robust gait. Soft legs, however, lack in both robustness and efficiency.
Force control for spring-mass walking and running
2010
We demonstrate in simulation that active force control applied to a passive spring-mass model for walking and running attenuates disturbances, while maintaining the energy economy of a completely passive system during steadystate operation. It is well known that spring-mass models approximate steady-state animal running, but these passive dynamic models are sensitive to disturbances that animals are able to accommodate. Active control can be used to add robustness to spring-mass walking and running, and most existing controllers add a fixed amount of energy to the system based on information from previous strides. Because spring-mass models are schematically similar to force control actuators, it is convenient to combine the two concepts in a single system. We show, in simulation, that the resulting system can attenuate sudden disturbances during a single stance phase by matching its toe force profile to that of the undisturbed spring-mass model.
Bioinspired template-based control of legged locomotion
2018
cient and robust locomotion is a crucial condition for the more extensive use of legged robots in real world applications. In that respect, robots can learn from animals, if the principles underlying locomotion in biological legged systems can be transferred to their artificial counterparts. However, legged locomotion in biological systems is a complex and not fully understood problem. A great progress to simplify understanding locomotion dynamics and control was made by introducing simple models, coined ``templates'', able to represent the overall dynamics of animal (including human) gaits. One of the most recognized models is the spring-loaded inverted pendulum (SLIP) which consists of a point mass atop a massless spring. This model provides a good description of human gaits, such as walking, hopping and running. Despite its high level of abstraction, it supported and inspired the development of successful legged robots and was used as explicit targets for control, over th...
DRS-LIP: Linear Inverted Pendulum Model for Legged Locomotion on Dynamic Rigid Surfaces
2022
Legged robot locomotion on a dynamic rigid surface (i.e., a rigid surface moving in the inertial frame) involves complex full-order dynamics that is high-dimensional, nonlinear, and time-varying. Towards deriving an analytically tractable dynamic model, this study theoretically extends the reduced-order linear inverted pendulum (LIP) model from legged locomotion on a stationary surface to locomotion on a dynamic rigid surface (DRS). The resulting model is herein termed as DRS-LIP. Furthermore, this study introduces an approximate analytical solution of the proposed DRS-LIP that is computationally efficient with high accuracy. To illustrate the practical uses of the analytical results, they are used to develop a hierarchical planning framework that efficiently generates physically feasible trajectories for DRS locomotion. The effectiveness of the proposed theoretical results and motion planner is demonstrated both through simulations and experimentally on a Laikago quadrupedal robot ...
Royal Society Open Science
Biomechanical models with different levels of complexity are of advantage to understand the underlying principles of legged locomotion. Following a minimalistic approach of gradually increasing model complexity based on Template & Anchor concept, in this paper, a spring-loaded inverted pendulum-based walking model is extended by a rigid trunk, hip muscles and reflex control, called nmF (neuromuscular force modulated compliant hip) model. Our control strategy includes leg force feedback to activate hip muscles (originated from the FMCH approach), and a discrete linear quadratic regulator for adapting muscle reflexes. The nmF model demonstrates human-like walking kinematic and dynamic features such as the virtual pendulum (VP) concept, inherited from the FMCH model. Moreover, the robustness against postural perturbations is two times higher in the nmF model compared to the FMCH model and even further increased in the adaptive nmF model. This is due to the intrinsic muscle dynamics and...
Mobile Robotics - Solutions and Challenges - Proceedings of the Twelfth International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines, 2010
The Spring-Loaded Inverted Pendulum (SLIP) model has been established both as a very accurate descriptive tool as well as a good basis for the design and control of running robots. In particular, approximate analytic solutions to the otherwise nonintegrable dynamics of this model provide principled ways in which gait controllers can be built, yielding invaluable insight into their stability properties. However, most existing work on the SLIP model completely disregards the effects of damping, which often cannot be neglected for physical robot platforms. In this paper, we introduce a new approximate analytical solution to the dynamics of this system that also takes into account viscous damping in the leg. We compare both the predictive performance of our approximation as well as the tracking performance of an associated deadbeat gait controller to similar existing methods in the literature and show that it significantly outperforms them in the presence of damping in the leg.
Viscous Damping in Legged Locomotion
2020
Damping likely plays an essential role in legged animal locomotion, but remains an insufficiently understood mechanism. Intrinsic damping muscle forces can potentially add to the joint torque output during unexpected impacts, stabilise movements, convert the system’s energy, and reject unexpected perturbations [1, 2]. Recent legged robots exploit virtual damping as part of a virtual compliance controller [3]: actively produced and sensor-controlled negative actuator work. Virtual damping requires high-frequency force control loops, and precise timing to identify loading conditions during touch-down and takeoff events. Virtual damping systems must feature high-power actuators mechanically and electrically capable of producing negative power, and absorbing negative power peaks. Mechanical damper leg configurations can act instantaneously and without the need for sensing and control feedback, similar to springs [4] (Fig. 1A). Dampers can also share impact loads with leg designs featuri...
Slip running with an articulated robotic leg
2010
SLIP models are generally known as one of the best and simplest abstractions describing the spring-like leg behavior found in human and animal running, and have thus been subject to exhaustive investigation. To exploit these findings in real robots, we utilize an operational space controller that projects the behavior of the SLIP model onto the dynamics of an actual segmented robotic leg. Additionally, we introduce a method to compensate for the energetic losses at the impact collisions, which are not accounted for in the simplified SLIP assumptions. This allows the direct application of existing dead-beat control strategies to arbitrary robotic legs, for which we can show that the collision and compensation effects in the actual leg enlarge the regions of stable running and reduce the minimally required locomotion speed. The necessary joint torque profiles can be generated in large part passively, for example by using high compliance series elastic actuators.
Stable and robust walking with compliant legs
… and Automation (ICRA), …
The implementation of bipedal gaits in legged robots is still a challenge in state-of-the-art engineering. Human gaits could be realized by imitating human leg dynamics where a spring-like leg behavior is found as represented in the bipedal spring-mass model. In this study we explore the gap between walking and running by investigating periodic gait patterns. We found an almost continuous morphing of gait patterns between walking and running. The technical feasibility of this transition is, however, restricted by the duration of swing phase. In practice, this requires an abrupt gait transition between both gaits, while a change of speed is not necessary.