Lateral stability of the spring-mass hopper suggests a two-step control strategy for running (original) (raw)
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BIPED HOPPING CONTROL BAzSED ON SPRING LOADED INVERTED PENDULUM MODEL
International Journal of Humanoid Robotics, 2010
Human running can be stabilized in a wide range of speeds by automatically adjusting 21 muscular properties of leg and torso. It is known that fast locomotion dynamics can be approximated by a spring loaded inverted pendulum (SLIP) system, in which leg is 23 replaced by a single spring connecting body mass to ground. Taking advantage of the inherent stability of SLIP model, a hybrid control strategy is developed that guarantees 25 a stable biped locomotion in sagittal plane. In the presented approach, nonlinear control methods are applied to synchronize the biped dynamics and the spring-mass dynamics.
A Simply Stabilized Running Model
SIAM Journal on Applied Dynamical Systems, 2003
The spring-loaded inverted pendulum (SLIP), or monopedal hopper, is an archetypal model for running in numerous animal species. Although locomotion is generally considered a complex task requiring sophisticated control strategies to account for coordination and stability, we show that stable gaits can be found in the SLIP with both linear and "air" springs, controlled by a simple fixed-leg reset policy. We first derive touchdown-to-touchdown Poincaré maps under the common assumption of negligible gravitational effects during the stance phase. We subsequently include and assess these effects and briefly consider coupling to pitching motions. We investigate the domains of attraction of symmetric periodic gaits and bifurcations from the branches of stable gaits in terms of nondimensional parameters.
Spring-mass running: simple approximate solution and application to gait stability
2005
The planar spring-mass model is frequently used to describe bouncing gaits (running,hopping,trotting,galloping) in animal and human locomotion and robotics. Although this model represents a rather simple mechanical system,an analytical solution predicting the center of mass trajectory during stance remains open. We derive an approximate solution in elementary functions assuming a small angular sweep and a small spring compression during stance.
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.
BIPED HOPPING CONTROL BASED ON SPRING LOADED INVERTED PENDULUM MODEL
Int. J. Human. …, 2010
Human running can be stabilized in a wide range of speeds by automatically adjusting muscular properties of leg and torso. It is known that fast locomotion dynamics can be approximated by a spring loaded inverted pendulum (SLIP) system, in which leg is replaced by a single spring connecting body mass to ground. Taking advantage of the inherent stability of SLIP model, a hybrid control strategy is developed that guarantees a stable biped locomotion in sagittal plane. In the presented approach, nonlinear control methods are applied to synchronize the biped dynamics and the spring-mass dynamics. As the biped center of mass follows the mass of the mass-spring model, the whole biped performs a stable locomotion corresponding to SLIP model. Simulations are done to obtain a repeatable hopping for a three-link underactuated biped model. Results show that periodic hopping gaits can be stabilized, and the presented control strategy provides feasible gait trajectories for stance and swing phases.
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.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2010
In this paper, we analyze self-stability properties of planar running with a dissipative spring-mass model driven by torque actuation at the hip. We first show that a two-dimensional, approximate analytic return map for uncontrolled locomotion with this system under a fixed touchdown leg angle policy and an open-loop ramp torque profile exhibits only marginal self-stability that does not always persist for the exact system. We then propose a per-stride feedback strategy for the hip torque that explicitly compensates for damping losses, reducing the return map to a single dimension and substantially improving the robust stability of fixed points. Subsequent presentation of simulation evidence establishes that the predictions of this approximate model are consistent with the behavior of the exact plant model. We illustrate the relevance and utility of our model both through the qualitative correspondence of its predictions to biological data as well as its use in the design of a task-level running controller.
Non-linear robust control for inverted-pendulum 2D walking
2015 IEEE International Conference on Robotics and Automation (ICRA), 2015
We present an approach to high-level control for bipedal walking exemplified with a 2D point-mass inextensiblelegs inverted-pendulum model. Balance control authority here is only from step position and trailing-leg push-off, both of which are bounded to reflect actuator limits. The controller is defined implicitly as the solution of an optimization problem. The optimization robustly avoids falling for given bounded disturbances and errors and, given that, minimizes the number of steps to reach a given target speed. The optimization can be computed in advance and stored for interpolated real-time use online. The general form of the resulting optimized controller suggests a few simple principles for regulating walking speed: 1) The robot should take bigger steps when speeding up and should also take bigger steps when slowing down 2) push-off is useful for regulating small changes in speed, but it is fully saturated or inactive for larger changes in speed. While the numerically optimized model is simple, the approach should be applicable to, and we plan to use it for, control of bipedal robots in 3D with many degrees of freedom.
The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric Hopper
IEEE Transactions on Automatic Control, 2009
A hybrid controller that induces provably stable running gaits on an Asymmetric Spring Loaded Inverted Pendulum (ASLIP) is developed. The controller acts on two levels. On the first level, continuous within-stride control asymptotically imposes a (virtual) holonomic constraint corresponding to a desired torso posture, and creates an invariant surface on which the two-degree-of-freedom restriction dynamics of the closed-loop system (i.e., the hybrid zero dynamics) is diffeomorphic to the center of mass dynamics of a Spring Loaded Inverted Pendulum (SLIP). On the second level, event-based control stabilizes the closed-loop hybrid system along a periodic orbit of the SLIP dynamics. The controller's performance is discussed through comparison with a second control law that creates a one-degreeof-freedom non-compliant hybrid zero dynamics. Both controllers induce identical steady-state behaviors (i.e. periodic solutions). Under transient conditions, however, the controller inducing a compliant hybrid zero dynamics based on the SLIP accommodates significantly larger disturbances, with less actuator effort, and without violation of the unilateral ground force constraints.
Control of Planar Spring–Mass Running Through Virtual Tuning of Radial Leg Damping
IEEE Transactions on Robotics, 2018
Existing research on dynamically capable legged robots, particularly those based on spring-mass models, generally considers improving in isolation either the stability and control accuracy on the rough terrain, or the energetic efficiency in steady state. In this paper, we propose a new method to address both, based on the hierarchical embedding of a simple spring-loaded inverted pendulum (SLIP) template model with a tunable radial damping coefficient into a realistic leg structure with series-elastic actuation. Our approach allows using the entire stance phase to inject/remove energy both for transient steps and in steady state, decreasing the maximum necessary actuator power while eliminating wasteful sources of the negative work. In doing so, we preserve the validity of the existing analytic approximations to the underlying SLIP model, propose improvements to increase the predictive accuracy, and construct accurate, model-based controllers that use the tunable damping coefficient of the template model. We provide extensive comparative simulations to establish the energy and power efficiency advantages of our approach, together with the accuracy of model-based gait control methods.