Modeling posture-dependent leg actuation in sagittal plane locomotion

Abstract

The spring loaded inverted pendulum template has been shown to accurately model the steady locomotion dynamics of a variety of running animals, and has served as the inspiration for an entire class of dynamic running robots. While the template models the leg dynamics by an energy-conserving spring, insects and animals have structures that dissipate, store and produce energy during a stance phase. Recent investigations into the spring-like properties of limbs, as well as animal response to drop-step perturbations, suggest that animals use their legs to manage energy storage and dissipation, and that this management is important for gait stability. In this paper, we extend our previous analysis of control of the spring loaded inverted pendulum template via changes in the leg touch-down angle to include energy variations during the stance phase. Energy variations are incorporated through leg actuation that varies the force-free leg length during the stance phase, yet maintains qualitatively correct force and velocity profiles. In contrast to the partially asymptotically stable gaits identified in previous analyses, incorporating energy and leg angle variations in this manner produces complete asymptotic stability. Drop-step perturbation simulations reveal that the control strategy is rather robust, with gaits recovering from drops of up to 30% of the nominal hip height.

Birds achieve high robustness in uneven terrain through active control of landing conditions

“…A SLIP model is not sufficient to model this behaviour; it requires an actuated dynamic template. Actuated SLIP models, including either torsional 'hip' or linear 'leg' actuation, can improve stability and robustness in unsteady locomotion (Schmitt and Clark, 2009;Seipel and Holmes, 2007). Future work should test whether our data could be modelled well using a modified SLIP model with a linear leg actuator, and with work output dependent on  TD .…”

“…Recent studies have used two main approaches to this topic: (1) theoretical analysis of dynamic stability characteristics, focusing on simplified models of body dynamics, often referred to as 'templates' (e.g. Full et al, 2002;Geyer et al, 2005;McGeer, 1990;Schmitt and Clark, 2009;Seipel and Holmes, 2007;Seipel et al, 2004;Seyfarth et al, 2003); and (2) experiments investigating how animals respond to specific terrain disturbances Ferris et al, 1998;Grimmer et al, 2008;Jindrich and Full, 2002;Marigold and Patla, 2005;Moritz and Farley, 2003;Sponberg and Full, 2008;Clark and Higham, 2011). Experimental approaches allow comparison of animal behaviour with model predictions, and can help identify whether proposed dynamic models adequately represent the neuro-mechanical control strategies used by animals.…”

“…. Alternative dynamic templates that include actuation have been proposed (Schmitt and Clark, 2009;Seipel and Holmes, 2007), but little experimental evidence exists to support one alternative template over another. Discovery of dynamic templates for unsteady locomotion would provide insights into mechanisms for robust stability in varied terrain, and could inspire novel control methods and mechanical designs for prosthetics and legged robots (Andrews et al, 2011;Grizzle et al, 2009).…”

Running over unknown rough terrain with a one-legged planar robot

“…There are two different versions of this control law, as described in [13] and [20]. Version one of this control law is given by…”

Two-element control for the active SLIP model

“…In [15], the authors modify the SLIP with a clock based torque at the hip, and then study its stability properties. More recently, the consequences and possible applications of adding a leg actuator in series with the spring has been investigated in [16], [17], and [18]. In [16], the authors consider energy variation during stance to produce asymptotically stable gaits, while [17] focus on a control action for actuator displacement that allows for an analytic solution to the stance phase equations.…”