Understanding preferred leg stiffness and layered control strategies for locomotion

Despite advancement in the field of robotics, current legged robots still cannot achieve the kind of locomotion stability animals and humans have. In order to develop legged robots with greater stability, we need to better understand general locomotion dynamics and control principles. Here we demonstrate that a mathematical modeling approach could greatly enable the discovery and understanding of general locomotion principles. ^ It is found that animal leg stiffness when scaled by its weight and leg length falls in a narrow region between 7 and 27. Rarely in biology does such a universal preference exist. It is not known completely why this preference exists. Here, through simulation of the simple actuated-SLIP model, we show that the biological relative leg stiffness corresponds to the theoretical minimum of mechanical cost of transport. This strongly implies that animals choose leg stiffness in this region to reduce energetic cost. In addition, it is found that the stability of center-of-mass motion is also optimal when biological relative leg stiffness values are selected for actuated-SLIP. Therefore, motion stability could be another reason why animals choose this particular relative leg stiffness range. ^ We then extended actuated-SLIP by including realistic trunk pitching dynamics. At first, to form the Trunk Spring-Loaded Inverted Pendulum (Trunk-SLIP) model, the point mass of actuated-SLIP is replaced by a rigid body trunk while the leg remains massless and springy. It is found that exproprioceptive feedback during the flight phase is essential to the overall motion stability including trunk pitching. Either proprioceptive or exproprioceptive feedback during stance could generate stable running motion provided that exproprioceptive feedback is used during flight. When both kinds of feedback are used during stance, the overall stability is improved. However, stability with respect to speed perturbations remains limited. ^ Built upon Trunk-SLIP, we develop a model called extended Trunk-SLIP with trunk and leg masses. We then develop a hierarchical control strategy where different layers of control are added and tuned. When each layer is added, the overall motion stability is improved. This layer by layer strategy is simple in nature and allows quick controller design and tuning as only a limited number of control parameters needs to be added and tuned at each step. In the end, we propose a future control layer where the commanded speed is controlled to achieve a higher level target such as might be needed during smooth walking to running transitions. ^ In summary, we show here that the simple actuated-SLIP model is able to predict animal center-of-mass translation stability and overall mechanical cost of transport. More advanced models are then developed based upon actuated-SLIP. With a simple layer by layer control strategy, robust running motion can be discovered. Overall, this knowledge could help better understand locomotion dynamics in general. In addition, the developed control strategy could, in principle be applied to future hip based legged robot design

Advancement of Legged Locomotion Models by Including Nonlinear Damping

Accurately predicting human locomotion has been a goal of various mathematical models. Early canonical models of locomotion were developed to predict the basic features of ground reaction forces (GRF). More recently, modified hip actuated and leg damped locomotion models have been developed to better predict the stability and robustness of human and animal locomotion. Such improvements have resulted in the loss of the characteristic GRF predicted by earlier models. Historically, GRF are among the most common measures to experimentally study human locomotion. Thus, it is important to develop new mathematical models that predict both accurate stability of motion, as well as GRF. We hypothesized that by replacing linear damping models with nonlinear leg damping, we can better replicate human GRF. We then derived the equations of motion for this new type of locomotion model and analyzed the system behavior. GRF from the modified model were compared with published human GRF data. Stability and robustness were also studied through the use of numerical analysis to make sure that the ability to predict stable motion was not compromised. We found that the modified model with nonlinear leg damping provides a significantly better prediction of GRF, especially in the early part of stance. Further, the model\u27s ability to predict the stability of locomotion is similar to the actuated model with linear damping. As a result, we expect that stable actuated models of locomotion can generally be combined with nonlinear leg damping models to better predict human locomotion GRF and stability