Spring Loaded Inverted Pendulum (SLIP) model is a well-established, simple, descriptive and accurate model to study the dynamics of hopping and running. It can be used as a template to understand and control running robots. To realize SLIP based legged robots with high energy efficiency and control accuracy, critical design decisions are actuation topology and controller, which are coupled problems.  Many of the recent studies concentrate upon comparing the following actuation topologies for SLIP model: series elastic actuation (SEA) and parallel elastic actuation (PEA) along with a variety of control techniques without a profound discussion. Independent from these studies; a recently introduced control method, virtual tuning of damping (VTD) have proven to be superior for SEA-SLIP over other control techniques without discussion of actuation. VTD for PEA-SLIP is not analyzed yet. Which strategy of control and actuation results in better energy efficiency and accuracy in legged robots is still an area of research. This paper combines the studies done in those two design problems and introduce a novel control technique for PEA-SLIP model for legged robots.

In the paper, PEA and SEA configurations of vertically constrained legged hoppers are compared in the sense of energetic efficiency and control accuracy along with template based VTD control strategy. Template model is F-SLIP which extends SLIP model with a constant forcing and virtually tunable damping constant that is introduced previously to apply VTD on SEA legged robots. Previous studies comparing PEA and SEA configurations do not emphasize the control strategies in general or presented ones do not emphasize motion accuracy. Motion is limited to apex to apex hopping. Such a simple motion definition enables us to use approximate analytical maps in control actions which reduces the computational cost. Control accuracy is defined with the error between reached and desired apex. Energetic efficiency is analyzed with cost of transport and energy losses such as electrical, friction and impact losses.

The dynamics of SEA-SLIP and F-SLIP are previously introduced. In the paper, the PEA-SLIP model is presented. Those are anchor models that are the abstractions of real robots but are more detailed than the template. To make realistic simulations, models are extended by including the dynamics of drive-train components including the actuator (electrical motors) and transmission (gearboxes) and batteries. Realistic limits such as torque saturation are applied on the models where corresponding parameters are obtained from the catalogues of manufacturers. After that, an approximate analytical Poincare map is defined from apex to apex in F-SLIP model. This map is used to determine the damping constant to reach the desired energy state. By controlling the forces applied by the actuators in SEA-SLIP and PEA-SLIP, the dynamics of F-SLIP are embedded into both of the higher level models. Control torques are calculated for models including drive-train elements where the effects of gearbox friction and reflected inertias are addressed.

Initially, models are simulated without drive-train elements to make guesses for required output forces. Afterwards, simulations are done for various gearboxes, motors, initial conditions, desired apex values and voltages. As a result, under VTD, best PEA among the simulations achieves 25 times more apex to apex accuracy, 40% higher energy efficiency and 38% higher cost of transport than the best SEA. Trajectories, applied torques and injected power are presented, compared, and discussed for those models. SEA tries to inject energy with lower speeds and higher forces because it needs to act against the spring force. This increases the weight of components included in SEA and electrical losses. An additional degree of freedom in SEA creates errors during the embedding of F-SLIP into SEA and reduces accuracy.


Comparison of Parallel Elastic and Series Elastic Configurations of Vertical Spring Mass Model Controlled With Virtual Tuning of Damping

Division / Sponsors: 
Design Engineering Division and Computers & Information In Engineering Division


Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2020/volume/83907

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