Series Damping Elastic Actuator

**The Detailed Report is attached at the bottom of this page.

My first independent project related to Robotics and Control is "Designing and Simulating a Force-based Impedance control using a Series Damping Elastic Actuator." Using my knowledge earned in RENEU Robotics Lab, and Dynamic Systems and Controls and Advanced Powertrain Systems Control classes, I was able to conduct this project which involves system design, control, and simulation. In my project, I propose a new design of the Series Elastic Actuator (SEA) in order to broaden the application of SEA and improve its performance.

I. Introduction/ Experimental Setup

Although series-elastic actuation has great potential in rehabilitation robotics, there is the tendency toward instability introduced by the purely elastic coupling of the motor and end-point mass. The resulting mechanical oscillator lends itself to instability as the purely elastic spring stores the energy of large and potentially unstable motions, and delivers the energy back into the system. Thus, we present a series damping-elastic actuator, which reduces excessive energy storage of the SEA by featuring a pure damping element in parallel with the elastic element, and in series with the motor and linkage. The following images represent the schematic of our proposed SDEA design.

We can derive the following two equations by conducting a force balance analysis about the motor mass and the load mass.

By following the two equations, we can simulate our SDEA system in MATLAB-Simulink as shown in the following figure:

To control the actuator, we implemented a PID controller with a closed loop torque feedback, as represented in the following figure, where the subsystem block represents the SDEA system model in previous figure:

The purpose of our SDEA is to effectively execute the force control for the rehabilitation robots. Therefore, we designed our control subject, a simple one degree of freedom pendulum which can represent one joint motion. The schematic for our system design is represented below:

Then, we simulated our system using Simulink by conducting a moment balance analysis about the motor mass as follows:

Now, the two systems, SDEA and 1 degree of freedom system, can be combined into one simulink model with impedance control and gravity and inertia compensations as represented in the following figures:

II. Results

The results show that the robot driven by the SDEA is capable of a more stable performance and a wider range of virtual stiffness and reducing the observable robot inertia by compared to the SEA.

In order to see the effects of an damping element, Bz in parallel to the spring in SDEA, we plotted the pole zero plot with different Bz values ranging from 0 to 0.35 Nm/s. A plot of the poles is represented in the following figure:

As shown, the higher Bz values we input, the further the poles of our transfer function moves to the negative side of the real axis on a pole zero plot, and therefore, our system becomes more stable. However, when Bz values are equal to or above 0.35 Nm/s, our system poles begin to lie on the real axis; the damping coefficient starts to dominate our system. This represents the limitations of SDA such as the output of a limited capacity for impact absorption as well as a severe bandwidth limitation, and a poor energy efficiency.

Because impedance control lends itself well to rehabilitation robotics, we tested the improvements that SDEA can offer for two important characteristics of our impedance based control: virtual stiffness and inertia compensation. To test effects on the increase in allowable virtual stiffness, we input to both systems a 45 degree step input, with a virtual damping of 1 N*m/(rad/s), and an inertia compensation of 40%. These parameters are expected to push the system toward instability, and thus represent an approximation of a worst case scenario. Then we iteratively ran the simulation, in order to determine the value of virtual stiffness that caused instability. The results show that the robot driven by the SDEA is capable of a 31% wider range of virtual stiffnesses. Thus, rehabilitation strategies that may not be possible to safely conduct with SEA could be possible under the larger range of safe and stable control we get with SDEA.

ZeroLoad (Fext=0) Position Response of 1 DoF, at a virtual stiffness of 9.0 N*m/rad

At a value of 9.0 N*m/rad, the SEA goes unstable, followed by the SDEA at 11.8 N*m/rad. The results show that the robot driven by the SDEA is capable of a 31% wider range of virtual stiffnesses. Thus, rehabilitation strategies that may not be possible to safely conduct with SEA could be possible under the larger range of safe and stable control we get with SDEA.

In addition to testing the allowable values of virtual stiffness, we also tested the effect on the maximum inertia compensation. The testing conditions consisted of a 45 degree step input, and a virtual stiffness of 8 N*m/rad, and a virtual damping of 1 N*m/(rad/s).

ZeroLoad (Fext=0) Position Response of 1 DoF, at 50% inertia compensation

Under these conditions, the SEAdriven robot exhibits unstable behavior at 47% compensation, and the SDEA counterpart at 63%. Thus, the SDEA is capable of reducing the observable robot inertia by 34% compared to the SEA. This reduction in the apparent inertia of the system is important to potential rehabilitation patients, as they may not be able to produce much strength while performing exercises in the device.

III. Conclusion and Future Works

The larger virtual stiffness expands the use of rehabilitation robots as it allows more various control strategies which require a high virtual stiffness. Also, the larger compensation can decrease the inertia of the rehabilitation robot, and therefore, allow patients to wear and exercise with the robot with much weaker strength. The next step is produce/ construct a mechanical design of a rotary SDEA, and incorporate it into a wearable robot to study the improvements. Also, we are currently working to simulate our SDEA system in a 2 DOF system which is more applicable to rehabilitation robots.