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Research Papers

Design of Series-Elastic Actuators for Dynamic Robots With Articulated Legs

[+] Author and Article Information
Simon Curran, David E. Orin

Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210

Brian T. Knox1

Mechanical Engineering, The Ohio State University, Columbus, OH 43210knox.81@osu.edu

James P. Schmiedeler

Mechanical Engineering, The Ohio State University, Columbus, OH 43210

To simplify the notation, note that $θ̇k(s)$ is used to represent the Laplace transform of $θ̇k(t)$, the angular velocity of the knee.

1

Corresponding author.

J. Mechanisms Robotics 1(1), 011006 (Jul 30, 2008) (9 pages) doi:10.1115/1.2960535 History: Received March 27, 2008; Revised June 25, 2008; Published July 30, 2008

Abstract

A series-elastic actuator (SEA) can provide remarkable performance benefits in a robotic system, allowing the execution of highly dynamic manuevers, such as a jump. While SEAs have been used in numerous robotic systems, no comprehensive understanding of an optimal design exists. This paper presents a new analytical basis for maximizing an SEA thrust performance for jumping from rest with an articulated leg. The analytical SEA model is validated with simulation and experimental results from a prototype leg. An SEA decouples the dynamic limitations of a dc motor actuator from the joint, allowing larger lift-off velocities than with a directly driven joint. A detailed analysis of the complex dynamic response of an SEA during the thrust phase leads to a new maximum impulse criterion, where motor speed is approximately half the no-load speed at the moment of peak motor torque. The analytical model and this proposed criterion are used to develop a simple equation for selecting SEA design parameters. Lastly, a novel unidirectional SEA design is presented that allows for accurate positioning of the leg during flight.

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Figures

Figure 1

Prototype leg on its vertical constraint rails

Figure 2

Simplified kinematic and dynamic model of the prototype leg

Figure 3

Comparison of body lift-off velocities ẏb for a DDA at both joints and an SEA at the knee, as computed from Eqs. 16,18, respectively. Typical spring torques at lift-off measured in the prototype leg are around 20Nm.

Figure 4

Comparison of body lift-off velocities ẏb for a DDA at both joints and an SEA at the knee, determined from the dynamic simulations. Both the series-elastic simulator and the experimental data obtain higher lift-off velocities than a DDA.

Figure 5

For a range of gear ratios, the jump height is maximal when Δωk is close to its minimum

Figure 6

For a range of spring constants, the jump height is maximal when Δωk is close to its minimum

Figure 7

For a range of foot positions, the jump height is maximal near where Δωk is minimal (xf≈−0.04m). Δωk is fit with a piecewise linear trendline for clarity.

Figure 8

A contour plot of simulated jump heights across a range of spring constants and gear ratios. The predicted Ks from Eq. 26 (solid line) yields a spring and gear ratio combination that produces a jump within 5% of the maximum jump height for either parameter.

Figure 9

CAD rendering of the USEA design used in the prototype leg

Figure 10

The geometric foot position error from the calibration point is shown for the last 100ms of flight before touchdown. The USEA case is represented with a thick line, and the case with the USEA removed is represented with a thin line.

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