Research Papers

Optimal Stiffness Design for an Exhaustive Parallel Compliance Matrix in Multiactuator Robotic Limbs

[+] Author and Article Information
Nathan M. Cahill

National Science Foundation Fellow
Department of Mechanical Engineering,
Arizona State University,
Tempe, AZ 85281
e-mail: nathan.m.cahill@asu.edu

Thomas Sugar

Department of Mechanical Engineering,
Arizona State University,
Tempe, AZ 85281
e-mail: Thomas.Sugar@asu.edu

Yi Ren

Department of Mechanical Engineering,
Arizona State University,
Tempe, AZ 85281
e-mail: yiren@asu.edu

Kyle Schroeder

SpringActive Inc.,
Tempe, AZ 85281
e-mail: kyle.schroeder@springactive.com

1Corresponding author.

Manuscript received May 9, 2017; final manuscript received February 28, 2018; published online April 26, 2018. Assoc. Editor: James J. Joo.

J. Mechanisms Robotics 10(3), 031014 (Apr 26, 2018) (7 pages) Paper No: JMR-17-1141; doi: 10.1115/1.4039772 History: Received May 09, 2017; Revised February 28, 2018

Comparatively slow growth in energy density of both power storage and generation technologies has placed added emphasis on the need for energy-efficient designs in legged robots. This paper explores the potential of parallel springs in robot limb design. We start by adding what we call the exhaustive parallel compliance matrix (EPCM) to the design. The EPCM is a set of parallel springs, which includes a parallel spring for each joint and a multijoint parallel spring for all possible combinations of the robot's joints. Then, we carefully formulate and compare two performance metrics, which improve various aspects of the system performance. Each performance metric is analyzed and compared, their strengths and weaknesses being rigorously presented. The performance benefits associated with this approach are dramatic. Implementing the spring matrix reduces the sum of square power (SSP) exerted by the actuators by up to 47%, the peak power requirement by almost 40%, the sum of squared current by 55%, and the peak current by 55%. These results were generated using a planar robot limb and a gait trajectory borrowed from biology. We use a fully dynamic model of the robotic system including inertial effects. We also test the design robustness using a perturbation study, which shows that the parallel springs are effective even in the presence of trajectory perturbation.

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Fig. 1

An illustration of the robot-spring model

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Fig. 4

Plot showing perturbed joint angle trajectories

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Fig. 5

Plot showing perturbed force trajectories

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Fig. 2

(a) Joint torques with inertial effects (N·m) and (b) joint velocities (rad/s)

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Fig. 3

Illustration showing the motion of the leg

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Fig. 6

Results of SSP minimization problem

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Fig. 7

Results of SSC minimization problem



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