0
Research Papers

Kinematic Design of an Underactuated Robot Leg for Passive Terrain Adaptability and Stability

[+] Author and Article Information
Oren Y. Kanner

e-mail: oren.kanner@yale.edu

Aaron M. Dollar

Assistant Professor
Mem. ASME
e-mail: aaron.dollar@yale.edu
Department of Mechanical Engineering,
Yale University,
New Haven, CT 06511

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received August 9, 2012; final manuscript received January 25, 2013; published online June 10, 2013. Assoc. Editor: Philippe Wenger.

J. Mechanisms Robotics 5(3), 031006 (Jun 24, 2013) (9 pages) Paper No: JMR-12-1115; doi: 10.1115/1.4024238 History: Received August 09, 2012; Revised January 25, 2013

This paper investigates how the passive adaptability of an underactuated robot leg to uneven terrain is affected by variations in design parameters. In particular, the joint torque coupling ratio, segment length ratio, and rest angles are varied to determine configurations that allow for maximum terrain roughness adaptability while minimizing the transmission of disturbance forces to the body. In addition, a series of alternate leg actuation configurations are considered. The results show that a proximal/distal joint torque coupling ratio of 2 with an inverted distal joint, a proximal/distal leg length ratio of 1.25, and an initial proximal joint angle of −53 deg maximize the terrain variability over which the robot can remain stable by exerting a near-constant vertical reaction force while minimizing lateral force and moment disturbances. In addition, the spring stiffness ratio allows for a tradeoff to be made between the different performance metrics. Finally, the robot's stability with respect to its posture is discussed.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

(a) Basic robot concept showing alternating tetrapod gait and (b) free-body diagram of an adaptive planar robot standing on uneven terrain. The underactuated leg mechanism allows the robot to be stable across a wide range of ground heights without the need to control the leg force directly.

Grahic Jump Location
Fig. 2

Diagram of coupled leg-pair actuation process

Grahic Jump Location
Fig. 3

Diagram of a 2-DOF underactuated leg showing its actuation motion. Note the single tendon driving both joints, which is rigidly attached to the distal joint pulley and couples both joints with a fixed torque ratio.

Grahic Jump Location
Fig. 7

Representative robot legs with τ1 > 0 and τ2 < 0 and either (a) θ1,0 < 0 or (b) θ1,0 > 0

Grahic Jump Location
Fig. 8

Representative “push-up” robot leg

Grahic Jump Location
Fig. 6

Representative robot legs with τ1 < 0 and τ3 > 0 and either (a) θ1,0 < 0 or (b) θ1,0 > 0

Grahic Jump Location
Fig. 5

Representative robot legs with τ1 > 0 and τ2 > 0 and either (a) θ1,0 < 0 or (b) θ1,0 > 0

Grahic Jump Location
Fig. 9

Comparison of vertical reaction force profiles for a number of different leg designs. Note the change in the overall length of the profiles as well as in their shapes (longer/flatter is better). Each column differs in terms of RL (link length ratio), while each row differs in terms of θ1,0 (initial joint angle). For each subplot, the force profiles are shown for RT (joint torque coupling ratio) equal to −2, 1, and 2.

Grahic Jump Location
Fig. 10

Comparison of horizontal reaction force profiles for a number of different leg designs. Note the change in the overall length of the profiles as well as in their shapes (longer/centered on zero is better). Each column differs in terms of RL (link length ratio), while each row differs in terms of θ1,0 (initial joint angle). For each subplot, the force profiles are shown for RT (joint torque coupling ratio) equal to −2, 1, and 2.

Grahic Jump Location
Fig. 14

Contour plots of the three performance metrics, ymax, CV(Fy), and avg(|Fx|/|Fy|) for Rk = 10 (RL = 0.5 and RL = 1.25). The marker on each subplot represents a configuration that balances all three metrics. Note the performance difference as compared to the Rk = 1 designs, especially with regards to the balanced performance location and lack thereof for RT < 0.

Grahic Jump Location
Fig. 16

Propulsion concept that decouples stance and forward motion. (a) Schematic of propulsion track and the four phases of gait that each leg set (which are 180 deg out of phase) passes through as it cycles and (b) a schematic side view of the legged robot at an instance in time during gait.

Grahic Jump Location
Fig. 4

Representative 2-DOF underactuated robot leg with parameters labeled. Note the inset coordinate frame illustration and definition of θ2 relative to the proximal link.

Grahic Jump Location
Fig. 11

Contour plots of the three performance metrics, ymax, CV(Fy), and avg(|Fx|/|Fy|) for three separate values of RL, 0.5, 1.0, and 1.25 (top to bottom). Note the change in behavior as RL increases. The marker on each row of subplots represents a configuration that balances all three metrics. In all plots, darker regions are preferable.

Grahic Jump Location
Fig. 12

(a) Diagram of balanced leg design for Rk = 1 and (b) reaction force profiles normalized to the tendon tension. On the top, note the normalized dimensions of the leg and the reaction force vectors. On the bottom, note that Fy is relatively smooth across the entire range of ground heights and is almost always substantially larger than Fx.

Grahic Jump Location
Fig. 13

Diagram of adaptive legged robot standing on rough terrain with approximate reaction force vectors (derived from balanced configuration) drawn and labeled. The ground heights are 0.3 on the right and 1.3 on the left.

Grahic Jump Location
Fig. 15

Representative robot configurations with NESM shown for (a) positive distal leg design and (b) negative distal leg design with equivalent ground heights

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In