Abstract

Maintaining stability in jumping robots remains a challenge due to their hybrid dynamics. Despite recent advances, existing research lacks a clear definition and comprehensive criteria for jumping stability. To address this gap, the definition of a post-landing stable state is presented and used to formulate state-space partitions, or post-landing stable state basins, that serve as general stability criteria for flight-to-stance tasks. A hybrid-phase approach is applied to solve the flight and stance phases as separate sub-problems through analytical and optimization-based methods, subject to nonlinear system dynamics, environmental contact constraints, and task requirements. Post-landing stable state basins are constructed for a monoped jumping robot, Salto-1P, for two tasks, targeted jumping and cat-like righting, to demonstrate the use of the basins as comprehensive criteria for jumping stability. The stance-phase sub-problem solution, or landing state basin, is analyzed to determine the effect of and identify safe sets of landing state variables for balance after landing. This basin is also validated against simulated controller-specific basins of attraction. The basins obtained reveal the relationships between stability, task requirements, initial state variables such as body orientation and velocity, and landing state variables such as body angle at landing.

References

1.
Wieber
,
P.-B.
,
Tedrake
,
R.
, and
Kuindersma
,
S.
,
2016
, “Modeling and Control of Legged Robots,”
Springer Handbook of Robotics
,
B.
Siciliano
, and
O.
Khatib
, eds.,
Springer International Publishing
,
Cham
, pp.
1203
1234
.
2.
Burdick
,
J.
, and
Fiorini
,
P.
,
2003
, “
Minimalist Jumping Robots for Celestial Exploration
,”
Int. J. Rob. Res.
,
22
(
7–8
), pp.
653
674
.
3.
Stoeter
,
S. A.
,
Rybski
,
P. E.
,
Gini
,
M.
, and
Papanikolopoulos
,
N.
,
2002
, “
Autonomous Stair-Hopping With Scout Robots
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
,
Lausanne, Switzerland
,
Sept. 30–Oct. 4
, Vol. 1, pp.
721
726
.
4.
Zhao
,
J.
,
Xu
,
J.
,
Gao
,
B.
,
Xi
,
N.
,
Cintrón
,
F. J.
,
Mutka
,
M. W.
, and
Xiao
,
L.
,
2013
, “
MSU Jumper: A Single-Motor-Actuated Miniature Steerable Jumping Robot
,”
IEEE Trans. Rob.
,
29
(
3
), pp.
602
614
.
5.
Kovač
,
M.
,
Wassim-Hraiz, Fauria
,
O.
,
Zufferey
,
J.-C.
, and
Floreano
,
D.
,
2011
, “
The EPFL Jumpglider: A Hybrid Jumping and Gliding Robot With Rigid or Folding Wings
,”
2011 IEEE International Conference on Robotics and Biomimetics
,
Karon Beach, Thailand
,
Dec. 7–11
, pp.
1503
1508
.
6.
Katz
,
B.
,
Di Carlo
,
J.
, and
Kim
,
S.
,
2019
, “
Mini Cheetah: A Platform for Pushing the Limits of Dynamic Quadruped Control
,”
2019 International Conference on Robotics and Automation (ICRA)
,
Montreal, Canada
,
May 20–24
, IEEE Press, pp.
6295
6301
.
7.
Kurtz
,
V.
,
Li
,
H.
,
Wensing
,
P. M.
, and
Lin
,
H.
,
2022
, “
Mini Cheetah, the Falling Cat: A Case Study in Machine Learning and Trajectory Optimization for Robot Acrobatics
,”
2022 International Conference on Robotics and Automation (ICRA)
,
Philadelphia, PA
,
May 23–27
, IEEE Press, pp.
4635
4641
.
8.
Goswami
,
D.
, and
Vadakkepat
,
P.
,
2009
, “
Planar Bipedal Jumping Gaits With Stable Landing
,”
IEEE Trans. Rob.
,
25
(
5
), pp.
1030
1046
.
9.
Yim
,
J. K.
,
Singh
,
B. R. P.
,
Wang
,
E. K.
,
Featherstone
,
R.
, and
Fearing
,
R. S.
,
2020
, “
Precision Robotic Leaping and Landing Using Stance-Phase Balance
,”
IEEE Rob. Autom. Lett.
,
5
(
2
), pp.
3422
3429
.
10.
Featherstone
,
R.
,
2016
, “
Quantitative Measures of a Robot's Physical Ability to Balance
,”
Int. J. Rob. Res.
,
35
(
14
), pp.
1681
1696
.
11.
Peng
,
W. Z.
,
Mummolo
,
C.
, and
Kim
,
J. H.
,
2020
, “
Stability Criteria of Balanced and Steppable Unbalanced States for Full-Body Systems With Implications in Robotic and Human Gait
,”
IEEE International Conference on Robotics and Automation
,
Paris, France
,
May 31–Aug. 31
, pp.
9789
9795
.
12.
Peng
,
W. Z.
,
Song
,
H.
, and
Kim
,
J. H.
,
2021
, “
Stability Region-Based Analysis of Walking and Push Recovery Control
,”
ASME J. Mech. Rob.
,
13
(
3
), p.
031005
.
13.
Peng
,
W. Z.
,
Mummolo
,
C.
,
Song
,
H.
, and
Kim
,
J. H.
,
2022
, “
Whole-Body Balance Stability Regions for Multi-level Momentum and Stepping Strategies
,”
Mech. Mach. Theory
,
174
, p.
104880
.
14.
Song
,
H.
,
Peng
,
W. Z.
, and
Kim
,
J. H.
,
2024
, “
Partition-Aware Stability Control for Humanoid Robot Push Recovery With Whole-Body Capturability
,”
ASME J. Mech. Rob.
,
16
(
1
), p.
011005
.
15.
Zaytsev
,
P.
,
Wolfslag
,
W.
, and
Ruina
,
A.
,
2018
, “
The Boundaries of Walking Stability: Viability and Controllability of Simple Models
,”
IEEE Trans. Rob.
,
34
(
2
), pp.
336
352
.
16.
Koolen
,
T.
,
De Boer
,
T.
,
Rebula
,
J.
,
Goswami
,
A.
, and
Pratt
,
J.
,
2012
, “
Capturability-Based Analysis and Control of Legged Locomotion, Part 1: Theory and Application to Three Simple Gait Models
,”
Int. J. Rob. Res.
,
31
(
9
), pp.
1094
1113
.
17.
Wensing
,
P. M.
,
Posa
,
M.
,
Hu
,
Y.
,
Escande
,
A.
,
Mansard
,
N.
, and
Del Prete
,
A.
,
2024
, “
Optimization-Based Control for Dynamic Legged Robots
,”
IEEE Trans. Rob.
,
40
, pp.
43
63
.
18.
Haldane
,
D. W.
,
Plecnik
,
M. M.
,
Yim
,
J. K.
, and
Fearing
,
R. S.
,
2016
, “
Robotic Vertical Jumping Agility Via Series-Elastic Power Modulation
,”
Sci. Rob.
,
1
(
1
), p.
eaag2048
.
19.
Gill
,
P. E.
,
Murray
,
W.
, and
Saunders
,
M. A.
,
2002
, “
SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
,”
SIAM J. Optim.
,
12
(
4
), pp.
979
1006
.
20.
Kelly
,
M.
,
2017
, “
An Introduction to Trajectory Optimization: How to Do Your Own Direct Collocation
,”
SIAM Rev.
,
59
(
4
), pp.
849
904
.
You do not currently have access to this content.