Slippage Down on Rolling Mobile Robots While Overcoming Inclined Obstacles

Jesús M. GARCÍA; Franklyn G. DUARTE

doi:10.2478/ama-2025-0065

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Slippage Down on Rolling Mobile Robots While Overcoming Inclined Obstacles

Acta Mechanica et Automatica

Volume 19 (2025): Issue 4 (December 2025)

By: Jesús M. GARCÍA and Franklyn G. DUARTE

Open Access

|Dec 2025

Figures & Tables

Lázaro robot showing dimensions and *X_c Y_c Z_c* frame a) Axono metric view; b) Side view

Tab. 1.

Dimensional parameters of Lázaro robot

Parameter	Magnitude
*x_f*	209.0 mm
*x_r*	191.0 mm
*x_t*	400.0 mm
*y_t*	398.0 mm
a₁	420.0 mm
d_2c	-282.5 mm

Geometric parameters used to characterize the obstacle

Forces at the wheel-ground contact point: a) robot wheel; b) wheel at the end effector

Direct angles of the maximum slope on Surface s and on the ***X_C Y_C*** plane

Results of simulations to estimate ***δ_n***

Robot overcoming obstacle with two wheels on each surface

Robot overcoming obstacle supported by 2 wheels and the end effector

Simulations to validate Is with the robot touching the ground with 4 wheels

Results corresponding to Test "a" (Fig. 9) with F_5z=0 N

Results corresponding to Test "d" (Fig. 9) with F_5z=15 N

Tab. 2.

Statistical analysis of simulation results to validate I_s Test

Test	F₅ (N)	F_s1			F_s2			μ₁			μ₂
Test	F₅ (N)	$\bar{μ} (N)$	σ (N)	MAPE (%)	$\bar{μ} (N)$	σ (N)	MAPE (%)	$\bar{μ}$	σ	MAPE (%)	$\bar{μ}$	σ	MAPE (%)
a	0	-2.01	4.61	1.99	1.68	6.22	1.19	0.00	0.01	0.80	-0.01	0.01	3.42
	15	-1.98	4.47	2.13	1.90	4.71	1.43	0.00	0.01	1.57	0.00	0.01	2.32
	30	-2.04	4.57	2.41	2.00	4.45	1.60	0.02	0.01	5.83	0.00	0.01	0.72
	45	-1.38	4.54	1.79	1.18	5.00	1.03	0.05	0.01	17.25	0.01	0.05	0.24
b	0	1.45	4.52	1.00	-1.95	4.63	2.02	0.00	0.00	0.41	0.00	0.01	1.08
	15	0.27	5.33	0.15	-0.66	5.79	0.75	0.00	0.03	2.25	0.00	0.04	4.53
	30	-1.75	5.52	1.47	1.45	6.11	1.73	0.00	0.03	0.37	-0.01	0.06	9.85
	45	-2.08	4.20	1.85	1.74	4.13	2.39	0.02	0.02	8.24	0.01	0.04	5.80
c	0	-7.54	7.56	5.16	7.09	6.31	7.50	0.00	0.04	2.27	-0.02	0.03	8.75
	15	-8.01	8.75	5.22	7.21	6.00	10.13	-0.01	0.05	3.21	-0.03	0.04	9.89
	30	-7.30	8.07	4.57	6.63	6.09	13.01	-0.01	0.05	6.60	-0.03	0.05	9.99
d	0	4.16	3.46	4.31	-4.47	2.88	3.10	0.01	0.01	3.56	-0.01	0.01	3.69
	15	3.80	3.61	3.61	-4.24	2.98	3.53	0.01	0.01	2.80	-0.01	0.01	3.72
	30	3.47	3.80	2.99	-4.03	3.90	4.25	0.01	0.01	2.15	-0.01	0.01	3.53
	45	3.35	4.25	2.71	-4.04	5.14	5.80	0.00	0.01	1.22	-0.01	0.01	3.93
e	0	-9.04	1.77	6.01	8.61	1.94	10.52	-0.01	0.02	4.50	0.05	0.01	5.44
	15	-9.13	1.78	6.44	9.03	1.50	11.73	-0.01	0.01	3.82	0.05	0.01	8.88
	30	-7.57	7.62	5.88	7.48	4.07	9.86	-0.02	0.06	24.78	0.04	0.01	15.52
	45	-8.15	2.08	6.77	8.14	2.58	11.61	0.00	0.01	0.45	0.04	0.06	17.69
f	0	3.35	4.66	3.24	-3.90	4.21	2.82	0.02	0.01	15.82	-0.02	0.03	6.28
	15	3.99	6.81	3.49	-4.48	6.66	3.95	0.02	0.01	14.91	-0.02	0.06	8.35
	30	1.32	5.69	0.99	-2.29	6.58	2.75	-0.02	0.04	12.12	-0.02	0.02	8.81
	45	0.77	5.85	0.53	-1.71	5.75	2.76	-0.02	0.03	10.13	-0.02	0.03	7.65

Results corresponding to Test "f" (Fig. 9) with F_5z=45 N

Simulations to validate *I_s* with the robot touching the ground at three points

Results corresponding to Test "b" (see Fig. 13)

Tab. 3.

Statistical analysis of the simulations when the robot touches the ground at 3 points

Test	F_s1			F_s2			μ₁			μ₂
Test	$\bar{μ} (N)$	σ (N)	MAPE (%)	$\bar{μ} (N)$	σ (N)	MAPE (%)	$\bar{μ}$	σ	MAPE (%)	$\bar{μ}$	σ	MAPE (%)
a	0.15	4.10	0.06	-	-	-	0.01	0.04	0.98	-	-	-
b	-	-	-	0.21	1.53	0.17	-	-	-	0.01	0.05	1.53
c	-0.21	1.20	0.16	-	-	-	0.01	0.04	0.13	-	-	-
d	-	-	-	-0.20	1.23	0.15	-	-	-	0.00	0.04	0.84
e	0.03	2.10	0.02	-	-	-	0.00	0.04	0.46	-	-	-
f	-	-	-	-0.58	1.84	0.44	-	-	-	0.01	0.05	1.67

Tab. 4.

Geometry of obstacles and static friction coefficients used

Simulation	Description	ϕ_s1 (°)	α_s1 (°)	ϕ_s2 (°)	α_s2 (°)	γ_b1 (°)	μ_s1	μ_s2
A	Frontal ascent	-5.00	0.00	-9.67	-2.58	74.94	1.0	0.2
B	Lateral descent	7.71	0.00	7.50	-4.33	150.22	0.4	0.4
C	Lateral trench	0.00	10.00	0.00	10.00	25.34	0.4	0.4

Analysis of stages for overcoming obstacles until slipping (Simulation A)

Analysis of stages for overcoming obstacles until slipping (Simulation B)

Tests conducted with the Lázaro robot to validate *I_s*

Results of the tests conducted with the Lázaro robot to validate *I_s*

References

Authors

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Articles in this issue

DOI: https://doi.org/10.2478/ama-2025-0065 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088

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Language: English

Page range: 568 - 584

Submitted on: Jan 27, 2025

Accepted on: Sep 28, 2025

Published on: Dec 19, 2025

Published by: Bialystok University of Technology

In partnership with: Paradigm Publishing Services

Keywords:

friction force,

slippage,

slip index,

instantaneous friction coefficients,

navigability,

overcoming obstacles

Related subjects:

Engineering,

Mechanical engineering,

Mechanics,

Bioengineering and biomedical engineering,

Biomechanics,

Civil engineering,

Environmental engineering

© 2025 Jesús M. GARCÍA, Franklyn G. DUARTE, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 19 (2025): Issue 4 (December 2025)

Slippage Down on Rolling Mobile Robots While Overcoming Inclined Obstacles

Figures & Tables

Fig. 1.

Fig. 2.

Tab. 1.

Fig. 3.

Fig. 4.

Fig. 5.

Fig. 6.

Fig. 7.

Fig. 8.

Fig. 9.

Fig. 10.

Fig. 11.

Tab. 2.

Fig. 12.

Fig. 13.

Fig. 14.

Tab. 3.

Tab. 4.

Fig. 15.

Fig. 16.

Fig. 17.

Fig. 18.

Paradigm

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