Tracked robot with underactuated tension-driven RRP transformable mechanism: ideas and design

doi:10.1007/s11465-023-0777-8

Front. Mech. Eng.

2024, Vol. 19

Issue (1) : 4 https://doi.org/10.1007/s11465-023-0777-8

Tracked robot with underactuated tension-driven RRP transformable mechanism: ideas and design

Ran XU¹, Chao LIU^1,²(

)

¹. School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China
². Key Laboratory of Vehicle Advanced Manufacturing, Measuring and Control Technology (Ministry of Education), Beijing Jiaotong University, Beijing 100044, China

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Abstract

Robots with transformable tracked mechanisms are widely used in complex terrains because of their high adaptability, and many studies on novel locomotion mechanisms have been conducted to make them able to climb higher obstacles. Developing underactuated transformable mechanisms for tracked robots could decrease the number of actuators used while maintaining the flexibility and obstacle-crossing capability of these robots, and increasing their cost performance. Therefore, the underactuated tracked robots have appreciable research potential. In this paper, a novel tracked robot with a newly proposed underactuated revolute‒revolute‒prismatic (RRP) transformable mechanism, which is inspired by the sit-up actions of humans, was developed. The newly proposed tracked robot has only two actuators installed on the track pulleys for moving and does not need extra actuators for transformations. Instead, it could concentrate the track belt’s tension toward one side, and the unbalanced tension would drive the linkage mechanisms to change its configuration. Through this method, the proposed underactuated design could change its external shape to create support points with the terrain and move its center of mass actively at the same time while climbing obstacles or crossing other kinds of terrains, thus greatly improving the climbing capability of the robot. The geometry and kinematic relationships of the robot and the crossing strategies for three kinds of typical obstacles are discussed. On the basis of such crossing motions, the parameters of links in the robot are designed to make sure the robot has sufficient stability while climbing obstacles. Terrain-crossing dynamic simulations were run and analyzed to prove the feasibility of the robot. A prototype was built and tested. Experiments show that the proposed robot could climb platforms with heights up to 33.3% of the robot’s length or cross gaps with widths up to 43.5% of the robot’s length.

Keywords mechanical design tracked robot underactuated mechanisms RRP mechanism obstacle crossing strategy

Corresponding Author(s): Chao LIU

Just Accepted Date: 07 December 2023 Issue Date: 29 February 2024

Cite this article:

Ran XU,Chao LIU. Tracked robot with underactuated tension-driven RRP transformable mechanism: ideas and design[J]. Front. Mech. Eng., 2024, 19(1): 4.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-023-0777-8
https://academic.hep.com.cn/fme/EN/Y2024/V19/I1/4

Fig.1 Mechanical structure of underactuated tension-motivated tracked robot.

Fig.2 Linkage structure of underactuated tension-motivated tracked robot.

Fig.3 Human-inspired actions of underactuated tension-motivated tracked robot motivated by track tension. COM: center of mass.

Fig.4 Detailed structures in underactuated tension-motivated tracked robot: (a) structure of the restriction mechanism, (b) working characteristic of the restriction mechanisms, and (c) structure of the tension pipe.

Fig.5 Coordinate systems of terrain, robot, and different contact segments of underactuated tension-motivated tracked robot (UTMTR).

Fig.6 Configurations of underactuated tension-motivated tracked robot in different steps and step-transforming threshold conditions.

Fig.7 Angle-relationship curves in each step and step-transforming threshold conditions.

Fig.8 Performing order of climbing a stair.

Fig.9 Performing order of crossing a gap. COM: center of mass, UTMTR: underactuated tension-motivated tracked robot.

Fig.10 Performing order of descending from a platform. COM: center of mass, UTMTR: underactuated tension-motivated tracked robot.

Condition	Necessary conditions	Figure
1	$X COM1 ≤ l 1$
2	$X COM2 ≥ l 1$

Tab.1 Conditions that the UTMTR needs to climb a stair

Fig.11 Linkage mechanism model of underactuated tension-motivated tracked robot for calculating center of mass (COM). The units for the values without specified units are in mm.

Fig.12 Calculation results around the 3D mechanism model: (a) minimum extra mass needed for the rear pulley to remain stable in condition 1 and (b)

Δ X COM

of underactuated tension-motivated tracked robot, which measures the stability of the robot in the climbing process.

Parameter	Value
Length of Link 1, $l 1$	190 mm
Length of Link 2, $l 2$	60 mm
Initial value of $l 3$	150 mm
Maximum revolve angle of Link 3, $θ lim$	60°
Distance between the center of rear pulley and COM of Link 1, $l 1m$	64.48 mm

Distance between revolute joint B and COM of Link 2, $l 2m$	29.21 mm
Distance between revolute joint A and COM of Link 3, $l 3m$	21.93 mm
Distance between the center of front pulley and COM of Link 4, $l 4m$	103.98 mm

Mass of front pulley, $m fp$	0.068 kg
Mass of rear pulley, $m rp$	0.109 kg
Mass of Link 1, $m 1$	0.782 kg
Mass of Link 2, $m 2$	0.066 kg
Mass of Link 3, $m 3$	0.064 kg
Mass of Link 4, $m 4$	0.671 kg

Tab.2 Parameters of the simulation model

Fig.13 Dynamic simulation model of underactuated tension-motivated tracked robot.

Fig.14 Transforming actions simulation of underactuated tension-motivated tracked robot: (a) simulation process and (b) revolving angle curves.

Fig.15 Underactuated tension-motivated tracked robot climbing a 140 mm high stair in simulation: (a) simulation process, (b) revolving angles curves, and (c) driving torques of the pulleys.

Fig.16 Underactuated tension-motivated tracked robot crossing a 200 mm wide gap in simulation: (a) simulation process, (b) revolving angle curves, and (c) driving torques of the pulleys.

Fig.17 Underactuated tension-motivated tracked robot descending from a 140 mm high platform in simulation: (a) simulation process, (b) revolving angle curves, and (c) driving torques of the pulleys.

Tab.3 Specifications of prototype

Fig.18 Structure of control and power systems of the underactuated tension-motivated tracked robot (UTMTR) prototype. DC: direct current, PWM: pulse-width modulation.

Fig.19 Prototype climbing a 140 mm high stair.

Fig.20 Prototype descending from a 140 mm high platform.

Fig.21 Prototype crossing a 200 mm wide gap.

Fig.22 Prototype experiments in different environments.

Fig.23 Two possible designs based on the underactuated tension-motivated tracked robot (UTMTR) models. (a) Design 1; (b) Design 2.

Abbreviations
COM	Center of mass
DOF	Degrees of freedom
RRP	Revolute?revolute?prismatic
PWM	Pulse-width modulation
UTMTR	Underactuated tension-motivated tracked robot
Variables
a, b, $γ$	Positions and postures of the UTMTR in the environment
A_x, B_x	Intermediate variables, which shows the relationships between x_cf and $l T$ (or $l Tr$ )
A_y, B_y	Intermediate variables, which shows the relationships between $y cf$ and $l T$ (or $l Tr$ )
l₁, l₂	Lengths of Links 1 and 2, respectively
l_1m	Distance between the center of rear pulley and COM of Link 1
l_2m	Distance between revolute joint B and COM of Link 2
l₃	Distance between revolute joint A and the axis of the front pulley
l_3m	Distance between revolute joint A and COM of Link 3
l_4m	Distance between the center of front pulley and COM of Link 4
l_T	Length of the tensioned segment of the track belt in steps 1?4
l_T0	Initial value of l_T
l_Tr	Length of the tensioned segment of the track belt in step 5, which is reversed with the ones in steps 1?4
l_Y, l_Z	Intermediate variables for the convince of formulation
L	Total length of the track belt
m_fp, m_rp	Masses of front and rear pulley, respectively
m_i (i = 1,2,...,4)	Mass of Link i
p₀, p₁, p₂	Homogeneous coordinates of a support point under robot coordinates
p_f0	Homogeneous coordinate of the front pulley’s center under the base coordinate of the robot
p_G	Homogeneous coordinate of a support point under ground coordinate
r	Dividing radius of pulleys
R	Transformation matrix between O_R0 and O_Ri (i = 1,2)
R₀₁, R₁₂	Transformation matrixes between robot coordinate systems
R_T	Transformation matrix between the ground coordinate and the base coordinate of the robot
T_front, T_rear	Driving torques of front and rear pulleys according to results of dynamic simulations, respectively
x_cf, y_cf	Coordinate values of the front pulley’s center under the base coordinate of the robot in the x and y directions, respectively
x_sp, y_sp	Coordinate values of the support point under robot coordinate in the x and y directions, respectively
X_COM1	Distances between COM and the shaft of the rear pulley along the moving direction before climbing actions
X_COM2	Distances between COM and the shaft of the rear pulley along the moving direction after climbing actions
ΔX_COM	Moving distance of COM while transforming
$ω rear$	Angular speed of the rear pulley
θ_A	Revolve angle of revolute joint A
θ_Acal, θ_Bcal	Revolving angles of revolute joints A and B according to calculation, respectively
θ_Asim, θ_Bsim	Revolving angles of revolute joints A and B according to results of dynamic simulations, respectively
θ_B	Revolve angle of revolute joint B
θ_lim	Maximum value of θ_A
Δθ	Two pulleys’ differential-rotate angle
Δθ (i = 1,3)	Values of Δθ at the end of step i

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[1]	Mingfeng WANG,Marco CECCARELLI,Giuseppe CARBONE. A feasibility study on the design and walking operation of a biped locomotor via dynamic simulation[J]. Front. Mech. Eng., 2016, 11(2): 144-158.

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