Design of reconfigurable mechanism for underactuated robot in the grounded applications

Figures & data

Table 1. An overview of the state-of-art related researches

Environment	Type	Author(s)	Description	Challenge(s)
Aerial	Active flight	. (Karásek et al., 2018)	During the flight, robot’s wings not only move forward relative to the air, they also flap up and down, plunge and sweep, so that both lift and thrust can be generated and balanced, accommodate uncertain surrounding environment, with superior flight stability and dynamics with highly varied speeds and missions.	Higher order averaging techniques may be needed to understand the dynamics of flapping-wing flight and to analyze its stability.
	Gliding	Shavarani et al., 2018	In this paper, a distance-constrained mobile hierarchical facility location problem is studied to discover the optimal number and locations of launch.	Minimization of waiting time, uncertainties, and drone’s capabilities must be addressed when more data are obtained.
	Ballooning	Phan & Park, 2019	The trajectory control of balloons will serve a dual purpose as independent explorers and as microprobe delivery systems for targeted observations of both atmospheric and surface phenomena.	A larger system should be considered to achieve targeting and to widen coverage.
Marine	Surface	Cho et al., 2020	A new integrated model between unmanned surface vehicle and unmanned underwater vehicle platform connected via underwater cable capable of acquiring real-time underwater data and long-time operation are investigated.	The synchronization control between surface vessel and underwater vehicle is hard in various weather conditions.
	Swimming	Romano & Stefanini, 2021	This investigation proposed the structure of the tensegrity robot consisting of rigid body segments and elastic cables that represents bone/tissue and muscles of fish, respectively. This structural configuration allows the tuning of the mechanical stiffness that is often considered as an important factor in fish swimming.	Improvement of the swimming performance by optimizing the geometry and materials is needed to evaluate the effectiveness compared to other existing methods.
	Underwater	(Sahoo et al., 2019)	The structural design of a novel water-jet-based spherical underwater robot is introduced in this paper. The propulsion system is made up of four water-jet thrusters and 8 steering servo motors which can adjust the polydirectional shift of thrusters nozzle to achieve 4-degrees-of-freedom (4-DOF) motion.	More appropriate control scheme and communication module are necessary to study further.
Terrestrial	Walking/Running	(Khan et al., 2021)	A framework for the trajectory optimization of the 5-link Biped Robot using the Beetle Antennae Search algorithm is presented. The biped robot is highly non-linear and has complex dynamical modeling. It is challenging to obtain a closed-form solution for the Robot.	The external disturbance must be added owing to the practical test scenario.
	Crawling	Rafsanjani et al., 2018	A soft actuator is considerably enhanced the crawling capability according to kirigami principles. The mechanical instabilities induce a transformation from flat sheets to 3D-textured surfaces akin to the scaled skin of snakes.	Real-world applications require systems which could operate without the constraint of a tether.
	Climbing	Nguyen & La, 2021	Tank-like robot design is recommended to climb on different steel structural shapes by using reciprocating mechanism and magnetic roller-chains.	Advanced techniques such visual odometry or deep learning should be invested.

Table 2. Summary of recent studies in underactuated robot

Issue	Type of robot	Author(s)	Achievement(s)	Disadvantage(s)
Classification of UR	First-order UR	Zhang, P. et al (He et al., 2019)	The position control of the system is realized using the continuous control method	The optimization for the number of evolution must be required
	Second-order UR	Meng, Q. et al (He et al., 2022)	It can realize the tip position control and vibration suppression by only using one control input generated by the active second joint motor	The ability of the proposed scheme needs to be improved
	High-order (n > 2) UR	Zhang et al., 2018	The proposed strategy is effective for the planar 3-DOF UR with different configurations	The complexity would increase if manipulator has more links
Mechanism of UR	The foot-type walking mechanism	Meng et al., 2020	The availability and adaptability of walking pose are guaranteed with stochastic varying damping parameters	It needs more efficient control strategy to eliminate the steady error between the controlled walking speed and the desired walking speed
	The crawler-type walking mechanisms	(Huang et al., 2020).	The results show that the grounding of the crawler device is much smaller, and the load impact can be greater while it often runs in the mines, sand and mud	The abrupt change in the constant speed might exceed the constant torque force mutation to climb the obstacle
	The wheeled walking mechanisms	(Wu et al., 2018)	The proposed robot has excellent performance in maneuverability, stability, maximum obstacle-negotiation height and mode switch process	The rate of failure in obstacle negotiation is still high for the slippery and muddy environment

Figure 1. Principle diagram of robot structure.

Figure 2. Model of inverted pendulum (a) stable position, (b) marginal position, (c) impact position.

Figure 3. The angular trajectory of wheels according to the exchange of legs.

Figure 4. Description for maximum dimensions of obstacle.

Figure 5. Analysis of forces when moving.

Figure 6. Description for dimensional parameters of wheel.

Figure 7. Initial position to move for one-leg contact.

Figure 8. Initial position to move for two-leg contact.

Table 3. List of dimensional values for wheel-legged mechanism

Symbol	Description	Value
Rmax	Wheels radius when the robot is in full legged mode	65 mm
Rmin	Wheels radius when the robot is in wheeled mode	23,5 mm
r0	Radius of moving part	14,5 mm
a	Rod length	28 mm
b	Foot lever length	17 mm
c	Body length	24,5 mm
e	Dynamic and static deviation	9 mm
Dmin	Wheels diameter when the robot is in wheeled mode	65 mm
Dmax	Wheels diameter when the robot is in full legged mode	130 mm
Hmax	Maximum theoretical obstacle height which the robot can pass	97,5 mm
L	Distance between wheel hub to rear ground point	200 mm
$d=\frac{L}{3}$	Center of gravity distance to drive wheel hub	66,67 mm

Figure 9. Analysis of forces to overcome the obstacle.

Figure 10. Result of function $f\left(\gamma ,\mu ,{\mu }_d,\omega \right)$ when overcoming the obstacle with μ = 0,5, μ_d = 0,4 and H = 97,5 mm.

Figure 11. Result of function $f\left(\gamma ,\mu ,{\mu }_d,\omega \right)$ when overcoming the obstacle with ω = 3,7 rad/s and H = 97,5 mm.

Figure 12. 3D model of hybrid mechanism, (a) component assembly, (b) motion state in wheel mode and (c) motion state in leg mode.

Figure 13. Diagram of electrical connection.

Figure 14. Diagram of hierarchical control in robot system.

Figure 15. Illustration of kinetic constraints for robot model.

Figure 16. Illustration of various motions for robot model.

Figure 17. Illustration of path planning using A–star algorithm.

Figure 18. Tracking trajectory using the proposed model.

Figure 19. Installation of ultrasonic sensor on robot.

Figure 20. Working map in static context (a) and chaotic one (b).

Figure 21. Update obstacles after planning by A–star.

Figure 22. Tracking performance of reference trajectory (dash) and actual trajectory (continuous).

Figure 23. Tracking performance of error (blue) and angle (red).

Table

Symbols	Description
$l$	The length of the legs
$v_0$	The velocity in the highest position
$\mathrm{\Delta }h$	The undulation of the center of mass
${\mathrm{\varnothing }}_m$	The angle between two adjacent legs
$\mathrm{\Delta }H$	Vertical displacement of center of mass
$l_s$	Distance between two adjacent legs
$E_{loss}$	Energy loss
$m$	The mass
${\omega }_1$	The angular velocity of first wheel
${\omega }_2$	The angular velocity of second wheel
$\mathrm{\Delta }x$	The displacement in the x direction
$\mathrm{\Delta }y$	The displacement in the y direction
$W$	The distance between two wheels
$\theta$	The angular between $x_R$ direction and x direcion
$\mathrm{\Delta }t$	The time to move from point to point

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