An effective approach to enhance the balancing control in bycycorobot using the soft computing techniques

Received Nov 8, 2021 Revised Dec 25, 2021 Accepted Dec 30, 2021 The balancing and control of bycycorobot is a challenging task. The prespecified controller available in the literature for balancing has been reduced with novel optimization to improve the effectiveness of balancing, uncertainty, and the complexity of the complete system. The novel Harris hawk optimization (HHO) which is based on the hunting behavior of the hawk has been utilized to improve the balancing of the bycycorobot. The paper proposes the decreased order controller of a pre-specified controller for a bycycorobot. The obtained controller response with bycycorobot in the complete closed loop is analyzed, and the best performance is compared with the reduced order controller available in the literature. The comparison is based on the response indices and response characteristics.


INTRODUCTION
As the first kind of personal mobility vehicle ever invented, bicycles play an important role in the history of transport. Bicycles are lightweight and are solely propelled by human power. They can contribute to the reduction of traffic congestion and air pollution in urban areas. Bicycles are classified as single-track vehicles and display interesting dynamic behavior. The intriguing behavior of bicycles poses challenging problems in modeling and control, which have attracted attention from the automatic control research community [1]. The balancing control problem of the bycycorobots is not new in the field of robotics. The bycycorobot is in great demand due to its basic construction, simpler dynamics, and applicability in wide sectors such as transportation, security, search and rescue, and labor reduction. These robots are inherently unstable and susceptible to external disturbances. Robust controls approached are required for appropriate and smooth balancing control and movement of such robots [2]. The stability of bicycles is an issue that has scarcely been understood in dynamics and is a commonly ignored problem. After two centuries of debate and unfinished modeling, new researches are paving the groundwork for increasing studies regarding this issue [3]. Thereby, some researchers have appeared thanks to new dynamics models and the computational power available nowadays. Their purpose is to propose and test different alternatives to stabilize a bicycle. Despite their common goal of making a bycycrobot stable, they propose a wide variety of applications for their stabilized bycycrobot [4].
The bicycle can be balanced using the rotation of the front wheel in the direction of lean, which changes the tire contact point with the ground in the same direction and is similar to balancing an inverted pendulum. In addition, the centrifugal force contributes to balance because of the circular motion. Moreover, uncontrolled bicycles can balance themselves within certain velocity ranges, which depend on different ISSN: 2722-2586  An effective approach to enhance the balancing control in bycycorobot using … (Aswant Kumar Sharma) 45 appropriate for the real-world applications of the two-wheeled bicycle model for this, composite method H2/H∞ control is presented, which is a sophisticated approach for constructing durable and optimum controllers for systems with unknown sources. However, it is widely understood that the structure-specified mixed H2/H∞ controller design typically creates a complicated and non-convex optimization issue that is difficult to address using traditional optimization methods. The optimization approaches using GA, PSO, and Cuckoo search have been suggested to tackle this problem. These techniques have offered to balance but the improvement of balancing also has the possibility in bycycorobot against uncertainty and external disruption. The reason of unmolded dynamics, parameter changes, and external disturbances complicates the system and necessitates a strong controller. As a result, a novel approach is required to enhance the balance control in bycycorobot.
The model order reduction methodology has been applied in order to obtain the reduced order controller. The MM techniques [22], continued fraction [23], mixed methods [24]- [28] are traditional methods tested and failed. The main objective of this manuscript is to obtain the effectively reduced order controller with bycycorobot response and enhance the balance control of it under uncertainty and external disturbances. For this, Harris hawk optimization (HHO) is having been selected due to aggressive and swarm behavior to design the controller efficiently. The approach represents the systems' model uncertainty as multiplicative uncertainty, and the system is considered to be influenced by external disturbances. HHO has been utilized for search parameters of and admissible structure-specified controller that minimizes the ISE while being subjected to robust stability constraints (H∞ norm) against model uncertainty and external disturbances. The suggested method is used to regulate the balance of a bicycle robot equipped with a gyroscopic stabilizer, known as bycycorobot. Using the Lagrange technique, a simplified dynamics model of a bycycorobot is constructed by disregarding forces caused by forwarding movement and steering. To evaluate the performance proposed system, it was compared with other techniques available in the literature. The proposed system is implemented using MATLAB software. The proposed algorithm-based controller will be effectively enhanced the performance of the balancing control in bycycorobot which is an unstable system with un-modeled dynamics, parameter changes, and external disturbances as sources of uncertainty.

HARRIS HAWK OPTIMIZATION (HHO)
HHO is based on the studies of hawk behavior usually in the period of hunting. The study has been carried out by Louis Lefebvre. The mathematical implementation in the engineering designing field using the HHO is carried out [29]. The behavior of hunting and chasing patterns for the capture of prey in nature is known as a surprise pounce. The searching of prey is a task done by the predator using the highest point of the area such as standing on top of trees or flying in the sky. The attack of the hawk on prey is called a pounce. As the prey is spotted another member is informed by visual displaying or vocalization. The HHO is divided into three-phase naming exploration, the transition from exploration to exploitation, and the exploitation phase. The exploitation stage is separated into four stages namely soft besiege, hard besiege, soft besiege with advanced quick dives, and hard besiege with progressive speedy dives. Figure 1 is showing the flow chart of HHO.

The exploration phases
To start this phase, the Hawk reaches the peak of tree/pole/top of the hill to trace the prey and also consider the other of Hawks positions. The situation is q ≥ 0.5 of branch on random giant trees for the situation of q ≤ 0.5. The condition ids are modeled as (1).
Where ( + 1) is the position vector of the hawk in the succeeding iteration t .
( ) is the present position vector of hawks 1 , 2 , 3 , 4 and are the random number confidential (0,1) upgraded with iteration. LB is the lower bounds, and UB is the upper bounds of numbers ( ) represents the arbitrarily hawk represents the arbitrary hawk from the present population is the average position of the current population is the average position of the current population of hawks. The primary rule creates solutions based on a random position. In the second rule of (1), the variance between the best positions and the average location of the group plus an arbitrary climbed factor depends on the number of variables. The scaling factor 3 increases the random nature of regulation once 4 adjacent value to 1 adjacent value to 1 and comparable distribution designs. Random factor scaling coefficients increase pattern diversification and explore various feature regions. The rules for buildings are capable of mimicking the actions of a hawk. The hawk's average location is obtained using (2).

Conversion from exploration to exploitation
The exploration to exploitation changes between exploitation performances founded on the absconding energy of the prey. The energy of a prey reduces throughout the escaping. The energy of the prey is modeled as (3).
Where E designates the absconding energy of prey, T is the maximum number of iterations, and E 0 is the initial state of energy.

Exploitation phase
The process begins with the surprise, and the imagined prey of the previous stage is hostile. The preys try to escape. The probability of fleeing from the prey is ( < 0.5) or not to escape efficaciously ( ≥ 0.5). The hawk executes rough or soft besieges concerning prey activity to capture the prey. Based on the vitality of the prey, the hawk encircles around the beast in various ways. The hawk gets closer to the desired prey to maximize its odds of cooperating in killing the rabbit. The gentle assault begins, and the rough assault takes place.

Besiege occurs
Besiege is the process at the time of capturing prey. It is divided into soft besiege and hard besiege with progressive dives of each respectively.

Soft besiege
The prey has energy and tries to escape using random confusing jumps. The value for escaping energy must be ≥ 0.5 and ≥ 0.5. If the values are below as stated, the prey is unable to jump. Hawk encircles prey gently to make it more tired and achieve the surprise dive. This conduct is modeled by subsequent rules represented in (4) and (5).

Hard besiege
The prey is exhausted and has less energy when values ≥ 0.5 and ≥ 0.5. The hawk barely encloses the intended prey and finally achieves the shock pounce. The present locations are updated as (6).
Dive is founded on the LF-based designs using the law represented in (7).
Where represents the dimension problem and represents a random vector by size 1 × and is the levy fight function, and calculated as (8).
Where, , uvare random values inside (0,1), is a constant set to 1.5. The last tactic for apprising the locations of hawks. The soft besiege stage can be achieved and given in (9).
The Y and Z are obtained using the (8) and (9).

Hard besiege with progressive dives
The | | < 0.5 and < 0.5. To escape and hard besiege is built earlier the surprise pounce to catch and kill the prey. The condition on the prey side is comparable to that of soft besiege except this time. The hawk seeks to reduce the difference between their regular position and the fleeing target.
The and are gained by (11) and (12).

MATHEMATICAL MODEL OF BYCYCOROBOT SYSTEM
The bycycorobot is shown in Figure 2. The main task the goal of the robot is to move without falling in any direction, with or without limited load. The major issue of the taken task is of balancing because of its unstable nature and various uncertainties. Different controllers/ algorithms are available to resolve the problem. Bycycorobot dynamics is derived using the Langrage (13).
Where denotes the total kinetic energy, represents the total potential energy of the system, is generalized coordinate, and denotes the external forces. The and relation are (14)- (17) Bycycorobot dynamics are derived using the Langrage (14).
Where, and represents the weight of bycycorobot and flywheel respectively. represents the lean angle, ̇ denotes angular velocity in Z-axis, represents the angle of flywheel along Z1 axis, ̇ is the angular velocity of the flywheel along X1 axis.
is the height of center of gravity of bycycorobot, f h represents the height of flywheel center of gravity. , , and are flywheel radial movement of inertial, flywheel polar movement of inertial and robot movement of inertia respectively. The value of = and the equation obtained in (18).
The chain transmission of bycycorobot and DC Motor dynamics is assumed to be 5:1 and the relation obtained is given in (19) and (20).
Where in (19), represents the torque constant of motor and in (20) is back e, m, f. constant, and are armature resistance and inductance of motor. The equation (19) is substituted in (18) and linearizing (17) and (18) around the equilibrium point, the relation achieved as (21) and (22). The state space equation of the system form is given in (23).
The values of the fourth order state space input part, output part is represented as (24)- (27).
In most cases, a flywheel is used to balance the generated torque with respect to gravity. The parameter consideration of bycycorobot is listed in Table 1. The state space into transfer function. The obtained transfer function of the two wheeled mobile robot is given as (28).
The output lean angle and the input voltage to the DC motor that controls the flywheel control axis. Assuming the following two cases: i) Case-1: the additional 10 Kg load and decrease the speed of the flywheel up-to 147 rad/sec. The transfer function from this condition is as (29); ii) Case-2: in this case, more 10 Kg load is added speed of flywheel is increased to 167 rad/sec. the transfer function is as (30).
Bycycorobot including both the special case of the system represents instability in Figure 3. The balancing control of the system is given by Thanh and Parnichkun in [20] with a controller based on particle swarm optimization using specifically mixed H2/H∞ controller. The transfer function of the controller is as (31).

DESIGN OF FIRST ORDER CONTROLLER USING HHO TECHNIQUE
The structure of first order controller is obtained using the HHO by minimizing the ISE. The unknown reduced order model of first order is represented as (32).  follows H-∞ controller closely and the uncertainties and disturbance are also removed. This indicates that in closed loop with bycycorobot in all three cases, it may perform with a better result. For Justification the response is also compared with the first order controller using GA and PSO [20] given as (34)  Recently the first order controller with improved performance using the cuckoo search optimization in [21]. The first order controller with improved performance using PSO, the structure specified H∞ loop shaping controller in [30] and is given as (37). The proposed controller needs to be tested and the response of it is compared with the controller available in the literature.

First order controller closed loop analysis with bycycorobot
The proposed first order controller in closed loop with the bycycorobot including the special case-1 and case-2 has been analyzed in this part. The performance has been analyzed on the basis of step response characteristics and response indices error in Figure 4. The step response of the 1 st order controller using HHO with bycycorobot in a complete closed loop is represented in Figures 5-7 respectively.
The performance in terms of step response characteristics and response indices error of proposed first order controller with the system in closed loop with all cases available in Table 2. The proposed controller response is better than the first order controller using GA and PSO [20], Cuckoo search optimization in [21], the structure specified H∞ loop shaping controller using PSO [30]. This can also be verified from the step response plot in Figure 5, Figure 6 for case-1, and Figure 7 for case-2. The data available in Table 2 concludes that the proposed controller is efficient and effective in all two cases and performs better. The controller analysis extended to the second order and its design using the HHO.

DESIGN OF SECOND ORDER CONTROLLER USING THE HARRIS HAWK OPTIMIZATION
The design of unknown second order reduced controller based on the structure of bycycorobot is represented as (38).
The response analysis of the system with higher order controller and reduced controller from the literature the lower bound selected as lb = [230 950 8 20]; and upper bound selected as ub = [300 1000 10 30] with 1 , 2 , 1 and 2 are unknown four parameters dimensions which are to be optimized using an algorithm so dimension is 4. The obtained parameter using the Harris hawk algorithm is represented in Figure 8, where Figure 8 (39) Figure 9 is showing the iteration graph of the controller with the fitness value and step response the higher order H∞ controller with the proposed reduced order, reduced order available in the literature is given in Figure 9(a). The step response in Error! Reference source not found.9(b), it is clear that the proposed 2 nd order reduced controller response approximately same as that of higher order controller and improved response from the controller from cuckoo search as (40) [21], and the second order controller using the PSO as (41) [30]. The effectiveness of the proposed order controller is also analyzed with the system in closed loop.

Second order controller closed loop analysis with bycycorobot
The second order controller in closed loop with the bycycorobot stabilizes the system by removing uncertainties. The response of the controller with response characteristics and response indices error is given in Table 3.
The response of the proposed second order approximately gives the same response as that of the 6 th order controller with bycycorobot. Figure 10 is showing step response characteristics of the proposed second order controller in closed loop and second order controller from literature, Figure 11 is showing step response characteristics of the proposed second order controller in closed loop and second order controller from literature case-1, and Figure 12 is showing step response characteristics of the proposed second order controller in closed loop and second order controller from literature case-2.
The response is also justified with the result from the cuckoo search [21] and particle swarm optimization [30] It is clear from Table 3 that the proposed controller provides the comparable performance and the response indices IAE, ITAE and ITSE is better than the result from cuckoo search and particle swarm optimization.  Step response characteristics of the proposed second order controller in closed loop and second order controller from literature case-2

DESIGN OF THIRD ORDER CONTROLLER USING THE HARRIS HAWK OPTIMIZATION
The third order controller with unknown is represented as (42). The unknown parameter of reduced order model is optimized and the obtained parameter is with respect to number of iterations is represented in Figure 13 and third order obtained as (43), Figure 13 The third order reduced system using the Schur analysis, balanced truncation and model truncation given in [31], is represented as (44) The proposed reduced order is analyzed with closed loop with the bycycorobot and equivalent reduced order from the literature [31]. The third order controller by cuckoo search algorithm [21], is represented as (47).

Third order controller closed loop analysis with bycycorobot
The proposed third order response has been analyzed with the system in closed-loop. The response of the system with the proposed controller in special cases is mentioned in Table 4 and compares with the response with the controller available in the literature [21], [31]. The third order proposed controller gives the approximate same response as compared to the controller present in literature [21], [31] and represents with step response characteristics in Figure 14, Figure 15 for case-1, and Figure 16 for case-2. The response indices IAE, ITAE and ITSE are minimum indicating the good approximation and superiority of the proposed reduced order justified. The approach has been verified with the pole location of the proposed first order, second order and third order controller with the result from the literature [20], [21], [30], [31]. Table 5 is showing poles of higher order and reduced order controller.  Figure 14.
Step response characteristics of the proposed third order controller in closed loop and third order controller from literature Figure 15.
Step response characteristics of the proposed third order controller in closed loop and third order controller from literature case-1 Figure 16.
Step response characteristics of the proposed third order controller in closed loop and third order controller from literature, case-2

CONCLUSION
The bycycorobot model balancing is achieved using the reduced order controller methodology. The sixth order controller is pre-specified in the literature. The controller when comes closed-loop with the system did not perform well, while in the complete closed-loop system, performance gets improved, while the order of the system in complete closed-loop increases to sixteen orders. Therefore, a reduced order controller is projected and successfully obtained using the HHO in the first, second, and third order. The result in a complete closed-loop is compared with the result of the higher-order controller, reduced order controller. The proposed controller not only balances the bycycorobot but also gives better performance in the first order, second order, and equivalent performance in third order as its performance is compared with the reduced order available in the literature.