This research presents an adaptive energy-saving
In recent decades, comprehensive applications of autonomous mobile robots (AMRs) have attracted considerable attention. These AMRs with extended energy endurance, more precise motion ability, and effective control approaches have been applied in the transportation, security, and inspection domains. Thus, a precise motion controller for AMRs and energy saving are becoming increasingly important in the robotics application field, which have been discussed in many studies [
For these reasons, an innovative nonlinear energy-saving control approach with a simple control structure that can provide high-performance trajectory tracking for AMRs is presented in this paper. To reduce computational costs and output low-energy torque, a novel energy-saving adaptive
The remainder of this paper is organized as follows. Section 2 describes the mathematical model of trajectory tracking error of AMRs. In Section 3, the adaptive
The trajectory tracking error mathematical model of AMRs is presented in this section. Based on the standard trajectory tracking error mathematical equation and the geometry relationship between the AMR and global coordinate systems, a controlled AMR with a nonlinear trajectory tracking error dynamic equation can be inferred as follows.
In
Under the nonslipping condition, a standard AMR system usually moves along the orientation of the driving wheels’ axis. Hence, the kinematics of the controlled AMR with constraints can be expressed using the following equation [
where
In this study, the dynamics of the controlled AMR are inferred using the Euler–Lagrange method, as expressed in
where
Details of the AMR dynamics are as follows:
where
Suppose
where
According to
Mathematically, it is difficult to use
where
where
From
where
and
If
then the dynamic equation of trajectory tracking error can be revised as follows:
where
An analytic adaptive
The aforementioned performance index can be achieved for all
In this section, we solve the AMR trajectory tracking control problem described in Section 2. To this end, we present a novel energy-saving adaptive
where
and
If
It is difficult to determine the adaptive
In general, it is difficult to solve
Because state-space transformation matrix
where
To investigate the second and third terms on the left-hand side of time-varying differential
By using the results of
In addition, the optimal control law and adaptive law can be expressed as
where
where
Using the definitions of
with
Then, the following adaptive
where
In this section, a verification scenario with the
To construct the simulation environment, the following parameters of the practical AMR are employed:
where
In the second simulation scenario, the verification results of the
Suboptimal trajectory tracking designs have been studied for autonomous mobile wheel robots in the past decades, and most of them have achieved acceptable control performance. However, they have disadvantages such as their extremely complex control structures, such as the sliding mode and backstepping control methods. For simultaneously achieving satisfactory tracking performance and a simple control structure, an analytical adaptive nonlinear control scheme was developed to track the trajectory of autonomous mobile wheel robots in this study. The proposed adaptive control design consists of an adaptive cancellation term that is used to cancel the nonlinear component of tracking errors and an optimal control term to minimize the power consumption when tracking the desired trajectories. Thus, the proposed control method has an impressive property; that is, without knowing the system parameters of autonomous mobile wheel robots, the desired trajectory tracking performance can be maintained by exploiting the adaptive learning ability of the proposed method. The simulation results indicate that the proposed adaptive nonlinear control method delivers promising trajectory tracking performance for WMRs because the tracking errors quickly converge to zero when a large amount of modeling uncertainties appear. Therefore, the proposed method has the advantages of being able to execute tasks such as the uploading and downloading of goods and regular patrolling.