Structure-Preserving Constrained Optimal Trajectory Planning of a Wheeled Inverted Pendulum

Albert, Klaus; Phogat, Karmvir Singh; Anhalt, Felix; Banavar, Ravi N.; Chatterjee, Debasish; Lohmann, Boris

doi:10.1109/tro.2020.2985579

Cited by 19 publications

(14 citation statements)

References 29 publications

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“…The coordinate systems and parameters of the WIP are as shown in Figure 1. A more detailed description of the WIP system may be found in Reference 15.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The discrete time dynamics of the WIP system 15(section 5.1) is given by the following recursion:

\begin{align} g_{k + 1} = g_{k} normalexp false(prefix- h A false(s_{k} false) v_{k} false) \end{align}

\begin{align} s_{k + 1} = s_{k} + h v_{k} \end{align}

\begin{align} M false(α_{k + 1} false) v_{k + 1} prefix- h C false(α_{k + 1}, v_{k + 1} false) = M false(α_{k} false) v_{k} + h τ_{k}, \end{align}

where h >0 is the step length, M and C denote the inertia and the coriolis terms, respectively, A represents the nonholonomic connection of the system, and

\exp : s e (2) \to S E (2)

is the exponential map on the Lie algebra

s e (2)

of the Lie group SE (2). The parameters for the WIP system in our simulations are lifted from the prototype developed by the Institute of Automatic Control, TU Munich 15 and are presented in Table 1.…”

Section: Numerical Resultsmentioning

confidence: 99%

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A frequency‐constrained geometric Pontryagin maximum principle on matrix Lie groups

Paruchuri

Kotpalliwar

Phogat

et al. 2020

Intl J Robust & Nonlinear

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We present a geometric discrete-time Pontryagin maximum principle (PMP) on matrix Lie groups that incorporates frequency constraints on the control trajectories in addition to pointwise constraints on the states and control actions directly at the stage of the problem formulation. This PMP gives first-order necessary conditions for optimality and leads to two-point boundary value problems that may be solved by numerical techniques to arrive at optimal trajectories. We demonstrate our theoretical results with numerical simulations on the optimal trajectory generation of a wheeled inverted pendulum and an attitude control problem of a spacecraft on the Lie group SO(3).

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“…The coordinate systems and parameters of the WIP are as shown in Figure 1. A more detailed description of the WIP system may be found in Reference 15.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The discrete time dynamics of the WIP system 15(section 5.1) is given by the following recursion:

\begin{align} g_{k + 1} = g_{k} normalexp false(prefix- h A false(s_{k} false) v_{k} false) \end{align}

\begin{align} s_{k + 1} = s_{k} + h v_{k} \end{align}

\begin{align} M false(α_{k + 1} false) v_{k + 1} prefix- h C false(α_{k + 1}, v_{k + 1} false) = M false(α_{k} false) v_{k} + h τ_{k}, \end{align}

where h >0 is the step length, M and C denote the inertia and the coriolis terms, respectively, A represents the nonholonomic connection of the system, and

\exp : s e (2) \to S E (2)

is the exponential map on the Lie algebra

s e (2)

Section: Numerical Resultsmentioning

confidence: 99%

A frequency‐constrained geometric Pontryagin maximum principle on matrix Lie groups

Paruchuri

Kotpalliwar

Phogat

et al. 2020

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

“…Nonholonomic constraint is a characteristic of the mechanical system. When the dimension of the control variable is lower than the state variable, the control variable can control the state variable [24,25]. If the system has nonholonomic constraints, the system is nonholonomic, so it cannot move in any path (for example, the car will drive forward or backward, not side-by-side) [26].…”

Section: Nonholonomic Constraints For Wheeled Mobile Robotsmentioning

confidence: 99%

“…Equations ( 23), (25), and (29) can easily be understood as ώ3 < ώ2 < ώ1. In addition, € is chosen very small in practice, and thus, ώ3 can be minimized by correct tuning of € and N additionally.…”

Section: Design Of Sliding Mode Controllermentioning

confidence: 99%

Nonholonomic Wheeled Mobile Robot Trajectory Tracking Control Based on Improved Sliding Mode Variable Structure

Cai¹,

Singh

2021

Wireless Communications and Mobile Computing

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Several research studies are conducted based on the control of wheeled mobile robots. Nonholonomy constraints associated with wheeled mobile robots have encouraged the development of highly nonlinear control techniques. Nonholonomic wheeled mobile robot systems might be exposed to numerous payloads as per the application requirements. This can affect statically or dynamically the complete system mass, inertia, the location of the center of mass, and additional hardware constraints. Due to the nonholonomic and motion limited properties of wheeled mobile robots, the precision of trajectory tracking control is poor. The nonholonomic wheeled mobile robot tracking system is therefore being explored. The kinematic model and sliding mode control model are analyzed, and the trajectory tracking control of the robot is carried out using an enhanced variable structure based on sliding mode. The shear and sliding mode controls are designed, and the control stability is reviewed to control the trajectory of a nonholonomic wheeled mobile robot. The simulation outcomes show that the projected trajectory track control technique is able to improve the mobile robot’s control, the error of a pose is small, and the linear velocity and angular speed can be controlled. Take the linear and angular velocity as the predicted trajectory.

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“…A more sophisticated, reliant, and robust predictive control mechanism also has been developed for a networked teleoperation space robot [26]. The stability of data communication with Xbee S2b Zigbee used on an Arduino-based sumo robot was investigated [27]. These findings implied that a medical telepresence robot could establish stable and secure real-time data communication using one of these technologies so that doctors can engage with patients or monitor patients' health conditions more safely.…”

mentioning

confidence: 99%

Using a Combination of PID Control and Kalman Filter to Design of IoT-based Telepresence Self-balancing Robots during COVID-19 Pandemic

et al. 2022

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COVID-19 is a very dangerous respiratory disease that can spread quickly through the air. Doctors, nurses, and medical personnel need protective clothing and are very careful in treating COVID-19 patients to avoid getting infected with the COVID-19 virus. Hence, a medical telepresence robot, which resembles a humanoid robot, is necessary to treat COVID-19 patients. The proposed self-balancing COVID-19 medical telepresence robot is a medical robot that handles COVID-19 patients, which resembles a stand-alone humanoid soccer robot with two wheels that can maneuver freely in hospital hallways. The proposed robot design has some control problems; it requires steady body positioning and is subjected to disturbance. A control method that functions to find the stability value such that the system response can reach the set-point is required to control the robot's stability and repel disturbances; this is known as disturbance rejection control. This study aimed to control the robot using a combination of Proportional-Integral-Derivative (PID) control and a Kalman filter. Mathematical equations were required to obtain a model of the robot's characteristics. The state-space model was derived from the self-balancing robot's mathematical equation. Since a PID control technique was used to keep the robot balanced, this state-space model was converted into a transfer function model. The second Ziegler-Nichols's rule oscillation method was used to tune the PID parameters. The values of the amplifier constants obtained were Kp=31.002, Ki=5.167, and Kd=125.992128. The robot was designed to be able to maintain its balance for more than one hour by using constant tuning, even when an external disturbance is applied to it. Doi: 10.28991/esj-2021-SP1-016 Full Text: PDF

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Structure-Preserving Constrained Optimal Trajectory Planning of a Wheeled Inverted Pendulum

Cited by 19 publications

References 29 publications

A frequency‐constrained geometric Pontryagin maximum principle on matrix Lie groups

A frequency‐constrained geometric Pontryagin maximum principle on matrix Lie groups

Nonholonomic Wheeled Mobile Robot Trajectory Tracking Control Based on Improved Sliding Mode Variable Structure

Using a Combination of PID Control and Kalman Filter to Design of IoT-based Telepresence Self-balancing Robots during COVID-19 Pandemic

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