Analysis of exit probability for a trajectory tracking robot in case of a rare event

Robotica ◽  
2021 ◽  
pp. 1-26
Author(s):  
Rohit Rana ◽  
Prerna Gaur ◽  
Vijyant Agarwal ◽  
Harish Parthasarathy
Keyword(s):  
Trajectory Tracking ◽  
Large Deviation ◽  
Tracking Error ◽  
Rare Event ◽  
Order System ◽  
Lagrange Equations ◽  
Robot Trajectory ◽  
Statistical Application ◽  
Error Energy ◽  
Exit Probability

Abstract In this paper, a novel statistical application of large deviation principle (LDP) to the robot trajectory tracking problem is presented. The exit probability of the trajectory from stability zone is evaluated, in the presence of small-amplitude Gaussian and Poisson noise. Afterward, the limit of the partition function for the average tracking error energy is derived by solving a fourth-order system of Euler–Lagrange equations. Stability and computational complexity of the proposed approach is investigated to show the superiority over the Lyapunov method. Finally, the proposed algorithm is validated by Monte Carlo simulations and on the commercially available Omni bundleTM robot.

Compensatory model predictive control for post-impact trajectory tracking via active front steering and differential torque vectoring

2020 ◽  
pp. 095440702097908
Author(s):  
Mingcong Cao ◽  
Chuan Hu ◽  
Rongrong Wang ◽  
Jinxiang Wang ◽  
Nan Chen
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Trajectory Tracking ◽  
Tracking Error ◽  
Collision Probability ◽  
Critical Conditions ◽  
Physical Analysis ◽  
Compensatory Model ◽  
Torque Vectoring ◽  
Post Impact

This paper investigates the trajectory tracking control of independently actuated autonomous vehicles after the first impact, aiming to mitigate the secondary collision probability. An integrated predictive control strategy is proposed to mitigate the deteriorated state propagation and facilitate safety objective achievement in critical conditions after a collision. Three highlights can be concluded in this work: (1) A compensatory model predictive control (MPC) strategy is proposed to incorporate a feedforward-feedback compensation control (FCC) method. Based on the definite physical analysis, it is verified that adequate reverse steering and differential torque vectoring render more potentials and flexibility for vehicle post-impact control; (2) With compensatory portions, the deteriorated states after a collision are far beyond the traditional stability envelope. Hence it can be further manipulated in MPC by constraint transformation, rather than introducing soft constraints and decreasing the control efforts on tracking error; (3) Considering time-varying saturation on input, input rate, and slip ratio, the proposed FCC-MPC controller is developed to improve faster deviation attenuation both in lateral and yaw motions. Finally two high-fidelity simulation cases implemented on CarSim-Simulink conjoint platform have demonstrated that the proposed controller has the advanced capabilities of vehicle safety improvement and better control performance achievement after severe impacts.

Effect of Short-Term Weather Predictions on Model Predictive Trajectory Tracking Performance of Unmanned Surface Vessels

2020 ◽  
Author(s):  
Benjamin Armentor ◽  
Joseph Stevens ◽  
Nathan Madsen ◽  
Andrew Durand ◽  
Joshua Vaughan
Keyword(s):  
Trajectory Tracking ◽  
Wind Waves ◽  
Tracking Error ◽  
Tracking Performance ◽  
Model Predictive Controller ◽  
Prediction Horizon ◽  
Surface Vessels ◽  
Waves And Currents ◽  
Predictive Controller ◽  
Disturbance Model

Abstract For mobile robots, such as Autonomous Surface Vessels (ASVs), limiting error from a target trajectory is necessary for effective and safe operation. This can be difficult when subjected to environmental disturbances like wind, waves, and currents. This work compares the tracking performance of an ASV using a Model Predictive Controller that includes a model of these disturbances. Two disturbance models are compared. One prediction model assumes the current disturbance measurements are constant over the entire prediction horizon. The other uses a statistical model of the disturbances over the prediction horizon. The Model Predictive Controller performance is also compared to a PI-controlled system under the same disturbance conditions. Including a disturbance model in the prediction of the dynamics decreases the trajectory tracking error over the entire disturbance spectrum, especially for longer horizon lengths.

RECURRENT NEURAL CONTROL FOR ROBOT TRAJECTORY TRACKING

2002 ◽  
Vol 35 (1) ◽  
pp. 283-288 ◽  
Author(s):  
Edgar N. Sanchez ◽  
Jose P. Perez ◽  
Luis J. Ricalde
Keyword(s):  
Trajectory Tracking ◽  
Neural Control ◽  
Robot Trajectory

Reducing Trajectory Tracking Error of Flexible Mobile Robots Using Command Shaping With Error-Limiting Constraints

2017 ◽  
Author(s):  
Gerald Eaglin ◽  
Joshua Vaughan
Keyword(s):  
Mobile Robots ◽  
Trajectory Tracking ◽  
Tracking Error ◽  
Input Shaping ◽  
Flexible Systems ◽  
Command Shaping ◽  
Modeling Errors ◽  
Temporal Tracking ◽  
Point Motion ◽  
Point To Point

The ability to track a trajectory without significant error is a vital requirement for mobile robots. Numerous methods have been proposed to mitigate tracking error. While these trajectory-tracking methods are efficient for rigid systems, many excite unwanted vibration when applied to flexible systems, leading to tracking error. This paper analyzes a modification of input shaping, which has been primarily used to limit residual vibration for point-to-point motion of flexible systems. Standard input shaping is modified using error-limiting constraints to reduce transient tracking error for the duration of the system’s motion. This method is simulated with trajectory inputs constructed using line segments and Catmull-Rom splines. Error-limiting commands are shown to improve both spatial and temporal tracking performance and can be made robust to modeling errors in natural frequency.

Many-Objective Optimal Design of Sliding Mode Controls

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Yousef Sardahi ◽  
Jian-Qiao Sun
Keyword(s):  
Optimal Design ◽  
Pareto Front ◽  
Sliding Mode ◽  
Design Method ◽  
Tracking Error ◽  
Control Design ◽  
Processing Algorithm ◽  
Order System ◽  
Post Processing ◽  
Control Effort

This paper presents a many-objective optimal (MOO) control design of an adaptive and robust sliding mode control (SMC). A second-order system is used as an example to demonstrate the design method. The robustness of the closed-loop system in terms of stability and disturbance rejection are explicitly considered in the optimal design, in addition to the typical time-domain performance specifications such as the rise time, tracking error, and control effort. The genetic algorithm is used to solve for the many-objective optimization problem (MOOP). The optimal solutions known as the Pareto set and the corresponding objective functions known as the Pareto front are presented. To assist the decision-maker to choose from the solution set, we present a post-processing algorithm that operates on the Pareto front. Numerical simulations show that the proposed many-objective optimal control design and the post-processing algorithm are promising.

Sign in / Sign up

Export Citation Format

Share Document