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Discrete-Time Linear Systems
Published in Hebertt Sira-Ramírez, Sunil K. Agrawal, Differentially Flat Systems, 2018
Hebertt Sira-Ramírez, Sunil K. Agrawal
Problem 5.7.2A simplified kinematic model of an unicycle, constituted by a perfectly symmetric wheel constrained to the vertical plane, has the following form () x˙=v cosθy˙=v sinθθ˙=ω
Motion Control of Multiple AUVs for Simultaneous Mapping and Navigation
Published in Chao Gao, Guorong Zhao, Hassen Fourati, Cooperative Localization and Navigation, 2019
Marcelo Borges Nogueira, Fernando Lobo Pereira
The vehicle model used for all AUVs in the simulations was a 2D unicycle model presented in Equation 23.7. The dead reckoning information available is the control signal u(k), which can be measured, for example, by an inertial measurement unit (IMU). The process noise matrix Q is a diagonal matrix with 0.02 in the first two entries and 0.35 in the third one. The external sensor, a range detector, has an error variance R = [0.5]. All the noises are considered to be white with zero mean. In all the simulations the time step is 0.1 seconds, the rate at which the KF runs the given proprioceptive data.
Problem Formulation and Examples
Published in Sabiha Wadoo, Pushkin Kachroo, Autonomous Underwater Vehicles, 2017
The simplest example of a nonholonomic system can be a wheel that rolls on a lane surface, such as a unicycle. The constraints here arise due to the roll without a slip condition. The configuration or the generalized coordinate vector is q = (x, y, θ). The coordinates x and y are the position coordinates of the wheel, and θ is the angle that the wheel makes with the x axis. The unicycle is shown in Figure 2.2. The constraint here is that the wheel cannot slip in the lateral direction.
Configuration-aware model predictive motion planning for Tractor–Trailer Mobile Robot
Published in Advanced Robotics, 2023
Nobuaki Ito, Hiroyuki Okuda, Tatsuya Suzuki
It is assumed that the TTMR drives at a low speed (e.g. ). Thus a kinematic TTMR model is adopted as a prediction model of MPC. All vehicles composing the TTMR are two-wheeled for simplicity. The model of each vehicle is essentially the same as the individual differential drive wheeled robot, as a unicycle model. The kinematic model of the unicycle model for the ith vehicle can be defined as follows: where and are the longitudinal and angular velocities of the tractor, respectively. and are the inputs for the tractor and are equal to the input of the TTMR because only the tractor is actuated, with the other vehicles and joints unactuated and passive. and for all i>1 are inputs for each trailer and are determined from the motion of the preceding vehicle.
Memory-loss resilient controller design for temporal logic constraints
Published in Cyber-Physical Systems, 2021
M. Abate, W. Stuckey, L. Lerner, E. Feron, S. Coogan
Consider an autonomous vehicle which must refuel periodically, while also avoiding obstacles. We abstract the vehicle dynamics in a 200 state nondeterministic transition system , representative of a discrete-time discrete-state unicycle model. Here, each state of denotes a unique position and rotation . The control inputs to the system are linear velocity and angular velocity . Nondeterminism in the system arises when the control input , i.e. when the system intends to drive forward and turn during the same time-step. In this case the system will nondeterministically enter either the state arising from moving forward one unit and then rotating, or the state arising from rotating first and then moving forward one unit. This problem setting is shown in Figure 6.
Extended balance stabilization control for humanoid robot on rotational slope based on seesaw-inverted-pendulum model
Published in Advanced Robotics, 2021
Kohei Kimura, Kei Okada, Masayuki Inaba
We explain the experimental equipment, wobble floor and unicycle Segway, as shown in Figure 7 as the objects of rotational slope used in the experiments. The wobble floor is a foothold environment in which a plate material is placed in the center on an elongated aluminum frame with a width of 0.04[m] as shown in the left side of Figure 7. And this is the experimental equipment with another frame sandwiched between the frame and the plate material so that the inclination can be sufficiently earned. The unicycle Segway is a vehicle with a plate material mounted in the center on a Segway with a rubber single-axis drive wheel with a width of 0.09 [m] as shown in the right side of Figure 7. And the Segway is used only one leg side of Segway Drift W11. Since the unicycle Segway is a rotational slope that can move back and forth unlike the wobble floor, it is also versatile as an aspect of expanding the mobility of humanoid robot. On the other hand, as a trade-off for the versatility of movement, it is required to integrate the controller for speed regulation of humanoid robot and the extended balance stabilization controller proposed in this paper so that the whole system can coexist withSegway.