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Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the problem is still open in many aspects, including guarantees on the quality of the obtained solution. In this paper we provide a thorough theoretical framework to assess...
Redundant robots performing multiple tasks of different priority levels are often handled by hierarchical control frameworks. This paper proposes a general hierarchical control approach that can handle not only a single standard lexicographic hierarchy, but also a complex priority network involving both strict and non-strict task priorities. In this approach, priorities can be defined by pairs of...
The RRT* algorithm has efficiently extended Rapidly-exploring Random Trees (RRTs) to endow it with asymptotic optimality. We propose Goal-Rooted Feedback Motion Trees (GR-FMTs) that honor state/input constraints and generate collision-free feedback policies. Given analytic solutions for optimal local steering, GR-FMTs obtain and realize safe, dynamically feasible, and asymptotically optimal trajectories...
We present an approach for asymptotically optimal motion planning for kinodynamic systems with arbitrary nonlinear dynamics amid obstacles. Optimal sampling-based planners like RRT*, FMT*, and BIT* when applied to kinodynamic systems require solving a two-point boundary value problem (BVP) to perform exact connections between nodes in the tree. Two-point BVPs are non-trivial to solve, hence the prevalence...
A data-driven predictive control methodology based on reduced Hankel matrix is proposed in this paper. Undersome assumptions, the properties of a system can be simply and visually behaved by the construction of input-output Hankel matrix. The row size of the Hankel matrix depends on the request of system excitation, which also determines the prediction and control horizons. In order to show the required...
Tracking a desired trajectory in joint space has been favored in several robot manipulators and end-effector control scheme due to the simplicity and high sampling rate offered by the joint space scheme. This usually require the trajectory conversion process, of the desired position, velocity, and acceleration, from Cartesian space to joint space using conventional inverse kinematics solutions which...
In the present work, a method based on belief space planning, assuming maximum likelihood of the observations, is applied to the planning of manipulation for an underwater robotic arm. The manipulator is rigidly connected to a floating platform, such as a ROV (Remotely Operated Vehicle) or an AUV (Autonomous Underwater Vehicle). The arm and platform motions are statistically independent from the motion...
This paper presents the design of predictive control with state constraints for the swing-up and stabilizing control of a cart with an inverted pendulum system where the state constraints are proposed on angle and velocity of pendulum, position and velocity of cart, Since the system has strong nonlinearity and inherent instability, a step of linearization is necessary to extract linear state space...
For the purpose of rarefying the effect of interior perturbations and exterior noise on path tracking performance of Unmanned Aerial Vehicles (UAVs), a robust control method is introduced. We earn the dynamic equations of an UAV from Euler-Lagrange formulation and convert it into state space representation. In order to achieve the tracking objective, a mixed H2/H∞ controller is utilized to stabilize...
This paper addresses a novel computation method of the Maximal Output Admissible (MOA) set for a limit cycle controller and its application to motion transition. By approximately calculating the MOA set via sample point cloud, we can obtain an analytic form of the MOA set even on a nonlinear system. Formulation provided in this paper can be applicable to various types of controllers. Using the MOA...
In this paper, we address the pursuit/evasion problem of capturing an omnidirectional evader using a Differential Drive Robot (DDR) in an obstacle-free environment. The goal of the evader is to keep the pursuer farther than the capture distance for as long as possible and for the pursuer the goal is to capture the evader as soon as possible. In [1] an open-loop time-optimal strategy is proposed for...
Robotic navigation applications often require on-line generation of trajectories that respect underactuated non-linear dynamics, while optimizing a cost function that depends only on a low-dimensional workspace (collision avoidance). Approaches to non-linear optimization, such as differential dynamic programming (DDP), suffer from the drawbacks of slow convergence by being limited to stay within the...
In visual servoing applications, two main approaches were defined by Sanderson and Weiss at the beginning of the eighties: Position Based Contivi and Image Based Control. The aim of this article is to present different control laws using these approaches, and discuss the main advantages and disadvantages of both approaches through experimental results. The target object is composed of four non-coplanar...
Switched linear systems exhibit a continuous state evolving along the continuous flow of time according to linear time invariant differential equations. Furthermore, a discrete interface to the environment is provided, acting on input signals by switching between a finite number of differential equations and generating output signals when the continuous state crosses certain boundaries. We suggest...
Learning robots are faced with two major issues: identification of the dynamics of the robot and identification of the environment as well as its interaction with the robot. We discuss in this paper a way to acquire representations of both these concepts through an iterative learning procedure. Furthermore we will concentrate on qualitative representations, since we are not necessarily interested...
In this paper a novel control method for geometric invariance control is proposed. Nonlinear SISO systems with unstable internal dynamics can be stabilized. In variance conditions of a given state space region are discussed. Sufficient conditions for an output stabilizing Lyapunov controller to assure invariance ofthat region are derived. Simulations of an underactuated, non-minimum phase example...
This paper aims at designing a novel Hybrid Lyapunov theory based Fuzzy Reinforcement Learning Controller with guaranteed stability for non linear systems. One of the major difficulties faced in applying Reinforcement Learning (RL) to real world problems is its limited capability to cope with continuous state spaces. In Fuzzy Q-Learning (FQL) fuzzy Inference systems have been used as universal function...
Technical processes characterized by the interaction of time-driven and event-driven dynamics are referred to as hybrid systems. During start-up procedures or batch processes a technical plant has to be guided along certain operating points. Thus, the basic control task is to lead the system trajectory from an initial to a target state. To cover a series of operating points, this task is to be carried...
In this note it is shown how the n-dimensional rigid body equation naturally leads to Hamilton's canonical equation and how this may be used for controller and observer designs by using the geometry of mechanical systems on manifolds avoiding the parameterization of Lie group SO(n). Based on this approach, it is possible to focus on the intrinsic property of the system and to show closed-loop stability,...
The robustness features versus unmatched uncertainties of a hybrid variable structure control strategy for a class of second order systems are analyzed in this paper. The hybrid control relies on a subdivision of the system state space into nested regions, and on an event-driven switching among the control laws associated with each region. By componing globally stabilizing variable structure laws,...
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