Motion Planning Of Nonholonomic Systems Research Articles

Motion planning for nonholonomic systems with earlier destination reaching

Motion planning for nonholonomic systems with earlier destination reaching

Development of Task-Space Nonholonomic Motion Planning Algorithm Based on Lie-Algebraic Method

In this paper, a Lie-algebraic nonholonomic motion planning technique, originally designed to work in a configuration space, was extended to plan a motion within a task-space resulting from an output function considered. In both planning spaces, a generalized Campbell–Baker–Hausdorff–Dynkin formula was utilized to transform a motion planning into an inverse kinematic task known for serial manipulators. A complete, general-purpose Lie-algebraic algorithm is provided for a local motion planning of nonholonomic systems with or without output functions. Similarities and differences in motion planning within configuration and task spaces were highlighted. It appears that motion planning in a task-space can simplify a planning task and also gives an opportunity to optimize a motion of nonholonomic systems. Unfortunately, in this planning there is no way to avoid working in a configuration space. The auxiliary objective of the paper is to verify, through simulations, an impact of initial parameters on the efficiency of the planning algorithm, and to provide some hints on how to set the parameters correctly.

Multiple-task motion planning of non-holonomic systems with dynamics

Abstract. This paper addresses the motion planning problem in non-holonomic robotic systems. The system's kinematics and dynamics are represented as a control affine system with outputs. The problem is defined in terms of the end-point map of this system, using the endogenous configuration space approach. Special attention is paid to the multiple-task motion planning problem, i.e. a problem that beyond the proper motion planning task includes a number of additional tasks. For multiple-task motion planning two strategies have been proposed, called the egalitarian approach and the prioritarian approach. Also, two computational strategies have been launched of solving the motion planning problem: the parametric and the non-parametric. The motion planning and computational strategies have been applied to a motion planning problem of the trident snake robot. Performance of the motion planning algorithms is illustrated with computer simulations.

Layer, Lie algebraic method of motion planning for nonholonomic systems

In this paper a layer, Lie algebraic method of motion planning for nonholonomic systems is presented. It plans locally a motion towards a goal by searching for optimal directions in equi-cost spaces. The spaces are easy to determine via exploiting Lie algebraic properties of vector fields that define the controlled system. The method was illustrated on the unicycle robot and the inverted pendulum.

Impact of control representations on efficiency of local nonholonomic motion planning

Impact of control representations on efficiency of local nonholonomic motion planning In this paper various control representations selected from a family of harmonic controls were examined for the task of locally optimal motion planning of nonholonomic systems. To avoid dependence of results either on a particular system or a current point in a state space, considerations were carried out in a sub-space of a formal Lie algebra associated with a family of controlled systems. Analytical and simulation results are presented for two inputs and three dimensional state space and some hints for higher dimensional state spaces were given. Results of the paper are important for designers of motion planning algorithms not only to preserve controllability of the systems but also to optimize their motion.

Constrained motion planning of nonholonomic systems

This paper addresses the constrained motion planning problem for nonholonomic systems represented by driftless control systems with output. The problem consists in defining a control function driving the system output to a desirable point at a given time instant, whereas state and control variables remain over the control horizon within prescribed bounds. The state and control constraints are handled by extending the control system with a pair of state equations driven by the violation of constraints, and adding regularizing perturbations. For the regularized system a Jacobian motion planning algorithm is designed, called imbalanced. Solutions of example constrained motion planning problems for the rolling ball illustrate the theoretical concepts.

Motion Planning of Nonholonomic Systems with Tracking Control Lyapunov Function

A common approach to motion planning of robots and vehicles involves finding suitable trajectories for the positions of each configuration variable, and then using feedback to regulate the system to these trajectories. However, when the system has less actuator than dynamical degrees of freedom, it is not always possible to do this arbitrarily. In this paper a tracking control Lyapunov function (TCLF) is proposed to guarantee that the trajectory generation is convergent and executable under nonholonomic constraint, and the simulation result conducted on surface vehicle shows its effectiveness.

Velocity space approach to motion planning of nonholonomic systems

SUMMARYIn this paper, a velocity space method of motion planning for nonholonomic systems is presented. This method, based on Lie algebraic principles and locally around consecutive current states, plans a motion towards a goal. It is effective as most of the computations can be carried out analytically. This method is illustrated on the unicycle robot and the inverted pendulum.

Optimal motion planning for nonholonomic systems using genetic algorithm with wavelet approximation

An optimal motion planning scheme using genetic algorithm with wavelet approximation is proposed for nonholonomic systems. The motion planning of nonholonomic systems can be formulated as an optimal control of a driftfree system. A cost function is introduced to incorporate the control energy and the final state errors. The control inputs are determined to minimize the cost functional. By using the method of wavelet, the infinite-dimensional optimal control problem is truncated to a finite-dimensional one based on the wavelet bases. The genetic algorithm is employed to solve a feasible trajectory satisfying nonholonomic constraints. The proposed scheme is applied to a free-floating robot consisting of two one-link arms connected to a main base via revolute joints. The numerical results demonstrate that the genetic algorithm with the wavelet approximation is an effective approach to steer a nonholonomic system from its initial state to its final state.

Pre-control form of the generalized Campbell–Baker–Hausdorff–Dynkin formula for affine nonholonomic systems

In this paper a pre-control form of the generalized Campbell–Baker–Hausdorff–Dynkin (gCBHD) formula is presented. This form is dedicated to nonholonomic (affine) systems often encountered in robotics. The simplest possible expression for the pre-control gCBHD is obtained as control-dependent functions pre-multiply elements of the Ph. Hall basis. Algorithmic aspects of deriving the formula are highlighted. An application of the pre-control form of the gCBHD formula in motion planning of nonholonomic systems is also reported.

Pre-control form of the gCBHD formula and its application to nonholonomic motion planning

In this paper a pre-control form of the generalized Campbell-BakerHausdorff-Dynkin (gCBHD) formula is presented. This form is dedicated to nonholonomic systems of robotics. A straightforward application of the pre-control form of the gCBHD formula in motion planning of nonholonomic systems is also provided.

Nonlinear Optimization-Based Motion Planning of Nonholonomic Systems using an Iterative Algorithm

ABSTRACTA nonlinear optimization-based scheme is developed for the motion planning of nonholonomic systems. By specifying the final states constraints and using the performance criteria involving the control energy, the motion planning of nonholonomic systems can be recast as a nonlinear optimization problem which is to find suitable control inputs for steering the system along a feasible path from an initial state to a final state. An iterative algorithm is proposed to solve for a feasible path satisfying nonholonomic constraints and necessary optimality conditions. First, multi-point shooting is used to convert the motion planning problem into the problem of finding the solution of nonlinear equations. Modified Newton's method with line search is then used to ensure the global convergence of the numerical algorithm. The proposed scheme is applied to an one-leg hopping robot and a two-wheeled mobile robot. The results of numerical simulation clearly demonstrate the effectiveness of the proposed motion pl...

Locally optimal motion planning of nonholonomic systems

Locally optimal motion planning of nonholonomic systems

Locally optimal motion planning of nonholonomic systems

Locally optimal motion planning of nonholonomic systems

Planning motions of a dual-arm free-floating manipulator keeping the base inertially fixed

Dual-arm free-floating manipulators will play an important role in space automated handling, and assembly. The motion planning of these manipulators is challenging due to nonholonomic nature and free-floating base. This paper deals with a novel scheme for motion planning of a dual-arm free-floating planar manipulator where one arm is commanded to perform desired tasks while the other provides compensating motions to keep the base inertially fixed. This scheme is based on the following analogy of two men of equal masses in a boat. If one man walks on the boat, instantaneously, the boat acquires a velocity in a direction opposite to that of the velocity of the man. If the two men walk with velocities equal in magnitude but opposite in direction, the boat remains stationary relative to the shore. In this paper, we present the necessary mathematical conditions for successful planning with this scheme. Algorithms for motion planning in joint coordinates and Cartesian coordinates are implemented in computer simulation. The algorithms are based on position kinematics of the system coupled with iterative procedure to satisfy the nonholonomic constraints and avoid singularities during motion. The use of rate kinematic equations in motion planning of nonholonomic systems is not new but the use of position kinematics coupled with iterative search is novel.

A Surface Integral Approach to the Motion Planning of Nonholonomic Systems

Nonholonomic mechanical systems are governed by constraints of motion that are nonintegrable differential expressions. Unlike holonomic constraints, these constraints do not reduce the number of dimensions of the configuration space of a system. Therefore a nonholonomic system can access a configuration space of dimension higher than the number of the degrees of freedom of the system. In this paper, we develop an algorithm for planning admissible trajectories for nonholonomic systems that will take the system from one point in its configuration space to another. In our algorithm the independent variables are first converged to their desired values. Subsequently, closed trajectories of the independent variables are used to converge the dependent variables. We use Green’s theorem in our algorithm to convert the problem of finding a closed path into that of finding a surface area in the space of the independent variables such that the dependent variables converge to their desired values as the independent variables traverse along the boundary of this surface area. Using this approach, we specifically address issues related to the reachability of the system, motion planning amidst additional constraints, and repeatable motion of nonholonomic systems. The salient features of our algorithm are quite apparent in the two examples we discuss: a planar space robot and a disk rolling without slipping on a flat surface.