Motion planning for mobile vehicles involves two disparate sub-problems: the satisfaction of high-level logical task requirements and the design of low-level vehicle control laws. A hierarchically separated solution of these sub-problems is efficient, but does not guarantee compatibility between the high-level planner and the dynamical constraints of the vehicle. To guarantee such compatibility, we propose a motion planning framework based on a special interaction between these two levels of planning. In particular, we solve a special shortest path problem on a graph at the higher level of planning, and we use the lower level of planning to determine the costs of paths in that graph.
We propose a path planning algorithm based on multi-resolution cell decompositions in the plane. The discrete wavelet transform is used to approximate an elevation map representing the environment, which approximates closely the elevation map in the immediate vicinity of the mobile agent, and approximates coarsely the map in regions farther away. The path planning algorithm is shown to be complete, and it offers significant computational efficiency in terms of both execution speed and memory requirements.
To exploit the full envelope of a ground vehicle's maneouvering capabilities in autonomous high-speed driving necessitates motion planning using a relatively high-fidelity vehicle dynamical model. Either a hierarchical, deterministic approach as above, or an optimal randomized sampling-based approach such as RRT* may be employed for optimal motion planning subject to these vehicle dynamical constraints. However, either approach requires a computationally efficient solution of a local steering problem that involves finding admissible control inputs driving the vehicle state from a given initial condition to a given terminal condition. In general this problem is difficult, but for the specific case of the half-car model (see figure below), we first generate a feasible geometric path followed by an appropriate time parametrization of this path. To this end, we determine tight, state-dependent constraints on the curvature of feasible geometric paths. This approach is closely related to the observation that a simplified version of the half-car model is differentially flat, where the flat outputs are the velocity components of either of a pair of fictitious points called the centers of oscillation (the front center of oscillation is indicated in the figure below).
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Summary coming soon. <Back to top>
We propose an efficient trajectory generation scheme that is repeatedly invoked by the aforementioned discrete planner. The proposed scheme is based on the model predictive control paradigm; the novelty of the proposed approach lies in the efficient computation of effective target sets, which enables a crucial transformation of non-convex state constraints to convex constraints. The efficacy of the overall hierarchical motion planner using this trajectory generation scheme is demonstrated via examples involving complex environments and non-trivial vehicle dynamical models.
We provide a Lyapunov result for uniform semi-global practical stability of time-varying, parameter dependent nonlinear systems. This sufficient condition is applied to a periodically time-varying system in the standard averaging form to obtain a sufficient condition on the averaged system for the time-varying system to be uniformly semi-globally practically stable. The sufficient condition requires the existence of a Lyapunov function that guarantees the semi-global practical stability of the averaged system, and is thus weaker than previous averaging based stability results which require the equilibrium of the averaged system to be exponentially or asymptotically stable.
The risk analysis and system safety literature often reports on “organizational” accidents or “system” accidents in sociotechnical systems. Whereas a “system theoretic approach” to accident analysis and safety has recently been advanced in the literature, formal system theoretic concepts of hierarchical and multilevel systems have been absent from the discussions of safety as a system theoretic problem. To address this gap, we introduce the concepts of coordinability and consistency from the analysis of hierarchical and multilevel systems to the risk analysis and system safety community, and we investigate the applicability of these concepts to system safety via an illustrative example. <Back to top>
We propose a motion planning scheme based on rapidly exploring random trees (RRTs) for a 7-DoF robotic manipulator. The manipulator is required to move objects placed on a planar surface by pushing the objects along the surface. A camera placed directly above the surface senses the geometric outlines and the configurations of the objects; the mass distribution, friction characteristics, and possible linkages between among objects are not known beforehand to the motion planner. The proposed motion planning scheme uses simple parameter-dependent models of the objects’ planar motion, and it includes algorithms for tuning these parameters according to the errors between the expected and the observed motions of the objects.
We consider the problem of decentralized path planning for multiple mobile agents. The proposed approach is based on artificial potential fields, where each agent treats all other agents as moving obstacles; harmonic potentials are used to avoid the problem of unwanted local minima. <Back to top>
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