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In this paper an accuracy of local motion planning based on the generalized Campbell-Baker-Hausdorff-Dynkin formula was evaluated for a few nonholonomic robotic systems. For a given set of controls, an exact trajectory is computable via an integration of equations of motion. This reference trajectory is compared with with a trajectory based on shrinked versions of the gCBHD formula. An impact of controls...
In this paper a repeatable kinematic task is considered, i.e. a loop in a configuration space is searched for which corresponds to a given loop in a task-space of a manipulator. In contrast to a classic formulation, an entry configuration, where the loop in a configuration space is initialized, is free to choose. Some methods to generate almost uniformly distributed entry configurations within a manifold...
In this paper a robotic representation of chemical compounds was proposed. The representation allows to model chemical molecules similarly to open-chain manipulators with tree-like structures. Transformations between known chemical representations (formats) and robotic one were established and the representations were compared to. Possible applications of the robotic representation were enumerated...
In this paper modification of a motion planning method based on the endogenous configuration space approach was proposed aimed at solving a prescribed motion planning task sequentially. In an iterative process, the basic method is called and final values of controls from the previous iteration set constraints on controls for the current iteration. In this way, some required properties of resulting...
In this paper a detailed description of constructive algorithms aimed at generating controllable nilpotent systems is presented. Exemplary nilpotent systems with varied degree of nilpotency, number of generators and state space dimensionality are provided. Some combinatorial questions concerning a structure of the systems are stated and answered. Nilpotent systems can serve as useful models for practical...
In this paper a nonholonomic motion planning task was solved using an algorithm proposed by Sussmann and Liu [8] and based on controls in the form of highly oscillatory series (HOS). Outputs of the algorithm were evaluated with respect to energy expenditure on controls and speed of its convergence. Based on characteristic features of the task, two modifications of the algorithm were proposed. Simulations...
Generating and solving the Chen-Fliess-Sussmann (CFS) equation for a given representation of motion is a crucial step in deriving controls to steer nilpotent nonholonomic systems using the Lafferriere-Sussmann method. The equation can be quite complicated, and its derivation differs substantially from one representation to another. Therefore instead to derive CFS for a given hard-to-compute representation...
In this paper a method to speed up a convergence of the Newton algorithm of motion planning for manipulators was presented. The method couples one dimensional optimization (with respect to a coefficient influencing the convergence property of the algorithm) with a virtual goal replacing a real goal of the planning. The first modification of the basic Newton algorithm can be used for any taskspace...
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