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On dynamically consistent Jacobian inverse for non-holonomic robotic systems

Ratajczak J., Tchoń K.

Archives of Control Sciences

2017

Vol. 27, no. 4

555--573

This paper presents the dynamically consistent Jacobian inverse for non-holonomic robotic system, and its application to solving the motion planning problem. The system’s kinematics are represented by a driftless control system, and defined in terms of its input-output map in accordance with the endogenous configuration space approach. The dynamically consistent Jacobian inverse (DCJI) has been introduced by means of a Riemannian metric in the endogenous configuration space, exploiting the reduced inertia matrix of the system’s dynamics. The consistency condition is formulated as the commutativity property of a diagram of maps. Singular configurations of DCJI are studied, and shown to coincide with the kinematic singularities. A parametric form of DCJI is derived, and used for solving example motion planning problems for the trident snake mobile robot. Some advantages in performance of DCJI in comparison to the Jacobian pseudoinverse are discovered.

Dynamic consistency under private information

Correa R.

Control and Cybernetics

1999

Vol. 28, no 2

225-232

Time inconsistency is often demonstrated in the context of the global Sta.ckelberg solution of a two-person, two-stage dynamic game. The loop model of dynamic games is used. The recommended solution to the problem is for both players to adopt open-loop strategies. VVe recast the problem in an imperfect informa-tion framework. In contrast to the standard result, (i) a consistency in the outcomes of the lash game and the associated Stackelberg game is shown and (ii) it is proved that under feedback information patterns, both players prefer to play the Stackelberg game rather than the associated Nash game.