2 EVENT-BASED PLANNING AND CONTROL 5
Some effort has been made to develop a path planning scheme based on sensory
information [6]. This method is, however, purely geometric and is not integrated with the
control execution.
The results of pioneering research on non-time-based robot motion analysis, planning,
representation, and control execution have appeared in the robotic literature. In [7] and
[66], the velocity-versus-position phase space technique is introduced, using harmonic
functions to relate velocity to position along a given geometric path. Phase space concepts
are applied in [8], [9], and [10] to find the optimal joint space trajectory of an arbitrary
robot manipulator that has to follow a prescribed path. In [11], a phase space variable is
used to obtain a dynamic model of a tricycle-type mobile robot, which can then easily be
linearized by feedback. In [12], a phase space approach is applied to the path following
control of a flexible joint robot. In these methods, the phase space technique is used as a
analytical tool to find an optimal time-based trajectory. In fact, phase space (velocity versus
position) has been widely used in physics and in early control theories to describe motion
trajectories.
The real challenge in motion planning is to develop a planning scheme integrated with a
control system that is able to detect and recognize unexpected events on the basis of sensory
information and adjust and modify the base plan at a high rate (same as the dynamic control
loop) to cope with time and location variations in the occurrence of events without
replanning. The first technical difficulty is the development of a mathematical model to
describe the plan so that it is inherently flexible relative to the final task goal and can be
easily adjusted in real time according to task measurements. The second difficulty is the
development of an efficient representation of a sensory information updating scheme that can
be used to transmit the task measurement to the planner at a high rate (same as the control
feedback rate). The third difficulty is the integration of the planner and controller to achieve
a coordinated action and avoid deadlocks or infinite loops.
2 EVENT-BASED PLANNING AND CONTROL
2.1 Introduction
A traditional planning and control system can be described as in Figure 1.1. The core of the
system is the feedback control loop, which ensures the system's stability, robustness, and
performance. The feedback turns the controller into an investigation-decision component.
The planning process, however, is done off line, which is understandable because the task is
usually predefined. The plan is described as a function of time, and the planner gives the
desired input to the system according to the original plan. Therefore it could be considered
as a memory component for storing the predefined plan. All uncertainty and unexpected
events that were not considered in planning are left to the feedback control loop to handle.
If a system works in a complicated environment, the controller alone is not able to ensure
that the system achieves satisfactory performance.
In the past 5 years, considerable effort has been made to improve the planner and
controller in order to handle unexpected or uncertain events, in other words, to achieve
intelligent planning and control. The concept of intelligent control was introduced as an
interdisciplinary name for artificial intelligence and automatic control systems [13]. Saridis
[14] and Saridis and Valavanis [15] proposed a three-layer hierarchy for the controller and
planner. Since then, based on a similar idea, various "intelligent" planning and control
schemes have been developed [16-18]. The basic idea of existing schemes is to add to the

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