Integrating Effective Planning Horizons into an Intelligent Systems

Architecture

J. P. Gunderson and L. F. Gunderson

Gunderson and Gunderson, Inc.

ABSTRACT

One metric of the intelligence of a system is its ability to

perform tasks in the face of dynamic changes to the

environment. This requires that an autonomous system be

capable of responding appropriately to such changes. One such

response is to effectively adapt the allocation of resources from

planning to execution.

By adapting the resource allocation between cognition

and execution, an intelligent system can produce shorter plans

more frequently in environments with high levels of

uncertainty, while producing longer, more complex plans when

the environment offers the opportunity to successfully execute

complex plans.

The effective planning horizon is developed from an

analysis of mathematical models of classic autonomous system

and from current research in cognitive science. Experimental

results are presented showing the performance gain from an

effective planning horizon based system.

From this simplified feedback control model, the

Effective Planning Horizon concept is extended to a more

realistic intelligent system architecture, and the concepts of

bounded rationality, intelligent heuristics and the judgment

analysis "lens model" are shown to be analogs of the effective

planning horizon.

Keywords: Effective Planning Horizon, Interleaved

Plan/Execution, Probabilistic Planning, Intelligent System.

1 INTRODUCTION

The world is not a perfect place, and if intelligent

systems are to function effectively they must be capable

of handling both the uncertainties of the world outside

themselves and those created by their own limitations.

One working definition of intelligence is the ability to

adapt to unexpected failure. Using this definition,

intelligence is defined by the ability of the system to

achieve goals in the face of failure. In order to do this,

the system must have some mechanism to detect that its

current method for satisfying its goals is insufficient, and

to select and apply new methods.

In this paper we present the concept of an effective

planning horizon as a requirement for intelligence. We

start by discussing the reasons that an effective planning

horizon is necessary. We place the model of an effective

planning horizon into a model of an intelligent system.

Then we develop a mathematical definition of the

effective planning horizon. This definition is tested in

the domain of a simulated Autonomous Underwater

Vehicle. In the final sections of the paper we present

arguments to show that the effective planning horizon

concept can easily be transformed into its analogs in

sensing, acting, and goal selection.

2 WHY AN EFFECTIVE PLANNING HORIZON

Why can’t an intelligent system just make one plan?

The answer to this lies in the balance between the

complexity of all environments and the limited

computational resources that any intelligent system can

apply to the problem.

It is obvious that all natural environments and all

but the simplest of synthetic environments are

stochastic. Even in a simple deterministic environment,

the observations made by an entity have a probability

distribution [1]. As demonstrated below, if the

environment is not deterministic, then the longer the

plan needed to meet the goal, the less likely it is to

succeed. However, even in an interleaved planningexecution system, too short a plan length will often lead

to sub-optimal plans.

Alternatively a system could generate all

conceivable plans in advance and maintain those in a

plan library [2]. But, in any realistic domain, it is not

possible for an intelligent system to completely explore

all the possible ramifications of a plan of action in a

realistic time [3]. In addition, to time constraints, there

are memory constraints. In fact for one nominally

intelligent system, only 7±2 objects can be held in

working memory at any one time [4]. This seriously

limits the number of plans that can be considered. This

has led to the concepts of “bounded rationality” in both

biologic [5] and machine based intelligence [6].

Thus, it appears that all intelligent systems (whether

biologic or electronic) must make trade-offs between

cognition and action. There are many mechanisms for

placing bounds on cognition, and in this paper we focus

on the concept of a planning horizon.

3 A MODEL OF AN INTELLIGENT SYSTEM

The model we use is based on the elementary loop of

functioning (E.L.F.) model of Meystel and Albus [6].

This model assigns responsibility for four critical tasks

to independent processes in an iterative - sense, model,
plan, act loop. We have extended this model by adding a

new process, validate. This new process has the ability

to compare the observed result of the previous cycle

with the expected result. It then updates the other

processes with the observed success or failure of the

cycle. This is show graphically in Figure 1.

This model allows for the representation of

intelligence as a semi-lattice. In this representation, the

intelligence of a system is defined by the ability of the

system to perform each of these processes. We utilize

goal satisfaction rates as a primary metric of

intelligence. The intelligence of the system is a 5-tuple

of the intelligence of each of the processes. The

intelligence of each of the processes is incommensurate

with the intelligence of the other processes, thus

establishing the partially ordered set needed for the

lattice.

Figure 1 Extended model of Intelligent Systems

4 INTELLIGENT SYSTEMS

Since the earliest work in machine intelligence, a

concern has been the computational burden required for

‘intelligent’ behavior. With the representation of

planning as search [8] came the exponential growth of

the number of world states explored with the increase in

search depth. The number of world states explored is a

measure of the computational complexity of the

planning process. It has been long accepted that as

uncertainty and dynamism increase in an environment,

the need for more reactive systems also becomes greater

[9]. In recent work, quantitative relationships have been

suggested for the impact of three types of domain

uncertainty on the ability of an autonomous system to

achieve goals.

This work classifies domain uncertainty into three

categories:

Sensor uncertainty;

Effector uncertainty; and,

Uncertainty caused by exogenous events.

These three types of uncertainty have been used in a

simulation system that measures the goal satisfaction of

a simulated maintenance robot under widely varying

levels of each of these types of uncertainty [10].

These results suggest that autonomous systems are

very sensitive to even low levels of uncertainty in the

environment, with overall goal satisfaction dropping to

75% with the introduction of 10% sensor errors. In

addition, this research discovered that the ability to retry

on failure was very effective at allowing the system to

maintain goal satisfaction in the face of all types of

uncertainty. The simulated robot was more robust (i.e.,

able to satisfy goals as the environment changed) when

it used different deliberation and execution mixes in

response to different levels of uncertainty in the

environment.

5 DEFINING THE EFFECTIVE PLANNING

HORIZON

Beginning with early two-player game models, it has

been common to place a limit on the search depth used

to explore options. This was often implemented as an

arbitrary limit on the ply-depth of an alpha-beta search

tree.

In two player games of perfect information, it is

implicitly assumed that if the computational resources

were sufficient, the ply-depth could be increased until a

perfect game analysis was performed. However, when

an intelligent system is playing against the real world,

conditions change. Since there is an inherent variability

in the world, perfect information is impossible. Under

these conditions, there appears to be a hard limit on the

planning horizon – a line beyond which planning is

useless, since it is impossible to know the state of the

world in which the planning is taking place.

We approach the idea of an effective planning

horizon from the perspective of the expected value of

additional planning. What is the value associated with

extending my plan, and what is the likelihood that the

world will be in the state I planned for?

E( plan) = Pr( plan) *Value(Plan) (1)

While solving the exact value of equation 1 may be

impossible, it is possible to make some reasonable

assumptions about the terms, and from these

assumptions draw some conclusions about the

characteristics of the expected value of planning in

dynamic and uncertain domains.

We make three assumptions about the actions in a

plan:

1. The action achieves some state that is needed to

achieve a goal (or goals);
2. Each action has some finite probability of

failure; and,

3. All the actions in the plan must succeed for the

plan to succeed.

Under these assumptions it is clear that a first

approximation of the probability of the plan succeeding

is:

= ∏stepsPr( plan) Pr(Step)

(2)

This can be further simplified by assuming that all

actions have some common probability of success,

reducing Equation 2 to:

length

Pr( plan) = Pr(step)

(3)

Approximating the value associated with a plan of given

length is more problematic, however for any given

domain and set of possible goals to achieve some useful

assumptions can be made.

First, let us envision the complete range of problems

that our intelligent system might be required to solve.

This range could be defined as the cross product of all

possible initial conditions with all possible final states.

Then let us imagine the plans that might be utilized to

transform the world as we find it into the world as we

desire it. Clearly, very few of the (Initial, Final) pairs

can be transformed by plans utilizing a single action. A

few more, perhaps, can be achieved with two-action

plans, more yet by three action plans, and so on. If we

further take the view that we wish the simplest, or most

likely, plan to satisfy our needs, then there will be few

pairs that require 1000 action plans, and fewer still that

require 2000 action plans. If we model the value of a

plan of size N as the number of (Initial, Final) pairs that

can be satisfied by a plan of length N or less, we get a

sigmoidal, or logistic curve. This curve can be closely

approximated with an equation like (3) below:

length

a

Value plan

1 2

( ) 1

+

= − (4)

Finally, combining the two terms into the expected value

of a plan of length N, for a given domain, and task

assignment, we find that the resulting curve has the

characteristic shape shown in Figure 2.

This finding is consistent with the analysis that, there

exists some point beyond which the costs associated

with planning exceed the benefits, which causes the

expected value to decrease. Under the assumptions made

above, we can conclude that there is a range of plans,

which provide the optimal benefit to the deliberative

system. This range is defined as the effective planning

horizon (EPH). If the planning depth is less than the

EPH, the probability that effective solutions will be

produced is too low. If the planning depth exceeds the

EPH, the probability that significant amounts of

computational resources will be expended planning for

situations that never occur is high. If those resources

had been applied more effectively, the rate of goal

satisfaction could increase. However, while this analysis

suggests that it is beneficial to adjust the planning

horizon to the domain and goals of the intelligent

system, it does not provide any mechanism to achieve

this adjustment.

Prediction of Expected Plan Value as a

function of plan length

0

0.5

1

1.5

2

13579

111315

1719

Plan Length

E(Plan)

Figure 2 - Expected Value of Planning

5.1 METHODS OF ADJUSTING THE PLANNING HORIZON

In this paper we investigate a method of selecting an

effective planning horizon, adapted directly from the

notion of placing a limit on the search depth. The

planning system used is an interleaved, probabilityaware, forward chaining planning and execution

environment. It is a general-purpose planner in that all

domain specific information is encoded as part of an

input file. Included in this domain specific information

are naive probabilities of success for the available

actions. The planning system uses this information to

produce the plan with the highest observed probability

of success.

These experiments were run using an autonomous

underwater vehicle domain. In this domain the planner is

embedded in the autonomous underwater vehicle

(AUV). The types of tasks assigned to the AUV include

autonomous navigation, the deployment of monitoring

devices within enemy controlled territory, and avoiding

or escaping detection by enemy Anti-Submarine

Warfare (ASW) surface vessels.

A typical task assignment would be to:

1. Begin from Home base, at the surface, carrying

a deployable monitor;
2. End at Home base, at the surface, with the

monitor deployed at a location just outside the

mouth of the enemy harbor; and,

3. By the way, don’t get detected by any enemy

ships while you do it.

If the system has perfect knowledge, and nothing

changes, this task is a straight forward planning exercise.

However, in this domain, the enemy ship moves while

the AUV is executing its mission and the AUV has

limited sensor range. This forces the planner to develop

a plan, begin to execute it, and respond to failures.

These failures could include finding the ASW ship in its

path or being detected during a move. More complex

failures might involve having to switch goals to escape

detection and then re-target the goal of dropping the

monitor, once it has lost its opponent.

The planning and execution system is interleaved,

so during the execution of actions, it receives feedback

about the actual state of the world (at least those parts

which it can sense) and it compares the actual state with

its expected state. As long as the expected state of the

world and the actual state agree, the system continues to

execute the planned actions. If the states do not match,

several options are available:

1. Continue with the current plan,

2. Develop a new plan to meet the current goals,

3. Re-evaluate the goals, and develop a plan to

meet the new goals, or

4. Do nothing, and hope that the world changes.

After this evaluation, a new action is issued, and the

process begins again. Since the planner is deeply

embedded in the execution loop, strict limits on

computation must be imposed to assure responsive

behavior of the system.

5.2 SEARCH DEPTH CONTROL

Search depth control has been used to limit computation

for as long as planning as search has been used. In

general there are two forms of this control: limiting the

exploration depth directly – such as ply-depth limits, or

plan length limits- and world set limits. In the latter case,

the planning system monitors the total number of

individual worlds explored, and at some pre-determined

limit, stops exploration. This has benefits when coupled

with search control rules which allow the planner to

‘focus attention’ on areas of the plan which might be

more fruitful. The experimental planning system used

here uses this world count form of search depth control.

To explore the impact of limiting search depth on

plan success rates the senario is analyzed under a range

of allowable search depths.

6 EXPERIMENTAL RESULTS

The experiments were designed to answer the question

“For a given domain, and a given task mix, at what point

does it stop paying to plan?” Using the analysis in

Section 5, we measure the marginal value of planning by

measuring the success rate of the plans produced, and

the computational complexity of producing the plan. All

experiments are run on the same interleaved planning

and execution system, coupled with an external

simulator of the domain.

6.1 EXPERIMENT SETUP

The domain used is that of the AUV, described above.

The AUV can navigate in a world of 18 possible

locations, at up to three depths for each location. Any

motion has a risk of causing the AUV to be detected,

however the deeper the AUV the lower the risk, In

addition to movement actions, the AUV can change

depth, deploy a monitor, and cause a tracking ASW

vessel to lose track by going deep and drifting. The

AUV carries one monitor, and the task requires the AUV

to deploy that monitor at a specific location and return to

base undetected.

Figure 3 - Autonomous Underwater Vehicle

domain

The task assigned to the AUV in these experiments

is to travel from home base (Location A) to Location P,

release a monitor, and return to Location L for pickup

(sub-lp10.prob). It has the additional requirement of

remaining undetected during the mission, and should it

be detected it must cause the enemy vessel to lose its

lock before being picked up (Figure 3). The AUV has

six general types of operators to apply:

Table 1 Relative probability of success for the

AUV domain. Failure can mean either the AUV is

detected, the operator fails, or both.

Operator Type A priori Probability

of Success

A

U

R T

G I

B C D

E

S

P Q

O

N

M

L

H

Shallow or Surface

Deep Water
Travel Surface 0.45

Travel Shallow 0.90

Travel Deep 0.95

Change Depth 0.99

Release Monitor 0.99

Drift (can cause opponent to lose

detection)

0.25

For the assigned task, the naïve probability of

success is approximately 0.46, if the plan with highest

probability is selected, or 0.00015 if the plan with the

minimum number of operators is selected. One

additional complicating factor is the behavior of the

ASW vessel. This unit moves around the map in a

random walk, and if it occupies a location it blocks the

AUV from traveling to that location. The location of the

ASW is initially unknown by the AUV, however, the

AUV can sense the presence of the enemy vessel if it

enters or leaves an adjacent location.

A single simulation consists of assigning a task,

executing the mission, and recording the number of

individual world states explored by the planner during

the execution of the mission and the success or failure of

the mission.

Two baseline simulations are initially run. In the

first the planning horizon required for success by a noninterleaved planning system is determined. Since a noninterleaved system must be able to produce a single plan

to meet all the mission goals, the required search depth

is much greater than that required by an interleaved

planner. In this experiment the planning horizon is

increased until the planning system reaches the point

where it can produce a complete, successful plan. This

established the minimum planning horizon for a noninterleaved planner. Since the planner is only allowed to

execute a single cycle, the success rates of this plan

cannot be effectively compared with the success rates of

the interleaved simulations.

The second baseline addresses this problem by

using the planning horizon established by the first

baseline. However, the planning/execution system is run

in interleaved mode, allowing the planner to correct

failures. This second baseline establishes the plan

success rate and the minimum number of world states

required for an interleaved planner operating without a

search depth limit.

The experimental simulations use an interleaved

planning system, with a range of planning horizons. In

all experiments a minimum of 100 independent

simulations are run at each planning horizon. In

interleave mode, the system is allowed to compete up to

five planning/execution cycles. The average number of

world states examined during the each simulation and

the average success rate of the mission are recorded.

6.2 DATA ANALYSIS

The data analysis is straightforward. We calculate the

value of the planning horizon (PH) as:

MegaWorldsExplored

SuccessRate

Value(PH ) = (5)

The value is the success rate over the work expended

(million worlds explored to achieve the success rate).

Baseline 1 established that it is necessary to

examine approximately 13,000 world states, and the

success probability is 0.14 for the non-interleaved

planning system. Due to the interaction with the ASW

vessel, this is significantly below the naïve probability

(0.46). In effect, most of the computational resources

used by the intelligent system are expended planning for

situations that simply do not occur during the execution.

For Baseline 1 the Value(PH) = 10.76.

Using the planning horizon established by Baseline

1, Baseline 2 achieves a success ratio of 0.74. However

it explores 66,000 world states, for a Value(PH) = 11.21.

Interestingly, even though the success ratio increased,

the number of world states explored did so

proportionally. This data is presented in Table 2.

Table 2 Baseline performance of complete

planning system. In Baseline1 a single iteration of the

planning system was allowed, in Baseline2 five

iterations were completed.

Test Worlds Success Rate Value(PH)

Baseline1 13,000 0.14 10.76

Baseline2 66,000 0.74 11.21

The experimental simulation was run with the range

of planning horizons shown in Table 3. Note that the

peak value of value(PH), 68.7 is approximately 6 times

the value achieved by Baseline 2. This shows that at the

effective planning horizon, the planning system is

achieving equivalent success rates with significantly less

computational cost.

Table 3 Table of the computational resources

required for varying planning horizons, the achieved

success rates, and the Value of the invested

computational resources.

Planning

Horizon

Worlds Success Rate Value(PH)

100 9,605 0.02 2.08

150 14,200 0.04 2.81

200 18,854 0.06 3.18

250 12,813 0.88 68.7
300 14,586 0.88 60.3

350 16,717 0.91 54.4

400 19,358 0.89 46.0

450 20,026 0.94 46.9

500 22,315 0.90 40.3

550 22,726 0.93 40.9

600 27,615 0.86 31.1

Sub-lp10 Problem

0

10

20

30

40

50

60

70

80

100200300400500600

Planning Horizon

Value(P

H)

Limited Planning Horizon

Baseline2

Figure 4 - Plotted Value of Effective Planning

Horizons from the AUV problem

In Figure 4, the value of the planning horizon, as

defined in Equation 5 is plotted against the search limit

imposed on the planner. The first three points are

characteristic of planning horizons that are too short to

allow the planning system to find successful plans. The

range from 250 – 350 represents the range of the EPH

where successful plans are being found with minimum

computational investment. The range above 350 is

characteristic of wasted resources, planning for

situations that never occur.

The effective planning horizon is the global

maximum of this curve. It should be noted, that this

figure closely resembles the analytic solution shown in

Figure 2. The “Baseline2” line is the value achieved by

Baseline 2.

It is clear that limiting the planning horizon in

interleaved intelligent systems allows the system to

achieve success rates which are comparable to complete

planning systems, at a fraction of the invested resources.

While the current data results from adjusting the search

limit utilized by the planning system, several other

mechanisms exist to adjust the planning horizon,

including waypoint based planning [11], and the use of

assumptive systems [12], which was successfully

applied during the 1994 AAAI Robot Contest.

7 EXTENSION TO A COMPLETE

INTELLIGENT SYSTEM MODEL

The preceding discussion describes the benefits of an

effective horizon in planning. However, this argument

can be extended to all of the other processes.

Sensing

Validation

Re-Goaling

Acting

In the next section we sketch some ways in which

effective horizons might be achieved for these processes.

Much of this discussion will be derived from work done

on biologic systems.

7.1 EFFECTIVE SENSING HORIZONS

One model of the sensing process can be taken from the

work of Egon Brunswik [1]. In this lens model, shown

graphically in Figure 5, perception can be modeled as a

linear weighted sum:

=

=

n

i

s i i

y w x

1

(6)

Where ys = the judgment of the condition of target s

ye = the actual environmental condition of

the target

n = the total number of cues available to the judgment

maker

xi = value of cue i, where i goes from 1 to n

wi = the weighting of cue i

ye

Distal

(Environmental)

Variable

x1

x2

xn

.

.

.

Ecological

Validity

ys

Subject

Judgment

Cue

Utilization

Validity

Achievement

w1

w2

wn

Figure 5 - The Lens Model of Egon Brunswik

For this process the effective sensing horizon will

be a balance between using so few cues that the

perception in invalid and using so many cues that the

cognitive system is overloaded.

7.2 EFFECTIVE VALIDATING HORIZONS

Validation of the successful completion of a cycle is

critical if the intelligent system is to adapt to unexpected
outcomes. However, given limited sensing ranges, and

long distance effects, it can be resource intensive to do

complete validation. In some cases, the system may have

to develop and achieve complete new sub-goals to

accomplish this phase. Yet, the costs of proceeding

without validation can be extreme. Thus any intelligent

system must strike a balance between the costs and

benefits of validating the world state.

In addition, when things go wrong, an intelligent

system must assess the probable causes of the failure,

and make improvements or the same ineffective actions

will occur again and again. If the mission failed because

a sensor was incorrectly interpreted causing a specific

action to fail, it is not intelligent to expend resources

improving the action. However, correctly attributing the

source of a failure is extremely resource intensive, and

limits must be placed on its application.

7.3 EFFECTIVE GOAL RE-PRIORITIZATION HORIZONS

Intelligent systems do not pursue the same goals at all

times. Consider the mother alligator, who under normal

circumstances has a hair trigger bite reflex. Yet, this

same alligator will carefully carry its young about

cradled in those same jaws. Clearly, this intelligent

system is re-prioritizing its goals in response to changes

in its environment.

However, this ability to re-goal comes at a cost. Regoaling requires the system to use cognitive resources

that could be applied in other ways, and errors in goal

prioritization can reduce the success probabilities of the

system. This is the same dynamic tension that exists in

the selection of an EPH.

7.4 EFFECTIVE ACTION HORIZONS

Just as all biologic intelligent systems have limits on

cognition, there are limits on both the number and range

of actions the system can undertake to achieve a goal,

and the quality of those actions. In biologic systems

“Use it or lose it” applies, yet limited time is available

for practice. With mechanical systems one tends to

think of the range of actions that are available as fixed at

the time of construction, and the quality (probability of

success) as constant. However, as bearings wear out, and

rubber gripping fingers age, the ability of the system to

meet its goals degrades, until new resources are applied.

While self-repair is beyond the current capabilities of

most machine-based intelligent systems, they can

possess the ability to update the reliability of actions to

reflect changes in the system itself.

8 CONCLUSIONS

The focus of this paper is on utilizing limited

computational resources to improve the effectiveness of

intelligent systems. Drawing on research from existing

biological intelligent systems and current research into

machine-based intelligent systems, an analytic definition

of the Effective Planning Horizon was developed.

Success probability in stochastic domains was

presented as the key metric for evaluating intelligent

systems, and several secondary measures including the

expected value of planning, and plan value as a function

of computational load were introduced as supporting

concepts for the Effective Planning Horizon.

The EPH is a measure of the dynamic and variable

nature of the environment, and the goals and limitations

of the intelligent system. From these characteristics it is

possible to establish a horizon beyond which additional

planning is ineffective.

A simulated domain was presented which is

representative of the types of tasks we expect deployed

intelligent systems to undertake, and using a planning

and execution system designed for these demanding

domains, experimental data was collected. The data

collected demonstrates that it is possible to achieve the

same levels of success as the computationally expensive

complete exploration of a plan space, at significantly

lower cost. This lowered cost translates into lowered

demands on the system, or increased speed of execution

by the intelligent system, which can be crucial design

requirements of future embedded intelligent systems.

Finally, the same principles which led to the

formalization of the Effective Planning Horizon were

applied to the other processes in feedback control theory

based intelligent systems, suggesting other mechanisms

that can be used to improve goal satisfaction by

intelligent systems.

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