Communicating Branching Plans for Human-Agent Decision Making
Abstract
Recent advances in visualisation technologies have opened up new possibilities for human-agent communication.
For systems where agents use automated planning, visualisation of agent planned actions can play an important role in allowing human users to understand agent intent and to help de- cide when control can be delegated to the agent or when they need to be involved.
We are interested in application areas where branched plans are required, due to the typical uncertainty experienced.
Our focus is how best to communicate, using visualisation, the key information content of a branched plan.
It is important that such visualisations communicate the complexity and variety of the possible executions captured in a branched plan, whilst also connecting to the practitioner’s understanding of the problem.
Thus we have developed an approach that: generates the complete branched plan, to be able to provide a full picture of its complexity; a mechanism to select a subset of diverse traces that characterise the possi- ble executions; and an interface that uses 3D visualisation to communicate details of these characterising execution traces to practitioners.
Using this interface, we conducted a study evaluating the impact of different modes of presentation on user understanding.
Our results support our expectation that visualisation of characterising branched plan execution traces increases user understanding of agent intention and range of plan execution possibilities.
Introduction
In systems requiring joint human and AI agent decision making there is a need for human users to understand the intentions of agents, along with the agent rationale for different decisions.
This requires the AI agent to be able to explain its reasoning to the human, something which remains a signiﬁcant challenge (Fox, Long, and Magazzeni 2017; Miller 2019).
This is reﬂected in initiatives like DARPA ’s Explainable AI Program (Gunning and Aha 2019) and events such as ( EXTRAAMAS 2020; XAI 2020; XAIP 2020).
For those application domains where AI agents (virtual or robot) use automated planning to control behaviour, the challenge is how to clearly communicate to the human the intentions of the agent which are encapsulated in its generated plans.
It has been shown that 3D visualisation and simulation of agent plans can help human user understanding of agent intent (Chakraborti et al. 2018; Zolotas and Demiris 2019).
However, generating understandable visualisations is challenging because a plan sequence already implicitly encapsulates the balance made between dependency, constraint and choice, as well as the implied implementation of the plan steps themselves.
This challenge is exacerbated when more complex plan structures are required, such as branched plans for partially observable domains due to inherent uncertainty.
In such contexts, the advantage of branched plans is that they allow efﬁcient action sequences to be captured for each of the possible worlds that might occur and thus capture a diverse space of alternative solutions.
However, the size of the space of possible executions makes it challenging to communicate this to a practitioner, along with the intentions of the agent whose behaviour is underpinned by the plan (e.g.,
Figure 1, the branched plan used in our evaluation).
Thus, the problem we address in this work is how to communicate key information content of branched agent plans to human decision makers.
This comprises: (i) how to communicate the complexity and variety of the possible executions captured within a branched plan; (ii) how to select subsets of execution traces that capture the scope of possibilities in branching plan structures to communicate to practitionerssomething which is essential, as it is not desirable, or possible, to present all linearisations of a branched plan; and (iii) how to communicate the complexity of the branched plan and the selected execution traces, in ways that connect with their understanding of the problem.
To address these sub-problems, we have developed an approach that: (i) generates a full branched plan by branching on sensor action values and emphasizes key action points; (ii) selects subsets of execution traces that capture the scope of possibilities in branching plan structures; and (iii) demonstrated increased user understanding of agent intention and plan execution possibilities resulting from characterising diverse trace informed visualisation.
The contribution of this work lies in the selection and adaptation of appropriate visualisations for human-agent branched plan communication.
Background
A partially observable planning problem, e.g., (Bonet and Geffner 2011), can be deﬁned by a tuple, P = (cid:104) F, A, M, I, G (cid:105) , with ﬂuents F , actions A , sensor model M , the initial state clauses I , over F , and goal, G .
The clauses of the initial state provide both the known positive and negative literals, as well as constraints over the currently un- known parts of the initial state.
An action is deﬁned by its preconditions and effects.
An action is applicable if its preconditions are satisﬁed in the agent’s partial state and the application of an action causes its effects to be applied to the agent’s current state.
Sensing actions are triggered whenever they become applicable and their observations update the agent’s state.
A solution to the problem is a branched plan, π , which has both deterministic action nodes and branching nodes, such that every branch of the tree results in a goal state.
The branching nodes are labelled with a proposition and have branches for each of the possible valuations.
The application of a branched plan requires traversing the plan tree applying the deterministic actions and selecting the appropriate branches by detecting the value of the proposition in the environment.
Partially observable planning problems, P , with a certain subset of exclusive-or knowledge can be compiled into deterministic classical planning problem, P DET , following the approach in (Bonet and Geffner 2011).
A key aspect of this encoding is that each sensing action is replaced by a pair of standard actions: one captures the effect of the sensor in the case that its proposition holds in the world and the other for the negative case.
As a result the valuation of the sensors becomes a choice for the planner to make.
A solution for
P DET is therefore an optimistic and partial solution for P , which we denote, π optimistic .
Virtual Construction Domain
As a test bed for this work we have developed a virtual construction domain and used this setting for the development of the 3D visual interface.
The planning domain captures various typical aspects of construction, including preparation, movement of robots and materials and the actual construction itself.
Scenarios feature uncertainty in both the required preparation of the ground to permit construction and movement, and in the integrity of building materials.
The planning domain model includes actions for movement, block-placing and sensing actions for identifying debris, such as rubble and rocks, in the environment.
We have also developed a virtual environment for presenting 3D visualisations of branched construction plans to practitioners.
We use this as a running example throughout the paper
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Branched Plan Generation
We are interested in application domains that require branched plans, due to the uncertainty that is experienced.
Branched plans allow efﬁcient action sequences to be captured for each of the possible worlds that might be encountered during execution (with respect to the model).
As a result branched plans can capture a diverse space of alternative solution sequences.
Moreover sensor values and traces are not associated with likelihoods, leading to an interpretation that each of the executions is as likely as any other.
Given our focus in this work
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we require a complete branching tree structure to be generated, so that we can provide a practitioner with a full picture of the complexity of the branched plan.
Our approach to this generation builds on the K-Replanner (Bonet and Geffner 2011): an online
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MOVEl-4-0-5 MOVEl-5-0MOVEl-7-0-5 MOVEl-7-0-4 FINISH
BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-7-0MOVEl-6-0-5 BUILDl-6-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH MOVEl-2-0-5 Rubble atl-3-0-5? CLEARl-3-0-5 TRUEMOVEl-3-0-5FALSE
Rubble atl-3-0-5?FALSETRUE BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0MOVEl-7-0Rock atl-2-0-1?
MOVEl-1-0-2 FALSE MOVEl-3-0-2 TRUE
MOVEl-6-0-5 BUILDl-6-0MOVEl-7-0-5 MOVEl-7-0-4 FINISH
BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-4-0-5 MOVEl-5-0Rubble atl-3-0-2?
Rock atl-3-0-2? FALSE
Rock atl-3-0-2?
TRUE
Rock atl-2-0-1?FALSE MOVEl-2-0-1 TRUE MOVEl-2-0-1 TRUE
Rock atl-2-0-1?FALSE
MOVEl-3-0-5 MOVEl-4-0MOVEl-2-0-5 Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE MOVEl-4-0-5MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0MOVEl-6-0-5 MOVEl-5-0CLEARl-3-0-5 MOVEl-3-0-5 MOVEl-4-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0BUILDl-5-0-4..
MOVEl-3-0-5 MOVEl-4-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0FINISH
MOVEl-4-0-1 MOVEl-4-0-2 MOVEl-4-0MOVEl-5-0-5 BUILDl-5-0-4..
FINISH
MOVEl-2-0FINISH MOVEl-7-0MOVEl-3-0-0 MOVEl-2-0-0 CLEARl-3-0-5 MOVEl-3-0-5 MOVEl-7-0-4 FINISH
MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0MOVEl-2-0-5 Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUEMOVEl-4-0-5MOVEl-3-0FINISH
BUILDl-5-0-4..
Rubble atl-2-0-5?
MOVEl-2-0-5FALSECLEARl-2-0-5TRUERubble atl-3-0-5?
BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0MOVEl-5-0MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-7-0MOVEl-1-0MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-3-0MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0MOVEl-7-0-4 FINISH
FALSECLEARl-3-0-5TRUE
BUILDl-5-0-4..
BUILDl-5-0-4.. MOVEl-6-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0MOVEl-4-0-1 MOVEl-4-0-2 Rubble atl-4-0-3?
Rubble atl-3-0-2?
FALSERubble atl-3-0-2?
TRUE MOVEl-4-0-3 FALSEMOVEl-4-0-3TRUECLEARl-4-0-3FALSECLEARl-
[Table]
0MOVEl-4-0BUILDl-6-0MOVEl-4-0-
Rubble atl-5-0-3?
CLEARl-5-0-3TRUEMOVEl-5-0-3FALSE
MOVEl-7-0-5 MOVEl-7-0MOVEl-4-0-2 Rubble atl-4-0-3?
CLEARl-4-0-3TRUEMOVEl-4-0-3FALSE MOVEl-4-0CLEARl-1-0-5 MOVEl-1-0MOVEl-2-0-0 MOVEl-3-0-0 MOVEl-4-0-0 MOVEl-2-0MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-3-0-5 CLEARl-3-0-5 Rubble atl-3-0-5?FALSETRUE MOVEl-2-0-5 CLEARl-2-0-5 Rubble atl-2-0-5?FALSETRUE MOVEl-1-0-5 Rubble atl-0-0-5?
MOVEl-0-0MOVEl-7-0-5 MOVEl-7-0MOVEl-5-0FINISH
MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
FINISH
MOVEl-7-0-4 FINISH
MOVEl-2-0MOVEl-3-0MOVEl-1-0-5 Rubble atl-2-0-5?
MOVEl-2-0-5FALSECLEARl-2-0-5TRUE
MOVEl-4-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-5-0-5 MOVEl-7-0-4 FINISH MOVEl-7-0-3 BUILDl-6-0-3 MOVEl-6-0MOVEl-7-0-5 MOVEl-7-0-4 FINISH
FINISH MOVEl-7-0-4 FALSECLEARl-3-0-5TRUE
FINISH
MOVEl-7-0-4 FINISH
MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-3-0MOVEl-4-0-5 MOVEl-5-0MOVEl-7-0-5 MOVEl-7-0MOVEl-7-0-5 MOVEl-7-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-7-0-3 MOVEl-7-0-4 FINISH
MOVEl-7-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
Rock atl-4-0-2? MOVEl-4-0-2 FALSE MOVEl-2-0-2TRUE MOVEl-1-0-2 CLEARl-3-0-5 MOVEl-3-0-5 MOVEl-4-0Rubble atl-5-0-3? MOVEl-5-0-3FALSECLEARl-5-0-3TRUE BUILDl-5-0-4..MOVEl-5-0Rubble atl-3-0-5?MOVEl-2-0CLEARl-1-0MOVEl-4-0Rubble atl-3-0-5?TRUEMOVEl-3-0-5FALSE MOVEl-4-0Rock atl-3-0-2?
Rock atl-
[Table] [Table]
FALSE MOVEl-
[Table]
1 TRUE
[Table] [Table]
[Table]
FINISH MOVEl-7-
[Table]
[Table]
MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-7-0-5 MOVEl-7-
[Table]
[Table]
MOVEl-7-0-5 BUILDl
[Table]
[Table] [Table]
MOVEl
[Table]
[Table] [Table]
5FALSECLEARl
[Table]
5TRUE MOVEl-
[Table] [Table]
[Table]
MOVEl
[Table]
MOVEl-
[Table] [Table]
[Table] [Table]
BUILDl-
[Table]
MOVEl
[Table] [Table]
MOVEl-
[Table]
[Table] [Table]
BUILDl-
[Table]
MOVEl
[Table]
[Table] [Table]
[Table]
-3-0-5TRUE MOVEl-4-0-5MOVEl-3-0BUILDl-5-0-4.. MOVEl-6-0Rubble atl-5-0-3? MOVEl-5-0-3FALSECLEARl-5-0-3TRUE BUILDl-5-0-4..MOVEl-5-0MOVEl-7-0-4 FINISH MOVEl-7-0FALSE CLEARl-2-0-5 TRUE MOVEl-2-0-5 Rubble atl-3-0-5?FALSE CLEARl-3-0-5TRUE MOVEl-3-0BUILDl-6-0-5 MOVEl-6-0-5 BUILDl-5-0-4..
MOVEl-7-0-4 FINISH
Rubble atl-3-0-5?
MOVEl-3-0-5 FALSECLEARl-3-0-5TRUE MOVEl-4-0-5MOVEl-3-0-5 MOVEl-6-0-5 BUILDl-6-0MOVEl-2-0Rubble atl-1-0-5?
MOVEl-1-0-5FALSE CLEARl-1-0-5TRUE Rubble atl-2-0-5?
MOVEl-1-0MOVEl-7-0-4 FINISH
MOVEl-2-0-5 Rubble atl-3-0-5?
FALSETRUE
MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0MOVEl-5-0-5 MOVEl-7-0-4 FINISH
MOVEl-7-0-4 MOVEl-7-0-5 BUILDl-6-0-5 MOVEl-6-0-5 BUILDl-5-0-4.. MOVEl-5-0-5 MOVEl-4-0-5 MOVEl-3-0FINISH MOVEl-7-0MOVEl-0-0-5 Rubble atl-1-0-5?
CLEARl-1-0-5TRUE MOVEl-1-0-5FALSE
MOVEl-2-0-5 Rubble atl-3-0-5?FALSECLEARl-3-0-5TRUE
FINISH MOVEl-7-0-4 MOVEl-7-0-5 BUILDl-6-0-5 MOVEl-6-0-5 BUILDl-5-0-4.. MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 CLEARl-3-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-3-0MOVEl-0-0-5FALSE Rubble atl-1-0-5?
MOVEl-6-0MOVEl-7-0-4 FINISH
MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-4-0-5 MOVEl-3-0-5 CLEARl-3-0-5 Rubble atl-3-0-5?FALSETRUE MOVEl-2-0FINISH MOVEl-7-0MOVEl-1-0-2 Rubble atl-2-0-2?
Rock atl-2-0-2?
TRUE
Rock atl-2-0-2? FALSE
FINISH MOVEl-7-0-4 MOVEl-7-0-5 BUILDl-6-0-5 MOVEl-6-0-5 BUILDl-5-0-4..
BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-1-0-1 TRUE CLEARl-2-0-2FALSE MOVEl-2-0MOVEl-7-0-3 MOVEl-7-0-4 FINISH MOVEl-6-0-3 BUILDl-6-0-3 TRUEMOVEl-5-0-3FALSE BUILDl-5-0-4..
MOVEl-2-0-5 Rubble atl-3-0-5?
[Table]
MOVEl-1-0-5FALSECLEARl-1-0-5TRUE Rubble atl-2-0-5? MOVEl-1-0-5 Rubble atl-2-0-5?
MOVEl-2-0-5 FALSE CLEARl-2-0-5 TRUE Rubble atl-3-0-5?
BUILDl-5-0-4.. MOVEl-5-0MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-0-0-5 Rubble atl-1-0-5?TRUEMOVEl-1-0-5FALSE
BUILDl-5-0-4..
FALSE CLEARl-2-0-5TRUE MOVEl-2-0-5 Rubble atl-3-0-5?
CLEARl-3-0-5TRUEMOVEl-3-0-5FALSE MOVEl-3-0-5 MOVEl-4-0FINISH
BUILDl-6-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0MOVEl-7-0-4 FINISH
MOVEl-6-0-5 BUILDl-5-0-4..
Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE MOVEl-4-0-5MOVEl-3-0MOVEl-6-0MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0MOVEl-7-0Rubble atl-2-0-5?TRUEMOVEl-2-0-5FALSE Rubble atl-2-0-5?
MOVEl-2-0-5FALSECLEARl-2-0-5TRUERubble atl-3-0-5?MOVEl-2-0MOVEl
[Table]
-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-0-0-5 Rubble atl-1-0-5?
MOVEl-1-0-5FALSECLEARl-1-0-5TRUE
MOVEl-0-0-3 Rubble atl-0-0-4?
CLEARl-0-0-4 TRUE
MOVEl-0-0-4 FALSE
MOVEl-7-0MOVEl-0-0CLEARl-3-0-5 MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0Rubble atl-2-0-5?
MOVEl-2-0-5 Rubble atl-3-0-5?TRUEMOVEl-3-0-5FALSE MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0BUILDl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
BUILDl-5-0-4.. MOVEl-6-0MOVEl-7-0-5 MOVEl-7-0MOVEl-4-0MOVEl-2-0MOVEl-5-0MOVEl-2-0-5 Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE
CLEARl-1-0-5 MOVEl-1-0-5 Rubble atl-2-0-5?
MOVEl-2-0-5FALSECLEARl-2-0-5TRUE Rubble atl-3-0-5?
Rock atl-0-0-5? CLEARl-0-0-5FALSE MOVEl-0-0-5 Rubble atl-1-0-5? TRUE
MOVEl-1-0-5FALSE
MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-
[Table]
-5 MOVEl-7-0Rubble atl-3-0-5?
MOVEl-4-0-5 MOVEl-5-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 MOVEl-6-0-5 FINISH
MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
CLEARl-3-0-5 MOVEl-3-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-2-0-5FALSECLEARl-2-0-5TRUE Rubble atl-3-0-5?
MOVEl-2-0MOVEl-5-0FINISH Rubble atl-2-0-5?
CLEARl-2-0-5 TRUEMOVEl-2-0-5FALSE
BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0FINISH
MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-3-0-5 MOVEl-4-0MOVEl-7-0-5 MOVEl-7-0FINISH
MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-7-0-5 MOVEl-7-0-4 FINISH MOVEl-6-0-5 BUILDl-6-0MOVEl-3-0-5FALSECLEARl-3-0-5TRUEMOVEl-4-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 MOVEl-5-0-5 BUILDl-5-0-4..
FINISH
MOVEl-5-0-5 CLEARl-3-0-5 MOVEl-3-0-5 MOVEl-4-0FINISH
MOVEl-3-0-5 MOVEl-4-0MOVEl-7-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0MOVEl-4-0-5 MOVEl-5-0MOVEl-7-0-4 FINISH
BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0-4 FINISH BUILDl-5-0-4.. MOVEl-6-0-3 Rubble atl-5-0-3?
CLEARl-5-0-3 TRUEMOVEl-5-0-3FALSE
MOVEl-4-0MOVEl-3-0-5FALSECLEARl-3-0-5TRUE
Rubble atl-3-0-5?FALSECLEARl-3-0-5TRUE
MOVEl-5-0MOVEl-3-0FINISH MOVEl-3-0-5 MOVEl-4-0MOVEl-7-0-3 MOVEl-7-0-4 FINISH BUILDl-6-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0CLEARl-5-0-3TRUEMOVEl-5-0-3FALSE
FINISH MOVEl-7-0-4 MOVEl-6-0-3 BUILDl-5-0-4.. MOVEl-5-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0MOVEl-2-0Rubble atl-3-0-5?
MOVEl-3-0-5 FALSECLEARl-3-0-5TRUE MOVEl-3-0-5 MOVEl-2-0-5 MOVEl-4-0-5 MOVEl-5-0-5 MOVEl-1-0-5 Rubble atl-2-0-5?FALSECLEARl-2-0-5TRUE
MOVEl-6-0-5 BUILDl-6-0FINISH MOVEl-7-0-4 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-7-0-5 BUILDl-6-0FALSECLEARl-3-0-5TRUE MOVEl-3-0FINISH MOVEl-7-0-4 MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4.. MOVEl-4-0-5 MOVEl-5-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-7-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0MOVEl-1-0-5 Rubble atl-2-0-5?
FALSECLEARl-2-0-5TRUE
MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
Rubble atl-2-0-5?
TRUEMOVEl-2-0-5FALSE
MOVEl-6-0-5 BUILDl-6-0CLEARl-1-0-5 MOVEl-1-0MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-7-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 MOVEl-6-0FINISH
MOVEl-5-0-5 MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-6-0-
[Table]
4.. MOVEl-5-0MOVEl-7-0-4 FINISH
CLEARl-0-0-3 MOVEl-0-0Rubble atl-2-0-5?
Rubble atl-2-0-5?
MOVEl-2-0-5FALSE CLEARl-2-0-5TRUE
MOVEl-0-0MOVEl-1-0MOVEl-0-0MOVEl-4-0Rubble atl-3-0-5?
CLEARl-3-0-5TRUEMOVEl-3-0-5FALSE BUILDl-5-0-4..
MOVEl-3-0-5 MOVEl-4-0Rubble atl-0-0-5?
TRUE
Rock atl-0-0-5?FALSE FALSE MOVEl-0-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-7-0-4 MOVEl-7-0-5 BUILDl-6-0MOVEl-6-0BUILDl-5-0-4..
MOVEl-6-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-1-0-1 TRUE MOVEl-2-0-2FALSE
CLEARl-2-0-2FALSE MOVEl-1-0-1 TRUE MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0MOVEl-7-0-5 MOVEl-7-0FINISH
MOVEl-7-0-4 FINISH
MOVEl-7-0-4 FINISH
MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0FALSETRUE
Rubble atl-2-0-5?
Rubble atl-4-0-3?
MOVEl-4-0-3 FALSECLEARl-4-0-3TRUE Rubble atl-5-0-3?MOVEl-4-0-3 MOVEl-4-0Rubble atl-5-0-3?
CLEARl-5-0-3 TRUEMOVEl-5-0-3FALSE MOVEl-5-0-3 BUILDl-5-0-4.. BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0MOVEl-2-0-5 Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE
Rock atl-2-0-1?
TRUE FALSE
MOVEl-4-0-5MOVEl-3-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0Rubble atl-2-0-5?FALSECLEARl-2-0-5TRUE MOVEl-7-0-3 MOVEl-7-0FINISH
MOVEl-2-0-5 Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE MOVEl-4-0-5MOVEl-3-0-5MOVEl-4-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0FINISH
MOVEl-7-0MOVEl-7-0MOVEl-1-0MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE MOVEl-4-0-5MOVEl-3-0MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0Rubble atl-1-0-5?
BUILDl-6-0MOVEl-2-0-5 Rubble atl-3-0-5?
FALSECLEARl-3-0-5TRUE CLEARl-2-0-5 Rubble atl-2-0-5?
FALSETRUE MOVEl-1-0-5 CLEARl-1-0-5 Rubble atl-1-0-5? TRUE
MOVEl-1-0-5FALSE MOVEl-0-0-5 CLEARl-0-0-5 MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0MOVEl-4-0BUILDl-5-0-4..
MOVEl-4-0MOVEl-6-0-5 BUILDl-6-0MOVEl-6-0MOVEl-1-0-5 Rubble atl-2-0-5?FALSE CLEARl-2-0-5 TRUE CLEARl-1-0MOVEl-2-0-5 Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUEMOVEl-4-0-5MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-5-0MOVEl-7-0MOVEl-2-0-5 Rubble atl-3-0-5?
CLEARl-3-0-5TRUEMOVEl-3-0-5FALSE
MOVEl-4-0-5 MOVEl-5-0MOVEl-5-0-5 BUILDl-5-0-4..
CLEARl-2-0BUILDl-5-0-4..
Rubble atl-2-0-5?TRUEMOVEl-2-0-5FALSE Rubble atl-3-0-5?
MOVEl-4-0-5 MOVEl-5-0-5 MOVEl-1-0MOVEl-4-0Rubble atl-2-0-5?
CLEARl-2-0-5 TRUEMOVEl-2-0-5FALSE Rubble atl-3-0-5?
MOVEl-7-0-3 MOVEl-7-0-4 FINISH
MOVEl-3-0MOVEl-3-0-5 MOVEl-4-0MOVEl-4-0MOVEl-7-0-5 MOVEl-7-0-4 FINISH
BUILDl-6-0MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
BUILDl-6-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-4-0-5 MOVEl-5-0MOVEl-0-0-5 Rubble atl-1-0-5?TRUEFALSE
MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-2-0BUILDl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0-4 FINISH
BUILDl-6-0-5 MOVEl-7-0FINISH MOVEl-7-0BUILDl-5-0-4.. BUILDl-6-0-5 MOVEl-7-0CLEARl-3-0-5 MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0FALSECLEARl-2-0-5TRUE
MOVEl-5-0Rubble atl-3-0-5?TRUEMOVEl-3-0-5FALSE MOVEl-4-0BUILDl-5-0-4.. FALSECLEARl-3-0-5TRUE MOVEl-3-0MOVEl-4-0MOVEl-1-0-5 Rubble atl-2-0-5?TRUE MOVEl-2-0-5FALSE
FINISH
Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE MOVEl-4-0-5MOVEl-3-0MOVEl-4-0MOVEl-1-0FALSETRUE
BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0FINISH
MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0-4 MOVEl-6-0-3 MOVEl-5-0-3 BUILDl-5-0-4..
BUILDl-6-0-3 MOVEl-7-0MOVEl-6-0MOVEl-1-0-5 Rubble atl-2-0-5?FALSETRUE
MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0-4 FINISH MOVEl-6-0FINISH
BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0Rubble atl-0-0-4?
FALSE CLEARl-0-0-4 TRUE MOVEl-0-0FINISH
CLEARl-5-0-3 MOVEl-5-0-3 BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0FINISH
MOVEl-5-0-3 BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0FINISH MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0CLEARl-3-0-5 TRUEMOVEl-3-0-5FALSE
BUILDl-5-0-4.. MOVEl-6-0FINISH
MOVEl-2-0-2 MOVEl-2-0BUILDl-5-0-4.. MOVEl-6-0Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE MOVEl-4-0-5MOVEl-3-0-
[Table]
-3-0-5TRUE MOVEl-3-0FINISH
MOVEl-0-0Rock atl-4-0-2?
MOVEl-7-0-5 MOVEl-7-0-4 FINISH
CLEARl-5-0-3 MOVEl-5-0-3 BUILDl-5-0-4..
BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0CLEARl-1-0-5 Rubble atl-1-0-5?TRUEMOVEl-1-0-5FALSE Rubble atl-2-0-5?
MOVEl-1-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4..
MOVEl-4-0-5 MOVEl-5-0-5 MOVEl-0-0-5 Rock atl-0-0-5?FALSE
BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH FINISH MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-7-0-4 FINISH
MOVEl-3-0-5 MOVEl-4-0MOVEl-7-0MOVEl-7-0-5 MOVEl-7-0MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0Rock atl-0-0-5?FALSE
TRUEMOVEl-3-0-5FALSE MOVEl-4-0MOVEl-5-0-3 BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0-4 FINISH BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0FINISH
MOVEl-6-0-5 BUILDl-6-0FINISH
BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0MOVEl-7-0-4 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-5-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0FINISH
MOVEl-7-0-4 FINISH
FINISH
MOVEl-7-0MOVEl-7-0-5 MOVEl-7-0MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 CLEARl-5-0-3 MOVEl-5-0-3 BUILDl-5-0-4.. MOVEl-4-0-3 Rubble atl-5-0-3?FALSETRUE
MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-7-0-5 MOVEl-7-0-4 FINISH MOVEl-4-0-5 MOVEl-5-0MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0FINISH MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-4-0MOVEl-5-0MOVEl-7-0-4 MOVEl-7-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-7-0FINISH
MOVEl-4-0CLEARl-1-0-5TRUE MOVEl-1-0-5FALSE
FINISH
MOVEl-1-0-5 Rubble atl-2-0-5?
MOVEl-7-0-5 MOVEl-7-0FINISH
MOVEl-2-0-5 Rubble atl-3-0-5?
CLEARl-3-0-5TRUEMOVEl-3-0-5FALSE
CLEARl-2-0-5 MOVEl-2-0-5 Rubble atl-3-0-5?
MOVEl-3-0-5 MOVEl-4-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0CLEARl-1-0-5 MOVEl-1-0-5 Rubble atl-2-0-5?
MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-5-
[Table]
MOVEl-7-0-5 MOVEl-7-0MOVEl-2-0MOVEl-7-0-4 FINISH
MOVEl-4-0-5MOVEl-3-0MOVEl-3-0-5 CLEARl-3-0MOVEl-7-0-4 FINISH
BUILDl-6-0-5 MOVEl-7-0MOVEl-7-0-4 FINISH
MOVEl-7-0-4 FINISH
MOVEl-7-0-5 MOVEl-7-0-4 FINISH Rubble atl-3-0-5?FALSETRUE MOVEl-2-0MOVEl-7-0-4 MOVEl-7-0-3 BUILDl-6-0-3 MOVEl-6-0-3 CLEARl-5-0-3 MOVEl-5-0-3 Rubble atl-5-0-3?
FALSETRUE MOVEl-4-0MOVEl-4-0-3 Rubble atl-5-0-3?TRUEFALSE
FINISH
FINISH MOVEl-7-0-4 MOVEl-7-0-3 BUILDl-6-0-3 MOVEl-6-0-3 BUILDl-5-0-4.. MOVEl-5-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-0-0-4 Rubble atl-0-0-5?TRUE Rock atl-0-0-5?FALSE
BUILDl-6-0-5 MOVEl-7-0MOVEl-7-0Rubble atl-1-0-5?
MOVEl-7-0MOVEl-2-0-5 Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE MOVEl-3-0MOVEl-7-0-4 FINISH BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-6-0MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-6-0CLEARl-0-0BUILDl-6-0Rubble atl-2-0-5?
MOVEl-7-0-3 MOVEl-7-0-4 FINISH
CLEARl-5-0-3TRUEMOVEl-5-0-3FALSE BUILDl-5-0-4..
MOVEl-5-0-3 BUILDl-5-0-4..
BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0MOVEl-7-0-4 FINISH
MOVEl-7-0MOVEl-5-0BUILDl-6-0MOVEl-5-0-3 BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0-3 BUILDl-6-0-5 MOVEl-7-0MOVEl-7-0-4 FINISH CLEARl-5-0-3 TRUEMOVEl-5-0-3FALSE MOVEl-7-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH BUILDl-5-0-4.. MOVEl-6-0BUILDl-5-0-4..
BUILDl-5-0-4..
MOVEl-4-0-1 MOVEl-4-0-2 MOVEl-4-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-6-0-5 BUILDl-6-0-
MOVEl-7-0MOVEl-1-0-
[Table]
-4 MOVEl-6-0-5 BUILDl-5-0-4.. MOVEl-5-0-5 MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0FINISH BUILDl-5-0-4.. MOVEl-6-0MOVEl-5-0MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 CLEARl-3-0MOVEl-7-0-4 FINISH
BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-7-0-4 FINISH
MOVEl-3-0-5 MOVEl-4-0Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE MOVEl-4-0-5MOVEl-3-0Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE MOVEl-4-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-5-0-5 CLEARl-3-0-5 MOVEl-3-0-5 MOVEl-4-0MOVEl-6-0-5 BUILDl-6-0MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-3-0Rubble atl-3-0-5?
CLEARl-3-0-5FALSETRUE
FALSECLEARl-3-0-5TRUE MOVEl-3-0MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-7-0-4 FINISH
MOVEl-4-0MOVEl-5-0-5 BUILDl-5-0-4..
FINISH MOVEl-7-0-4 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-6-0MOVEl-5-0-5 MOVEl-5-0-5 MOVEl-4-0MOVEl-7-0-5 MOVEl-7-0FINISH
MOVEl-4-0-5 MOVEl-5-0MOVEl-3-0-5FALSECLEARl-3-0-5TRUE
MOVEl-7-0-5 MOVEl-7-0-4 FINISH
BUILDl-5-0-4.. MOVEl-6-0FALSECLEARl-3-0-5TRUE MOVEl-3-0MOVEl-0-0MOVEl-6-0-5 BUILDl-6-0BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0-4 MOVEl-6-0-3 BUILDl-5-0-4.. MOVEl-5-0-3 CLEARl-5-0BUILDl-5-0-4..
MOVEl-4-0-3 Rubble atl-5-0-3?TRUEMOVEl-5-0-3FALSE CLEARl-4-0-3 FALSETRUE
MOVEl-0-0FINISH
Rubble atl-3-0-5?
MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0FALSE MOVEl-3-0-2 TRUE
BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
FALSE CLEARl-0-0-5TRUE MOVEl-0-0-5 Rubble atl-1-0-5?
CLEARl-1-0-5TRUE MOVEl-1-0-5FALSE
MOVEl-4-0MOVEl-2-0-5 CLEARl-2-0-5 Rubble atl
[Table]
-5-0-4.. MOVEl-6-0BUILDl-6-0-3 MOVEl-7-0MOVEl-5-0-3 BUILDl-5-0-4..
FINISH
BUILDl-5-0-4.. MOVEl-6-0BUILDl-6-0-5 MOVEl-6-0-5 MOVEl-5-0CLEARl-3-0-5 MOVEl-4-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl
[Table]
[Table]
BUILDl-5-0-4.. MOVEl-5-0MOVEl-7-0TRUEMOVEl-3-0-5FALSE
FINISH
MOVEl
[Table] [Table]
BUILDl
[Table]
FINISH
MOVEl-
[Table] [Table]
MOVEl
[Table]
Rock
[Table]
[Table]
MOVEl-7-0-5 MOVEl-7-0-4 FINISH BUILDl-6-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-5-0-5 MOVEl-4-0MOVEl-2-0-0 MOVEl-3-0MOVEl-7-0-5 MOVEl-7-0MOVEl-4-0MOVEl-7-0-3 MOVEl-7-0-4 FINISH MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-5-0-3 BUILDl-5-0-4..
MOVEl-6-0CLEARl-5-0-3 Rubble atl-5-0-3?TRUEMOVEl-5-0-3FALSE
BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH MOVEl-4-0-5 MOVEl-5-0-5 MOVEl-3-0-5 MOVEl-4-0MOVEl-3-0-0 MOVEl-4-0MOVEl-0-0Rubble atl-4-0-3?
FALSECLEARl-4-0-3TRUE MOVEl-4-0BUILDl-5-0-4..
Rock atl-0-0-5?FALSE
Rubble atl-0-0-4?
FALSE CLEARl-0-0-4TRUE MOVEl-0-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 MOVEl-6-0-5 FINISH MOVEl-7-0-4 MOVEl-7-0-5 BUILDl-6-0-5 BUILDl-5-0-4.. MOVEl-5-0-5 MOVEl-4-0MOVEl-3-0-5 MOVEl-7-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH MOVEl-2-0-5 Rubble atl-3-0-5?FALSECLEARl-3-0-5TRUE MOVEl-3-0-5 MOVEl-4-0FINISH
MOVEl-5-0MOVEl-5-0-5 MOVEl-3-0-5 MOVEl-4-0-5 CLEARl-3-0-5 Rubble atl-3-0-5?TRUEMOVEl-3-0-5FALSE MOVEl-4-0FINISH MOVEl-7-0-4 MOVEl-7-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE
Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE MOVEl-4-0-5MOVEl-3-0-5 MOVEl-4-0MOVEl-6-0MOVEl-7-0-5 MOVEl-7-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-3-0-5 MOVEl-4-0-5 Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE
FINISH
MOVEl-2-0MOVEl-6-0-5 BUILDl-6-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0Rubble atl-0-0-5?FALSE Rock atl-0-0-5?
TRUE CLEARl-0-0-5 FALSE
MOVEl-7-0-4 FINISH MOVEl-7-0-4 FINISH
BUILDl-5-0-4.. MOVEl-6-0BUILDl-6-0BUILDl-6-0-5 MOVEl-7-0MOVEl-7-0-4 FINISH
MOVEl-6-0MOVEl-7-0Rubble atl-3-0-5?FALSECLEARl-3-0-5TRUE MOVEl-3-0BUILDl-6-0-5 MOVEl-7-0MOVEl-7-0BUILDl-5-0-4.. MOVEl-5-0-5 MOVEl-4-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH BUILDl-5-0-4.. MOVEl-6-0FALSECLEARl-2-0-5TRUE MOVEl-2-0Rock atl-3-0-2?
TRUE FALSE
MOVEl-7-0-4 FINISH
MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-7-0-5 MOVEl-6-0-5 BUILDl-6-0MOVEl-7-0-4 FINISH BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 FINISH
MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0-4 FINISH FINISH
BUILDl-5-0-4.. MOVEl-6-0MOVEl-5-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0BUILDl-5-0-4..
MOVEl-7-0-4 FINISH
MOVEl-4-0-5 MOVEl-3-0-5 MOVEl-2-0-5 Rubble atl-3-0-
[Table]
-5 MOVEl-7-0-5 MOVEl-7-0MOVEl-5-0Rubble atl-3-0-5?
MOVEl-3-0-5 FALSECLEARl-3-0-5TRUE MOVEl-4-0-5MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. Rubble atl-5-0-3?
TRUEFALSE
MOVEl-7-0-4 FINISH
MOVEl-4-0-1 MOVEl-4-0BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0FINISH
MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-7-0-4 FINISH BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-4-0-5 MOVEl-5-0MOVEl-4-0CLEARl-2-0-5 MOVEl-2-0Rubble atl-1-0-5?FALSE CLEARl-1-0-5TRUE MOVEl-1-0-5 Rubble atl-2-0-5?FALSETRUE
MOVEl-7-0-5 MOVEl-7-0-4 FINISH
FINISH
MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0BUILDl-6-0FINISH
MOVEl-6-0BUILDl-6-0BUILDl-5-0-4..
MOVEl-7-0-4 FINISH
Rubble atl-3-0-5?FALSETRUE
MOVEl-5-0-5 MOVEl-4-0MOVEl-7-0MOVEl-4-0FINISH
MOVEl-3-0MOVEl-6-0CLEARl-3-0Rubble atl-3-0-5?TRUEMOVEl-3-0-5FALSE MOVEl-4-0-5 MOVEl-2-0BUILDl-5-0-4.. MOVEl-6-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-7-0-5 MOVEl-7-0-4 FINISH Rubble atl-3-0-5?
MOVEl-3-0-5 FALSECLEARl-3-0-5TRUE MOVEl-4-0-5MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0FINISH
MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH TRUEFALSE
Rock atl-0-0-5?
MOVEl-0-0-5FALSE Rubble atl-1-0-5?TRUE MOVEl-1-0-5FALSE
TRUEFALSE
BUILDl-5-0-4.. MOVEl-5-0BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0-4 FINISH
BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-5-0BUILDl-6-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-4-0CLEARl-2-0-5TRUEMOVEl-2-0-5FALSE MOVEl-2-0MOVEl-4-0FINISH
MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 Rubble atl-3-0-5?
CLEARl-3-0-5 TRUEMOVEl-3-0-5FALSE MOVEl-4-0MOVEl-3-0MOVEl-7-0BUILDl-5-0-4..
MOVEl-7-0-4 FINISH CLEARl-5-0-3 MOVEl-5-0FINISH MOVEl-7-0-4 MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 CLEARl-3-0-5 Rubble atl-3-0-5?TRUEMOVEl-3-0-5FALSE
MOVEl-5-0-5 BUILDl-5-0-4..
BUILDl-5-0-4.. MOVEl-6-0Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE MOVEl-4-0Rubble atl-0-0-5?
MOVEl-4-0MOVEl-5-0CLEARl-3-0-5 MOVEl-3-0-5 MOVEl-2-0-5 Rubble atl-3-0-5?FALSETRUE FALSE CLEARl-2-0-5TRUE
MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-3-0FALSE CLEARl-0-0-5TRUE
BUILDl-6-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-5-0MOVEl-7-0-5 MOVEl-7-0-4 CLEARl-3-0-5 MOVEl-3-0-5 MOVEl-4-0-5 Rubble atl-3-0-5?FALSETRUE
MOVEl-1-0CLEARl-5-0-3 MOVEl-5-0-3 BUILDl-5-0-4.. Rubble atl-5-0-3?TRUEMOVEl-5-0-3FALSE BUILDl-5-0-4..
FINISH MOVEl-7-0-4 MOVEl-7-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-4-0-5 MOVEl-7-0MOVEl-7-0-4 FINISH
MOVEl-6-0-3 BUILDl-6-0MOVEl-7-0-4 FINISH MOVEl-7-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0Rubble atl-1-0-5?
MOVEl-0-0MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-3-0-5 MOVEl-6-0-5 BUILDl-6-0MOVEl-7-0-5 MOVEl-7-0MOVEl-5-0MOVEl-6-0-5 BUILDl-6-0MOVEl-4-0FINISH
BUILDl-5-0-4..
FALSETRUE
FALSETRUE
FINISH MOVEl-7-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4..
BUILDl-6-0-5 MOVEl-7-0FINISH MOVEl-7-0MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0Rubble atl-3-0-5?
CLEARl-3-0-5TRUEMOVEl-3-0-5FALSE
BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
Rubble atl-2-0-5?
BUILDl-6-0FINISH
MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-5-0MOVEl-2-0-5FALSECLEARl-2-0-5TRUE
MOVEl-7-0-4 FINISH MOVEl-7-0-5 MOVEl-6-0-5 BUILDl-6-0CLEARl-3-0-5 MOVEl-3-0-5 MOVEl-4-0-5 Rubble atl-3-0-5?TRUEMOVEl-3-0-5FALSE MOVEl-4-0-5 MOVEl-2-0FINISH MOVEl-7-0-4 MOVEl-7-0MOVEl-5-0-5 BUILDl-5-0-4..
[Table]
[Table] [Table]
BUILDl-
[Table] [Table]
[Table] [Table]
[Table]
MOVEl
[Table] [Table]
4 FINISH
[Table]
FINISH
Rubble atl-
[Table] [Table]
MOVEl
[Table]
5FALSECLEARl
[Table]
5TRUE
FINISH
[Table] [Table]
[Table] [Table]
Rock
[Table]
TRUE FALSE
[Table]
[Table] [Table]
[Table] [Table]
MOVEl
[Table] [Table]
[Table] [Table]
[Table]
0-3 BUILDl-6-0-3 MOVEl-7-0-3 BUILDl-5-0-4.. MOVEl-5-0-3 CLEARl-5-0-3 FINISH MOVEl-7-0FINISH
MOVEl-6-0-3 BUILDl-6-0MOVEl-7-0MOVEl-4-0MOVEl-2-0-5FALSECLEARl-2-0-5TRUE MOVEl-2-0MOVEl-4-0BUILDl-6-0-5 MOVEl-7-0MOVEl-6-0FINISH
MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4..
MOVEl-7-0-4 FINISH MOVEl-7-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4.. MOVEl-4-0-5 MOVEl-5-0-5 MOVEl-3-0Rock atl-0-0-5?
MOVEl-0-0-5FALSE Rubble atl-1-0-5?
MOVEl-7-0-4 FINISH
MOVEl-5-0MOVEl-3-0Rubble atl-3-0-2?
CLEARl-4-0-3FALSECLEARl-4-0-3TRUEMOVEl-4-0-3MOVEl-4-0-3 Rubble atl-5-0-3?
MOVEl-7-0-5 BUILDl-6-0MOVEl-5-0-3 BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0FINISH
BUILDl-6-0-5 MOVEl-7-0Rubble atl-2-0-5?
Rubble atl-1-0-5?
MOVEl-1-0-5 FALSE CLEARl-1-0-5 TRUE MOVEl-1-0FINISH
MOVEl-3-0-5 CLEARl-3-0MOVEl-4-0FALSE CLEARl-1-0-5TRUE MOVEl-1-0-5 Rubble atl-2-0-5?
CLEARl-2-0-5 TRUEMOVEl-2-0-5FALSE MOVEl-2-0-5 Rubble atl-3-0-5?
BUILDl-5-0-4..
FALSETRUE MOVEl-0-0-5 CLEARl-0-0-5 Rock atl-0-0-5?FALSE
Rubble atl-3-0-5?
MOVEl-0-0-4 Rubble atl-0-0-5?TRUE Rock atl-0-0-5?FALSE CLEARl-0-0-4 Rubble atl-0-0-4?
FALSE TRUE
MOVEl-0-0MOVEl-0-0Rubble atl-3-0-5?FALSECLEARl-3-0-5TRUE
FINISH MOVEl-7-0-4 MOVEl-7-0-5 BUILDl-6-0-5 MOVEl-6-0MOVEl-2-0-5 Rubble atl-3-0-5?FALSECLEARl-3-0-5TRUE CLEARl-2-0-5 MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-6-0MOVEl-7-0-3 MOVEl-7-0-4 FINISH BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 FALSE
CLEARl-3-0-2 TRUE
BUILDl-5-0-4..
MOVEl-5-0MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0-4 FINISH BUILDl-5-0-4..
MOVEl-5-0BUILDl-6-0-5 MOVEl-6-0FINISH MOVEl-7-0-4 BUILDl-5-0-4.. MOVEl-5-0MOVEl-2-0-5 Rubble atl-3-0-5?TRUEFALSE
MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 CLEARl-3-0-5TRUEMOVEl-3-0-5FALSEMOVEl-4-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0TRUEMOVEl-2-0-5FALSE Rubble atl-3-0-5?
FALSE
MOVEl-7-0-4 FINISH
FINISH
BUILDl-5-0-4.. MOVEl-5-0MOVEl-7-0BUILDl-6-0-5 MOVEl-6-0-5 BUILDl-5-0-4.. MOVEl-5-0Rubble atl-3-0-5? MOVEl-5-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE
BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0FINISH
Rubble atl-0-0-5?FALSE Rock atl-0-0-5?TRUE CLEARl-0-0-5FALSE MOVEl-0-0Rubble atl-2-0-5?
MOVEl-6-0-5 BUILDl-6-0MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0MOVEl-7-0-5 MOVEl-7-0-4 FINISH
FINISH
MOVEl-4-0BUILDl-5-0-4.. FALSECLEARl-3-0-5TRUE MOVEl-3-0MOVEl-5-0-5 BUILDl-5-0-4..
BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-5-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-6-0-5 BUILDl-5-0-4.. MOVEl-4-0-5MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0MOVEl-4-0TRUEMOVEl-3-0-5FALSE MOVEl-4-0MOVEl-7-0-4 FINISH BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-5-0-5 BUILDl-6-0MOVEl-5-0-5MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-2-0-5 Rubble atl-3-0-5?FALSECLEARl-3-0-5TRUE MOVEl-3-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-4-0-5 MOVEl-5-0MOVEl-2-0-5 CLEARl-2-0MOVEl-4-0MOVEl-5-0-5 BUILDl-5-0-4..
Rubble atl-2-0-5?TRUEMOVEl-2-0-5FALSE MOVEl-1-0MOVEl-5-0BUILDl-5-0-4..
MOVEl-7-0-4 FINISH
MOVEl-0-0-5FALSE
CLEARl-0-0-3 MOVEl-0-0FALSECLEARl-3-0-5TRUE
FINISH
MOVEl-5-0-3 BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0FINISH
MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-5-0FINISH
MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
FINISH
MOVEl-4-0CLEARl-2-0MOVEl-4-0-5 MOVEl-5-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0MOVEl-7-0-4 FINISH BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-4-0-5 MOVEl-5-0FALSETRUE
MOVEl-4-0-5 MOVEl-5-0BUILDl-6-0-5 MOVEl-7-0MOVEl-4-0-5 MOVEl-5-0MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0Rubble atl-5-0-3?
FINISH MOVEl-7-0-5 MOVEl-7-0-4 MOVEl-6-0-5 BUILDl-6-0MOVEl-6-0-5 BUILDl-6-0FALSETRUE
MOVEl-7-0-5 MOVEl-7-0-4 FINISH
BUILDl-5-0-4..
MOVEl-7-0MOVEl-7-0-5 MOVEl-7-0Rubble atl-2-0-5?
CLEARl-0-0-4 MOVEl-0-0-4 Rubble atl-0-0-5?
MOVEl-6-0-5 BUILDl-6-0FALSE Rock atl-0-0-5?TRUE
BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-5-0CLEARl-2-0-5TRUEMOVEl-2-0-5FALSE
MOVEl-7-0-4 FINISH
MOVEl-6-0-5 FINISH
Rock atl-0-0-5? CLEARl-0-0-5FALSE MOVEl-0-0-5 FINISH
MOVEl-2-0-1 MOVEl-2-0-0 MOVEl-3-0-0 MOVEl-4-0-1 MOVEl-4-0-2 Rubble atl-4-0-3?
MOVEl-4-0-0 FALSETRUE
Rubble atl-1-0-5?
MOVEl-5-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-7-0-4 FINISH
BUILDl-5-0-4.. MOVEl-6-0MOVEl-7-0FINISH
Rubble atl-1-0-5?
MOVEl-7-0-4 FINISH FINISH MOVEl-5-0-3 BUILDl-5-0-4.. MOVEl-7-0-3 MOVEl-7-0MOVEl-5-0FALSETRUE
FALSE TRUE
Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUEMOVEl-4-0-5MOVEl-3-0MOVEl-7-0-5 MOVEl-7-0Rubble atl-3-0-5?
FALSECLEARl-3-0-5TRUE MOVEl-2-0-5Rubble atl-3-0-5?
MOVEl-3-0-0 MOVEl-4-0Rubble atl-3-0-2?
TRUE FALSE
BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0MOVEl-4-0-3 CLEARl-4-0FALSE TRUE
MOVEl-7-0-4 FINISH BUILDl-6-0-5 MOVEl-7-0MOVEl-3-0-0 MOVEl-4-0-0 MOVEl-4-0-1 MOVEl-4-0-2 Rubble atl-4-0-3?FALSETRUE
MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-7-0-4 FINISH MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-6-0BUILDl-5-0-4.. MOVEl-6-0MOVEl-7-0BUILDl-6-0-5 MOVEl-7-0MOVEl-7-0-5 BUILDl-6-0MOVEl-7-0MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 CLEARl-3-0-5 Rubble atl-3-0-5?TRUEMOVEl-3-0-5FALSE MOVEl-2-0MOVEl-6-0-5 BUILDl-5-0-4..
MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-4-0-5 MOVEl-6-0BUILDl-5-0-4..
MOVEl-6-0FINISH
FINISH
MOVEl-2-0MOVEl-4-0-3 Rubble atl-5-0-3?TRUEFALSE
FINISH MOVEl-7-0-4 MOVEl-7-0-5 BUILDl-6-0TRUEFALSE
Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE
MOVEl-5-0BUILDl-6-0MOVEl-7-0-5 MOVEl-7-0MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-0-0FINISH MOVEl-7-0-4 MOVEl-7-0-5 BUILDl-6-0MOVEl-5-0Rubble atl-2-0-5?FALSECLEARl-2-0-5TRUE
FALSE
MOVEl-5-0-5 BUILDl-5-0-4..
FINISH
MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0MOVEl-5-0CLEARl-2-0-5FALSETRUE
FINISH MOVEl-7-0-4 MOVEl-7-0-5 BUILDl-6-0-5 MOVEl-6-0-5 BUILDl-5-0-4.. MOVEl-5-0MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-3-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH MOVEl-2-0-5 MOVEl-7-0-5 MOVEl-7-0FINISH
MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-7-0-5 MOVEl-7-0-4 FINISH MOVEl-6-0-5 BUILDl-6-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-3-0-5 MOVEl-4-0FINISH
MOVEl-2-0MOVEl-7-0-4 MOVEl-7-0CLEARl-5-0-3 MOVEl-5-0-3 BUILDl-5-0-4.. FALSETRUE BUILDl-6-0-3 MOVEl-6-0MOVEl-7-0FINISH MOVEl-7-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-4-0-5 MOVEl-7-0-5 BUILDl-6-0-5 Rubble atl-2-0-5?FALSECLEARl-2-0-5TRUE MOVEl-2-0MOVEl-3-0BUILDl-5-0-4..
FALSECLEARl-3-0-5TRUE
FINISH MOVEl-7-0MOVEl-4-0MOVEl-5-0-3 BUILDl-5-0-4.. MOVEl-6-0-3 CLEARl-5-0-3 TRUEMOVEl-5-0-3FALSE BUILDl-5-0-4..
MOVEl-7-0-3 BUILDl-6-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-3-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0MOVEl-7-0-5 BUILDl-6-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-7-0-
FINISH MOVEl-7-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-5-0-5 BUILDl-5-0-4..
Rubble atl-3-0-5?FALSECLEARl-3-0-5TRUE MOVEl-3-0BUILDl-5-0-4..
MOVEl-5-0-5 BUILDl-5-0-4.. BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 BUILDl-5-0-4.. MOVEl-6-0MOVEl-3-0-5 MOVEl-4-0MOVEl-6-0Rubble atl-2-0-5?FALSE CLEARl-2-0-5TRUE
MOVEl-3-0-5 MOVEl-4-0CLEARl-2-0-5 Rubble atl-2-0-5?FALSETRUE
Rubble atl-5-0-3?FALSECLEARl-5-0-3TRUE MOVEl-5-0BUILDl-6-0MOVEl-1-0MOVEl-1-0CLEARl-3-0-5 MOVEl-3-0-5 MOVEl-4-0-5 Rubble atl-3-0-5?FALSETRUE MOVEl-2-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0MOVEl-7-0-4 FINISH BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4.. MOVEl-6-0Rubble atl-0-0-4?
MOVEl-7-0-4 FINISH BUILDl-6-0-3 MOVEl-7-0-3 BUILDl-5-0-4.. MOVEl-6-0MOVEl-7-0BUILDl-5-0-4..
CLEARl-5-0-3 MOVEl-5-0-3 BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-4 FINISH MOVEl-7-0-3 FALSETRUE
MOVEl-6-0-5 BUILDl-6-0MOVEl-7-0-4 FINISH
FINISH MOVEl-7-0-4 MOVEl-7-0-3 BUILDl-6-0-3 MOVEl-6-0MOVEl-7-0-5 MOVEl-7-0-4 FINISH MOVEl-5-0FINISH MOVEl-7-0-3 MOVEl-7-0-4 MOVEl-6-0-3 BUILDl-6-0MOVEl-5-0-5 BUILDl-5-0-4..
CLEARl-2-0-5 MOVEl-2-0-5 MOVEl-6-0Rubble atl-1-0-5?
FINISH
MOVEl-1-0-5 Rubble atl-2-0-5?FALSETRUE CLEARl-1-0-5 FALSETRUE
CLEARl-1-0-5 MOVEl-1-0FINISH MOVEl-7-0-4 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-4-0MOVEl-5-0FINISH MOVEl-7-0-4 MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4.. MOVEl-5-0FALSE TRUE
MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-4-0-5 MOVEl-6-0-5 BUILDl-6-0MOVEl-7-0FINISH
MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0BUILDl-6-0-5 MOVEl-7-0BUILDl-6-0CLEARl-3-0-5 MOVEl-3-0-5 MOVEl-4-0-5 Rubble atl-3-0-5?TRUEMOVEl-3-0-5FALSE
BUILDl-5-0-4.. MOVEl-6-0MOVEl-5-0-5 BUILDl-5-0-4..
FINISH
MOVEl-5-0MOVEl-7-0-5 MOVEl-7-0-4 BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0-3 MOVEl-7-0FINISH
MOVEl-6-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 FINISH MOVEl-7-0MOVEl-3-0-5 MOVEl-4-0BUILDl-5-0-4.. MOVEl-4-0-5 MOVEl-5-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-4-0-5 MOVEl-5-0-5 CLEARl-3-0-5 MOVEl-3-0TRUEMOVEl-2-0-5FALSE Rubble atl-3-0-5?
MOVEl-7-0-5 MOVEl-7-0MOVEl-7-0-5 MOVEl-7-0MOVEl-6-0-5 BUILDl-6-0BUILDl-5-0-4.. MOVEl-5-0-5 MOVEl-4-0MOVEl-4-0-5 MOVEl-5-0MOVEl-6-0-5 FINISH
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE MOVEl-4-0-5MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-5-0BUILDl-5-0-4..
BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-4-0-5 MOVEl-5-0TRUE FALSE
MOVEl-7-0MOVEl-7-0-5 BUILDl-6-0MOVEl-7-0Rubble atl-3-0-5?FALSECLEARl-3-0-5TRUE MOVEl-3-0FINISH
CLEARl-3-0-5 MOVEl-3-0Rubble atl-3-0-5?FALSECLEARl-3-0-5TRUE MOVEl-3-0-5 MOVEl-2-0-5 MOVEl-4-0-5 MOVEl-5-0FALSECLEARl-2-0-5TRUE
BUILDl-5-0-4.. MOVEl-6-0FALSETRUE
MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4..
BUILDl-6-0-5 MOVEl-7-0MOVEl-4-0Rubble atl-2-0-5?FALSECLEARl-2-0-5TRUE MOVEl-2-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0Rubble atl-3-0-5?
MOVEl-3-0-5FALSECLEARl-3-0-5TRUE MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-2-0-5 Rubble atl-3-0-5?
FALSECLEARl-2-0-5TRUE
FINISH
BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-5-0MOVEl-7-0BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0-4 FINISH MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 BUILDl-5-0-4.. MOVEl-7-0-4 FINISH
MOVEl-5-0BUILDl-5-0-4..
BUILDl-5-0-4..
MOVEl-6-0FINISH
FALSECLEARl-3-0-5TRUE MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0BUILDl-5-0-4.. MOVEl-5-0MOVEl-7-0-4 FINISH BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-5-0-5 BUILDl-5-0-4.. BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH BUILDl-5-0-4.. MOVEl-6-0MOVEl-4-0-2 FALSE MOVEl-2-0-2TRUE MOVEl-1-0-2 MOVEl-0-0-2 CLEARl-0-0MOVEl-7-0-4 FINISH MOVEl-7-0MOVEl-7-0-4 FINISH
MOVEl-7-0-5 MOVEl-7-0-4 FINISH MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0FINISH
TRUEFALSE
FINISH
FALSETRUE
MOVEl-7-0FALSETRUE
FALSE CLEARl-2-0-5 TRUE MOVEl-2-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
BUILDl-5-0-4.. MOVEl-5-0-5 MOVEl-4-0MOVEl-6-0-5 BUILDl-6-0-5 BUILDl-5-0-4.. MOVEl-5-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-4-0-5 MOVEl-5-0Rubble atl-2-0-5?FALSECLEARl-2-0-5TRUE MOVEl-2-0MOVEl-7-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-3-0-5 MOVEl-4-0MOVEl-7-0-4 FINISH BUILDl-6-0-5 MOVEl-7-0FINISH
TRUEMOVEl-3-0-5FALSE
MOVEl-7-0-5 MOVEl-7-0-4 MOVEl-6-0-5 BUILDl-6-0FINISH MOVEl-7-0FALSECLEARl-3-0-5TRUE MOVEl-3-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4..
FALSECLEARl-3-0-5TRUE MOVEl-3-0MOVEl-7-0MOVEl-4-0-5 MOVEl-5-0BUILDl-5-0-4..
MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0Rubble atl-3-0-5?FALSETRUE
MOVEl-7-0-4 FINISH MOVEl-7-0-5 BUILDl-6-0-5 MOVEl-6-0MOVEl-5-0-5 BUILDl-5-0-4..
Rubble atl-0-0-4?
FALSE CLEARl-0-0-4 TRUE MOVEl-0-0MOVEl-2-0FINISH
MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4..
MOVEl-7-0-4 FINISH MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-3-0MOVEl-5-0MOVEl-5-0MOVEl-4-0MOVEl-6-0-5 BUILDl-6-0MOVEl-3-0-5 MOVEl-4-0-5 BUILDl-5-0-4..
MOVEl-7-0-4 MOVEl-7-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-5-0MOVEl-3-0-5 BUILDl-5-0-4.. MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0-4 FINISH MOVEl-4-0-3 Rubble atl-5-0-3? MOVEl-5-0-3FALSECLEARl-5-0-3TRUE MOVEl-5-0MOVEl-7-0-5 BUILDl-6-0-5 MOVEl-6-0MOVEl-5-0FINISH MOVEl-7-0-4 MOVEl-7-0-5 BUILDl-6-0-5 MOVEl-6-0BUILDl-5-0-4.. MOVEl-6-0FALSETRUE
FALSECLEARl-5-0-3TRUE
MOVEl-6-0-5 BUILDl-6-0MOVEl-6-0-5 BUILDl-6-0MOVEl-7-0-4 MOVEl-7-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0FALSECLEARl-3-0-5TRUE
MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH BUILDl-6-0BUILDl-5-0-4..
MOVEl-7-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0CLEARl-3-0-5FALSETRUE
FINISH
BUILDl-6-0-5 MOVEl-6-0MOVEl-6-0-3 BUILDl-6-0MOVEl-4-0BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0-4 FINISH
MOVEl-4-0-5 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0MOVEl-6-0-3 BUILDl-6-0-3 MOVEl-7-0-3 MOVEl-7-0-4 FINISH FINISH
FINISH MOVEl-7-0-4 MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-4-0MOVEl-7-0-5 BUILDl-6-0-5 Rock atl-0-0-5? CLEARl-0-0-5FALSE
FALSETRUE
MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0Rubble atl-0-0-5?FALSETRUE
MOVEl-6-0-5 BUILDl-5-0-4..
FALSECLEARl-3-0-5TRUE MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
MOVEl-5-0TRUEFALSE
MOVEl-5-0-5 BUILDl-5-0-4..
MOVEl-4-0-5 MOVEl-5-0BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH
CLEARl-4-0-3FALSETRUE FALSE CLEARl-2-0-5TRUE
MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0-4 FINISH BUILDl-6-0-5 MOVEl-7-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 MOVEl-5-0FINISH
CLEARl-3-0-5 MOVEl-3-0-5 MOVEl-4-0-5 MOVEl-5-0-5 Rubble atl-3-0-5?FALSETRUE
BUILDl-6-0-5 BUILDl-5-0-4.. MOVEl-6-0MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-5-0-5 BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0-5 MOVEl-7-0BUILDl-5-0-4.. MOVEl-6-0FINISH MOVEl-7-0-3 MOVEl-7-0-4 MOVEl-6-0-3 BUILDl-6-0MOVEl-4-0-5 MOVEl-5-0FINISH
MOVEl-7-0-4 FINISH
MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0BUILDl-5-0-4.. MOVEl-6-0-5 BUILDl-6-0-5 MOVEl-7-0MOVEl-4-0-5 MOVEl-5-0- approach to partially observable planning which supports efﬁcient plan generation through a compilation to classical planning.
The underlying classical planner is used to generate an optimistic plan, π optimistic and the K-Replanner approach follows this plan until an inconsistency is discovered, at which point it replans.
However, as K-Replanner only explores individual real worlds, we extend it to generate the full plan, following the approach of (Komarnitsky and Shani 2016).
Ateach sensing action encountered in the optimistic plan, the plan is branched for each of the possible values and each of these branches is explored iteratively.
Although not explored in this work, we observe that if the entire tree is prohibitively large it would be possible to explore a partial plan, by bounding the number of branching points.
The action sequences from this partial plan could be bounded and used as input for our visualisation tools (this is particularly suited to one of our presentation modes, referred to as I NTERLEAVED mode, as discussed in section “Empirical Evaluation”).
Also, the K-Replanner’s optimistic plan, π optimistic , plays an important role in our approach to communicating, through visualisation, the branched plan possibilities to a practitioner.
As this optimistic plan is used to drive the planner’s strategy during planning it means that our visualisation is consistent with the intention of the system.
Whereas with more direct approaches to partially observable planning it might prove challenging to accurately mirror their strategies,
K-Replanner’s strategy is particularly amenable.
For further detail on optimistic plan visualisation see section: “User Interface: Presenting 3D Visualisations”.
Selecting Characterising Plan Traces
Our focus is communicating branched plans to human practitioners, however it is not typically possible, or desirable, to present all linearisations.
Thus we propose using a small
[Table]
-2.. TRUE
MOVEl-0-0MOVEl-0-0-1 MOVEl-0-0-0 FINISH
MOVEl-0-0-0 FINISH
BUILDl-2-0-2..
Rubble at l-2-0-1?
FALSE TRUE
MOVEl-0-0-0 FINISH
MOVEl-0-0-0 FINISH MOVEl-0-0-0 FINISH
Rubble at l-2-0-1?
FALSE TRUE
BUILDl-2-0-2.. MOVEl-0-0MOVEl-0-0Rubble at l-2-0-1?
TRUE
BUILDl-2-0-2.. FALSE MOVEl-0-0FINISH
MOVEl-0-0-0 FINISH
Rubble at l-2-0-1?
FALSE BUILDl-2-0-2..TRUE
MOVEl-1-0FINISH MOVEl-0-0MOVEl-0-0-0 FINISH
MOVEl-0-0-0 FINISH
BUILDl-2-0-2.. MOVEl-0-0-1 MOVEl-0-0FINISH MOVEl-0-0-0 MOVEl-0-0-1 BUILDl-2-0-2..
Rubble at l-2-0-1?
FALSE TRUE subset of the execution traces to provide examples from across the broad scope of the alternatives captured in the plan.
The intention is to provide the user with the intuition of what is captured within the plan without the burden of fully examining every trace.
We are therefore interested in selecting a small number of execution traces that characterise the range of executions represented by the branched plan.
Our selection mechanism uses a dissimilarity measure to estimate the difference between two alternative action sequences.
Using this measure on action sequences ignores other features in the trace, and means that the similarity of two traces is determined by the difference in the agent’s actions and not differences in such things as sensor readings, which can be irrelevant.
Using the dissimilarity measure allows the full set of linearisations to be clustered to identify its key groupings.
Clustering provides ﬂexibility, allowing a balance between the number of clusters and loss of detail.
Dissimilarity Measure To estimate the dissimilarity between two execution sequences we use the Levenshtein distance (Levenshtein 1966): the distance between two word sequences which provides a measure of the edit difference between the sequences, while also respecting ordering.
In our case we use unique words for each ground action.
This measure was used as it is directly applicable to partially observable planning domains and it has been demonstrated that the approach leads to the identiﬁcation of diverse plans (Coman and Munoz-Avila 2011).
Clustering Execution Traces Clustering identiﬁes groups of elements, which are similar (or close) to the elements in their own group, while being dissimilar (or far away from) elements in other groups.
We therefore aim to break the space of possibilities into clusters, each representing similar execution traces.
We used the Partitioning Around Medoids (PAM) implementation of the k -medoids method (Kaufmann and
Rousseeuw 1987).
This approach partitions the data into k clusters, each associated with a representative data point (the medoid ), considered the most central in the cluster.
This approach operates from a dissimilarity matrix, which can be computed by comparing each pair of traces using the dissimilarity measure.
The medoids are central members of their respective clusters, and so we use them as the representatives of their clusters.
For an appropriate value of k , this set of medoids will identify diverse execution traces, characterising the execution traces in the plan.
Selecting the Number of Clusters
The appropriate choice of k is likely to depend on the application domain and the depth of understanding that is appropriate for the user, which might relate to the seriousness of inappropriate action, e.g., safety and security concerns.
We therefore prefer the relatively lightweight k -medoids algorithm, which provides the necessary ﬂexibility.
One way to select a reasonable value for k is to calculate the average silhouette score for the clusters (Rousseeuw 1987), which evaluates the clusters by averaging the similarity within clusters and dissimilarity between clusters, with respect to the distance measure.
This can only be evaluated accurately for at least 2 clusters, so we ﬁrst test to determine whether more than 1 cluster is appropriate (Duda, Hart et al. 1973).
The optimal average silhouette score indicates a good trade-off between the size of k and the amount of dissimilarity in each cluster.
We therefore see this as a suitable default value.
1. Communicating Branched Plan Possibilities
The size of branched plans makes it challenging to communicate the space of possible executions to practitioners and consequently the intentions of agents whose behaviours are underpinned by such a plan.
Our approach to address this exploits two visualisation methods to: (i) communicate the space of alternative execution traces captured in the plan; and (ii) highlight the set of characterising execution traces (selected using the approach discussed earlier).
(i) Communicating Space of Alternative Executions
We use a visualisation of the complete space of alternative executions in order to provide an indication of the number and complexity of the possible alternatives.
Although there is no intention that this will lead to an understanding of the actual traces, we extend the visualisation to allow practitioners to explore the possible executions in some detail.
Branched plans allow efﬁcient solutions to be captured for each of the possible concrete states.
For our branched plan generator, the branching nodes are associated with sensing actions allowing an appropriate course of action to be selected for each sensor valuation.
In scenarios with a small amount of uncertainty the plan might be captured by a concise tree.
As the level of (relevant) uncertainty increases, the size of the tree will grow and in some cases the tree will be very large.
We observe that there is a natural similarity between a branched tree and a classical planning state space.
This allows us to build on recent results in state space visualisation (Magnaguagno et al.
2017, 2020) to effectively communicate the size and complexity of the branched plan.
We use a radial layout to visualise the tree.
The root of the tree naturally sits in the centre of the visualisation and the branches of the tree expand from the root outwards.
The graph has action and sensor action nodes and edges from sensor actions are labelled with the associated sensor value (i.e., True or False ).
An example visualisation of the branched plan for a small construction problem is presented in Figure 2 and the branched plan for the problem used in our evaluation is presented in Figure 1.
Whereas in (Magnaguagno et al.
the search spaces branch on alternative choices, our plans branch on the valuation of sensor actions.
It is therefore appropriate that the distance from the centre reﬂects the length of the execution, so that clearly longer executions can easily be identiﬁed.
We have extended visualisation by emphasising the key action nodes, i.e. those that achieve subgoals (shown with emboldened border in Figures 1 and 2).
In order to reduce the complexity of the visualisation, the nodes are annotated with simpliﬁed representations of the actions and sensor actions.
Further information is provided through tooltips, which provide longer descriptions of the actions and decision points, as well as key state information.
(ii) Highlighting Characterising Execution Traces
We have used these selected execution traces to enhance the branched plan radial visualisation and provide meaningful guidance to assist practitioners to navigate the tree and understand its alternatives.
Figure 2 illustrates the visualisation of diverse alternative execution traces for our construction world, with differently coloured lines added to the radial plan visualisation for each diverse trace.
Importantly, these characterising execution traces are the ones communicated to the practitioner, using 3D visualisation, as discussed next.
2. Communicating Selected Execution Traces
The 3D visualisation of a characterising execution trace provides an effective mechanism for clearly communicating the agent intention captured in that particular trace.
We contrast this 3D visualisation of an individual trace to the radial visualisation of a branched plan discussed earlier, as it refers to the use of 3D graphics to provide a visual run through of the sequence of actions, via animations, in a virtual environment.
This 3D visualisation can be either: prior to execution, i.e. simulation ; or the actual execution itself.
We have developed a graphical user interface for presenting such 3D visualisations to practitioners.
The interface is implemented using the Unity3D game engine.
An example is shown in Figure 3.
It provides side-by-side synchronous views of the current action being visualised: a top-down view of the agent acting in the world (left-hand side), and a 3D isometric view (right-hand side).
In addition, the interface has an icon-based representation of the sequence of actions in the execution trace (along the bottom).
The icons are coloured as follows: grey if the action is yet to be visualised; yellow if currently being visualised; or green if fully visualised.
3D Visualisation of Action Sequences
The generation of 3D visualisations of agent actions relies upon the ability of the interface to convey realistic and semantically meaningful animations within the virtual environment.
To maximise the practitioner’s understanding of the execution traces that are visualised, we created contextually identiﬁable discrete sets of 3D animations constituting meaningful representations of agent actions.
An important requirement for the 3D visualisation is to provide visual representations that clearly differentiate between simulation and execution , and to ensure animations are consistent and graphically similar.
Thus, actions use the same graphical animations in simulation and execution but use a different rendering style: simulation actions are rendered in turquoise-coloured wireframe render; whilst execution actions are rendered in fully-shaded grey (Figure 4).
A key concept in branched plan generation is the use of sensing actions (see section “Background”), which must be visualised so that practitioners can understand the implication of the valuation process.
For instance, as shown in Figure 5, it might be that if rubble is identiﬁed the agent’s plan is to clear the rubble before proceeding further.
As an illustration of 3D visualization of an agent sequence, as shown to a practitioner, Figure 6 shows a full trace of an execution of actions.
The ﬁgure includes several sensing actions, actions clearing rubble and construction.
3D Visualisation of Inference Rules
Our approach to branched plan generation allows for agent inferences about locations of certain objects within the domain, as reported by (Bonet and Geffner 2011).
For our application, inference rules are linked to agent sensing actions with respect to “exclusive-or” knowledge about locations suspected to contain rubble or rock.
For 3D visualisation, such locations are shown with a question mark (grey square, green question mark), as in Figure 7(a).
Over a series of sensing actions the agent gathers more information about locations and the results are visualised, with question mark replaced by either a representation of the object sensed if True ; or a red cross for False (e.g. sensing actions in Figure 7).
User Interface: Presenting 3D Visualisations
An important aspect of eXplainable AI Planning (XAIP) is helping users understand what decisions have been made in a plan, and why.
As it is not always feasible to present all branched plan linearisations, our approach is to select a diverse set of execution traces, that characterise the possibilities captured within the full branched plan, and to present these to the practitioner via a series of 3D visualisations within the user interface.
Here, we describe the ways in which presentations can be organised to exploit plan structure, as appropriate, to assist practitioners understanding by giving some transparency to the agents’ planning strategy.
Consistency with the Agent’s Intent
Building on (Bonet and Geffner 2011), our approach to branching plan generation is based on a speciﬁc strategy: construct the branched plan starting from a single optimistic plan, π optimistic , and iteratively branch for alternative sensor values.
We mirror this planning strategy in our approach to presenting execution visualisations: we use this optimistic plan as the “backbone” for presentation of 3D visualisations.
Thus, within the user interface, both the agent’s optimistic plan and the selected set of characterising plan traces can be presented to the practitioner – in order to establish common ground between the practitioner and the agent (the agent could follow one of the diverse plans; however, because it is not used to guide plan construction it may lack the rationality and focus of the optimistic plan).
User Interface Modes
The appropriate mode of presentation of information will often vary between applications.
For example, in some scenarios, where the practitioner must have complete understanding of the agent plan before execution starts (e.g., high risk applications), simulation can be used to safely explore different possible plan alternatives prior to execution.
Whereas in other situations it might be appropriate to interleave the presentation of information, via simulation , throughout the execution (e.g., relatively slow execution applications).
We observe that during actual agent execution the uncertainty in the concrete state will reduce, isolating a smaller portion of the overall branched plan.
Therefore, where appropriate, presenting information at stages during execution can provide sets of execution continuations that are more focused towards the unfolding execution.
Thus, the user interface was developed with the following modes of presentation:
• Simulation: presentation of 3D visualisations of selected traces from the full branched plan prior to execution.
In simulation mode, each trace implies a set of assumed sensor valuations for the sensing actions, which are used to generate the appropriate visualisations (differentiated using a different render mode as discussed earlier).
• Execution: presentation of 3D visualisation of the actual execution from a concrete starting state through to either a breakpoint , or the ﬁnal goal.
A breakpoint is a point where the actual sensor valuations differ from the assumed sensor valuations in the plan trace being executed.
We note that breakpoints provide a useful opportunity to supply further information to the practitioner, and is something we explored in our user study (next section).
Empirical Evaluation
For evaluation we developed a prototype interface for our construction world (see section “Background”) featuring:
• Branched plan generation, based on the K-Replanner, extended to output the full contingency tree.
• Selection of a set of execution traces characterising the scope of possibilities within generated branched plans.
• Radial visualisation of branched plans, using an approach building on (Magnaguagno et al. 2017, 2020) • Virtual environment for presentation to practitioners via 3D visualisation of selected traces.
User Study
We set up a user study to investigate the impact of different modes of information presentation and exploration on understanding of agent plans, in terms of awareness of agent intended actions under uncertainty, the agents’ overall goal and participant ratings of preparedness to answer questions.
We recruited 24 native english speakers to participate in the study.
The participants were not experts in planning.
The study was delivered via an online questionnaire and all participants were provided with an introduction to the setting and aspects of the visualisation e.g. the visual difference between simulation and execution , as in Figure 4.
For the study a single planning instance was used, withbreakpoints, i.e., points where, at execution, the actual sensor values differ from those assumed in the optimistic plan.
Experimental Conditions Participants were randomly assigned to one of three conditions which differed with respect to: (i) whether the range of branched plan possibilities were communicated i.e. shown radial visualisation of the full branched plan; (ii) the number of selected branching plan traces they were shown in simulation mode ; and (iii) the timing of visualisation of branched plan simulations in
Q1: “... sufﬁcient information about the possible alternative ex- ecutions for you to anticipate the execution steps ..?”
Q2: “... what do you think the agent will do next?”
Q3: “How conﬁdent are you about your answer?”
Q4: “ ... do you know what the agent’s goal was? ...
How conﬁ- dent are you? ...
State what the agent’s goal was”
[Figure]
“... How well prepared were
[Figure]
[Figure] [Figure]
I
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[Figure] [Figure]
[Figure]
Q
(6- scale: idea
High): high for U PFRONT with similar and B ASELINE .
See text details.
relation to actual execution .
These conditions are as follows and illustrated in Figure 8:
• B ASELINE : participants were shown simulation of the optimistic plan a , followed by execution of the optimistic plan to the next breakpoint b ), or the goal.
After each breakpoint this continued, with simulation of the optimistic plan from the current state, followed with execution of the optimistic plan looping through to the goal.
• U PFRONT : participants were shown the radial visualisation of the full branched graph c .
Then simulation of each of k diverse traces (rationale for k below) and the optimistic plan d , followed by execution of the optimistic plan through to the ﬁrst breakpoint e .
Continuation from the ﬁrst breakpoint, repeatedly loops, showing simulation of the optimistic plan from the current state f , followed by execution of the optimistic plan to the next breakpoint or goal g , repeating through to the goal.
I NTERLEAVED :
participants were shown the radial visualisation of the full branched graph h .
Then simulation of each of k diverse traces (rationale for k below) and the optimistic plan i , followed by execution of the optimistic plan, through to the next breakpoint or the goal j ).
Continuation from each breakpoint repeatedly loops starting from the optimistic plan from the new current state.
Rationale for values of k
For I
NTERLEAVED k was 2, the mode of the silhouette scores across the breakpoints.
It
Q
[Figure]
Q
[Figure]
Preparedness
[Figure] [Figure]
(C); % correct goal awareness (A).
Q5 Preparedness: (5 point Likert scale: 0=
Not Prepared, 5=
Well Prepared).
Overall, results show increases in conﬁdence, accuracy and preparedness rating for more informed users (U PFRONT and I NTERLEAVED ).
was decided not to use the silhouette scores directly, as this would mean presenting different number of plans at each breakpoint and would introduce too much variation into the study.
For U PFRONT , k was 10 to ensure these participant saw a similar number of videos overall to I NTERLEAVED .
Expectation Our expectation was that the U PFRONT participants would have a strong sense of how the initial stages of execution would progress, but perhaps lose conﬁdence towards the end, as the execution (perhaps) deviated from the plans they observed at the start.
We expected that the I NTERLEAVED participants would perform fairly well, but possibly feel less prepared in early stages, or where the execution deviated from the small collection of plans they observed.
Results
Breakpoint Questions During execution, at each breakpoint, all participants were asked about the information they had seen so far, what they thought the agent would do next and their level of conﬁdence.
Text for these questions, Q1Q3, is in Figure 9, and responses summarised in Figure 10.
For Q1, sufﬁcient information, the more informed conditions, I NTERLEAVED and U PFRONT , gave higher rankings than B ASELINE , with respect to receiving sufﬁcient information to anticipate execution steps they observed.
This is to be expected, as it reﬂects these participants receiving more information prior to execution.
Of interest is the increased rankings over breakpoints 1-4 for B ASELINE .
We suspect this results from clariﬁcation through exposure to execution visualisations in the absence of diverse trace simulations.
For Q2, participant understanding of agent intentions (Next Action), results show similar performance for I NTERLEAVED and B ASELINE (overall avg.
75% and 78% respectively) with poorer overall performance for U PFRONT (56%).
However analysis of responses for breakpoint 1 are interesting: for this question all U PFRONT participants got the direction correct, in stark contrast to B ASELINE where all incorrect responses indicated moving in the wrong direction.
We observed similar behaviour at each breakpoint (in particular, breakpoint 3).
This strongly suggests that the U PFRONT participants understood the intended direction, but some failed to understand the wireframe communication of clearing rubble (e.g. some participants noted, in the open text questions at the end of the questionnaire, that the visualisations had been unclear about whether rubble should be removed or passed through).
From this interpretation, the results are consistent with our expectation: there will be more variation on participant understanding of how the agent intends to proceed (in terms of direction) with B ASELINE .
Q3, Conﬁdence ratings, are high for U PFRONT (avg.
3.8) with similar overall conﬁdence for I NTERLEAVED and
B ASELINE .
For U PFRONT , this is to be expected given the upfront simulation of diverse traces.
Interestingly, despite this conﬁdence for participants in U PFRONT , they weren’t necessarily correct in their answers as shown for Q2 (avg.
56%), in contrast to higher correctness scores for I NTERLEAVED and B ASELINE .
Post-Execution Questions Following completion of execution all participants were asked about their awareness of the agents overall goal and their overall feelings of preparedness (Q4-Q5 shown in Figure 9).
Responses to these questions are shown in Figure 11.
For U PFRONT this shows consistently high rankings of conﬁdence and preparedness, in line with responses to execution questions.
In contrast to the execution questions, users in this condition exhibited similar accuracy, with respect to the agent goal, to I NTERLEAVED .
This improvement suggests increase in level of informedness from exposure to the execution visualisation itself.
The low rankings for Q4-Q5 for B ASELINE are to be expected given they are less informed than the other conditions.
Overall Our expectation was that U PFRONT would have a strong sense of how the initial execution would progress, but perhaps lose conﬁdence as the execution (perhaps) deviated from the initial plans they saw.
We expected that I NTERLEAVED would perform fairly well, but possibly feel less prepared in early stages, or where execution deviated from the small collection of plans they had seen so far.
For U PFRONT participants performed beyond expectations, appearing to use what they had understood from visualisation at the outset to guide their predictions.
However, for
I NTERLEAVED it appears that the number of plans was insufﬁcient for them to interpolate accurately and conﬁdently.
This is an important result, which indicates that the silhouette score might not be appropriate, at least for beginners.
Related Work
Explainable AI Planning (XAIP)
(Fox, Long, and Magazzeni 2017), is an area of growing importance and focus in planning, which is motivated by the need for trust, interaction and transparency between users and AI controlled agents (Hoffmann and Magazzeni 2019;
Kambhampati 2019; Lindsay 2019; Sohrabi, Baier, and McIlraith 2011).
Communicating the intentions of the agent plays an important role in XAIP.
The form of visualisation for communicating intention vary from annotations indicating objects that are involved in the agent’s plan (Chakraborti et al. 2018), the indication of intended movements of the robot (Chadalavada et al. 2015) and a visualisation of the agent’s internal decision making (Chakraborti et al.
2017a).
A common approach is to use specialised visualisations to present the intentions of an agent to a system user, e.g., through projection (Leutert, Herrmann, and
Schilling 2013; Chadalavada et al. 2015) or augmented reality (Chakraborti et al.
; Zolotas and Demiris 2019).
In (Chadalavada et al. 2015) it is demonstrated that projecting the robots intentions improves the user rating of the robot.
In (Chakraborti et al. 2018)
they build a domain speciﬁc visualisation, using augmented reality to project a robot’s intentions, which also allows manipulation.
The approach for visualising the complete branched plan that we use here, is related to other domain independent visualisations (Magnaguagno, Pereira, and Meneguzzi 2016; Magnaguagno et al. 2017, 2020).
In (Magnaguagno, Pereira, and
Meneguzzi 2016)
they present a plan visualisation, which exploits a visual metaphor in order to communicate abstract planning concepts, such as action preconditions.
Our branched plan visualisation was inspired by the state space visualisation of (Magnaguagno et al. 2017).
(Chakraborti et al. 2017b) assume the user model is available so they can isolate speciﬁc situations where the user’s understanding of the current sequence might fail.
In this way they consider explanations as model corrections.
We do not assume a user model, rather, that a common ground can be established by exploiting sequential plan visualisations.
Selecting or generating sets of diverse plans has been investigated in classical planning (Katz and Sohrabi 2020), and various applications have been identiﬁed, including risk assessment (Sohrabi et al. 2018) and user preferences (Nguyen et al. 2012).
(Coman and Munoz-Avila 2011) adopt two diversity measures, including the measure we use, and demonstrate that both approaches lead to identifying diverse plans.
They also demonstrate that a domain speciﬁc diversity measure was particularly effective.
Our approach is compatible with any approach that can return a set of diverse plans (especially those able to vary set size).
Discussion and Conclusion
In this work we have considered the problem of visualising a contingent plan and providing the user with visualisation of the intended plan and key information about the contingency tree.
The aim is to provide access to the potential alternatives captured in the contingency tree, so users can better understand and assess time required and risk implied by the plan.
We have presented a general approach that provides a template for constructing branched plan visualisations.
It focuses on general aspects of branched plans, such as diversity and inference, thus making it.
generalisable to other settings e.g. using tools such as P LANIMATION (Chen et al. 2020).
The results of a user study assessing our approach are promising.
They indicate that users can gain an awareness of agent intentions and the scope of alternative possibilities through exposure to selected traces which characterise the branched plan space.
In future work, the different modes of presentation and use of the silhouette score will be further explored, along with user preferences for different modes of presentation and the interface itself, especially in the context of in-situ visualisation of actions through mixed-reality, which will further support interactive exploration of the agents’ plan traces. Acknowledgments
This work was partially funded by the ORCA Hub ( orcahub.org ), under EPSRC grant EP/R026173/1; and
DSI Collaborative Grant CR-0016.