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arxiv: 2604.09578 · v1 · submitted 2026-02-24 · 💻 cs.AI

Recognition: no theorem link

Explainable Planning for Hybrid Systems

Mir Md Sajid Sarwar
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Pith reviewed 2026-05-15 19:35 UTC · model grok-4.3

classification 💻 cs.AI
keywords explainable planninghybrid systemsautomated planningXAIPartificial intelligencereal-world applicationsplanning explanations
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The pith

Explainable planning methods can be built for hybrid systems that model real-world problems with continuous and discrete elements.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The thesis develops techniques to generate human-readable explanations for automated planning decisions in hybrid systems. These systems combine continuous changes such as time or speed with discrete decisions and appear in domains like self-driving cars, energy grids, and robotics. The core effort shows that explanations can be added while preserving the ability of planners to solve complex tasks. A reader would care because many safety-critical applications now depend on such planners, and unexplained outputs make it hard to verify or trust the results. The work treats hybrid modeling as the key bridge between theoretical planning and practical deployment.

Core claim

The paper establishes that explainable artificial intelligence planning approaches can be extended to hybrid systems, delivering both valid plans and explanations in settings that capture real-world dynamics more closely than discrete-only models.

What carries the argument

XAIP methods adapted for hybrid systems that combine discrete and continuous variables to support simultaneous planning and explanation generation.

Load-bearing premise

The developed XAIP approaches remain effective and applicable to hybrid systems in practice without reducing planning performance.

What would settle it

A concrete test in which an XAIP planner for a hybrid system such as autonomous vehicle routing either fails to produce a valid plan or fails to produce an explanation while a standard planner succeeds on the same instance.

Figures

Figures reproduced from arXiv: 2604.09578 by Mir Md Sajid Sarwar.

Figure 1.1
Figure 1.1. Figure 1.1: XAIP perspectives • End user: These are the individuals who will use or be impacted by the implement￾ation of new technology and processes. They interact with the system in the form of a user. For example, this may be a passenger on an autonomous car, or a human teammate in a human-robot team (Chakraborti et al. [2019b]) who is affected by, or is a direct stakeholder in the agent’s plans, or a user who c… view at source ↗
Figure 1.2
Figure 1.2. Figure 1.2: The proposed organization to discuss the challenges and research direc [PITH_FULL_IMAGE:figures/full_fig_p038_1_2.png] view at source ↗
Figure 2.1
Figure 2.1. Figure 2.1: Stealth surveillance system for monitoring hostage scenario [PITH_FULL_IMAGE:figures/full_fig_p051_2_1.png] view at source ↗
Figure 2.2
Figure 2.2. Figure 2.2: CoppeliaSim model of the quadruped robot [PITH_FULL_IMAGE:figures/full_fig_p055_2_2.png] view at source ↗
Figure 2.3
Figure 2.3. Figure 2.3: The robotic software architecture for SLAM, path-planning, and control. [PITH_FULL_IMAGE:figures/full_fig_p056_2_3.png] view at source ↗
Figure 2.4
Figure 2.4. Figure 2.4: Phases of Move-forward and Rotate-Clockwise maneuvering of the robot 1) Move-forward: The motion primitive Move-forward is used to perform a forward direc￾tion movement for the robot. In the first phase, the robot lifts its front-right and back-left legs together while front-joint and back-joint are rotated by 30° and −30° angles, re￾spectively. As front-left and back-right legs are grounded at that time… view at source ↗
Figure 2.5
Figure 2.5. Figure 2.5: Robot movement The movement of the robot following a projected path is shown in [PITH_FULL_IMAGE:figures/full_fig_p060_2_5.png] view at source ↗
Figure 2.6
Figure 2.6. Figure 2.6: Robot’s trajectory We assume a buffer zone of distance ±E around the projected path as shown in [PITH_FULL_IMAGE:figures/full_fig_p060_2_6.png] view at source ↗
Figure 2.7
Figure 2.7. Figure 2.7: Robot’s deviation from the path The angle ϕ between the line AB and CB can be derived as: ϕ = arctan ∥ m2 − m1 1 + m2 ∗ m1 ∥ The length a of CB is calculated as: a = q (x2 − x) 2 + (y2 − y) 2 The robot’s deviation from the projected path is calculated as: d = a ∗ sin ϕ Hybrid controller: The hybrid controller for our robot is shown in [PITH_FULL_IMAGE:figures/full_fig_p061_2_7.png] view at source ↗
Figure 2.8
Figure 2.8. Figure 2.8: Hybrid controller details of this integration are shown in Algorithm 2.3. The algorithm takes the goal po￾sition (xg, yg), a set of pose samples St−1, measurement data zt , control data ut , depth map dt and probabilistic partial map PMt−1 as inputs. The algorithm begins with ini￾tializing the time t, St−1, PMt−1, and the problem instance prob in line 2. In line 3, it receives the robot’s current pose pt… view at source ↗
Figure 2.9
Figure 2.9. Figure 2.9: Planning and Navigation: simulation results of plan generation and nav [PITH_FULL_IMAGE:figures/full_fig_p065_2_9.png] view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: The hybrid automaton model of the Car domain [PITH_FULL_IMAGE:figures/full_fig_p074_3_1.png] view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: Example scenarios where makespan is useful. In the figure, t encodes time, and a and b are variables. In our contrastive plan explanation framework, which is discussed in Section 3.2, some of the contrastive questions are concerning the sequence of actions appearing in a plan. We 46 [PITH_FULL_IMAGE:figures/full_fig_p074_3_2.png] view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3: The Contrastive Plan Explanation Framework. [PITH_FULL_IMAGE:figures/full_fig_p077_3_3.png] view at source ↗
Figure 3.4
Figure 3.4. Figure 3.4: The hybrid automaton for the corresponding [PITH_FULL_IMAGE:figures/full_fig_p083_3_4.png] view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: The hybrid automaton for the corresponding [PITH_FULL_IMAGE:figures/full_fig_p085_3_5.png] view at source ↗
Figure 3.6
Figure 3.6. Figure 3.6: The hybrid automaton for the corresponding [PITH_FULL_IMAGE:figures/full_fig_p088_3_6.png] view at source ↗
Figure 3.7
Figure 3.7. Figure 3.7: The hybrid automaton for the corresponding [PITH_FULL_IMAGE:figures/full_fig_p089_3_7.png] view at source ↗
Figure 3.8
Figure 3.8. Figure 3.8: The hybrid automaton for the corresponding [PITH_FULL_IMAGE:figures/full_fig_p092_3_8.png] view at source ↗
Figure 3.9
Figure 3.9. Figure 3.9: The hybrid automaton for the corresponding [PITH_FULL_IMAGE:figures/full_fig_p102_3_9.png] view at source ↗
Figure 3.10
Figure 3.10. Figure 3.10: The hybrid automaton for the corresponding [PITH_FULL_IMAGE:figures/full_fig_p104_3_10.png] view at source ↗
Figure 3.11
Figure 3.11. Figure 3.11: Scatter graph comparing the HPlan generation time over the original plan. OP represents the original plan whereas QN1, QN2, QN3, QN4, QN5, QN7 and QN8 represent the HPlans generated against the compilations for the contrastive questions discussed in Sec. 3.3.1, 3.3.2, 3.3.3, 3.3.4, 3.3.5, 3.3.7 and 3.3.8, respectively. 86 [PITH_FULL_IMAGE:figures/full_fig_p114_3_11.png] view at source ↗
Figure 3.12
Figure 3.12. Figure 3.12: Scatter graph comparing the memory usages by the planner for the [PITH_FULL_IMAGE:figures/full_fig_p115_3_12.png] view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Tool Workflow P rob is a planning problem instance that constitutes an initial state and a goal condition. The planning problem Π is fed to a hybrid system planner SMTPlan+ (Cashmore et al. [2020]) or ENHSP (Scala et al. [2016]) based on the user’s choice. The planner produces a plan ϕ which is presented to the user. This plan is referred to as the original plan. A plan is a time-annotated sequence of ac… view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: A snapshot of the tool’s GUI Interpreter: This module involves transforming the user’s contrastive inquiry into a formalized question. This is accomplished by feeding the user-chosen templatized con￾trastive question together with template bindings of actions, time-instances, and frequency of actions of the domain, leading to the generation of a concrete question. In the plan presented in Listing 4.3, a … view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: Binding templatized question with instances. [PITH_FULL_IMAGE:figures/full_fig_p124_4_3.png] view at source ↗
Figure 4.4
Figure 4.4. Figure 4.4: An HPlan generated by SMTPlan+ according to the contrastive question. [PITH_FULL_IMAGE:figures/full_fig_p125_4_4.png] view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: The human and the agent view of the warehouse environment is depicted. [PITH_FULL_IMAGE:figures/full_fig_p131_5_1.png] view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: Infeasibility of the plan explained by continuous dynamics, particularly [PITH_FULL_IMAGE:figures/full_fig_p134_5_2.png] view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: The HA model for the warehouse automation problem, where locations [PITH_FULL_IMAGE:figures/full_fig_p135_5_3.png] view at source ↗
Figure 5.4
Figure 5.4. Figure 5.4: The flow diagram of our model reconciliation framework [PITH_FULL_IMAGE:figures/full_fig_p137_5_4.png] view at source ↗
Figure 6.1
Figure 6.1. Figure 6.1: The rover domain is depicted. Initially, the rover is at cell 11. Mountains [PITH_FULL_IMAGE:figures/full_fig_p152_6_1.png] view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: A hybrid automaton model of the planetary rover domain (partially [PITH_FULL_IMAGE:figures/full_fig_p153_6_2.png] view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: Proposed Explanation Framework. In this section, we describe our explanation algorithm, which takes an unsolvable planning problem Π as input and computes an artifact Explanation(Π), which we define later in the text (Def. 6.3.4). Our explanation algorithm attempts to divide an unsolvable planning problem Π into several sub-problems, following the common divide-and-conquer paradigm of problem-solving. Th… view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: All runs of valid plans from the initial set to the goal set must pass [PITH_FULL_IMAGE:figures/full_fig_p157_6_4.png] view at source ↗
Figure 6.5
Figure 6.5. Figure 6.5: A depiction of a graph of a H. Let S and D be the source and the goal locations in a planning problem Π. Every path from S to D visits locations A and B in sequence. Thus, S-A-B-D is the LCS of paths in PS(Π). Clearly, if a valid run of a plan exists in the H, the run must visit the invariants of S, A, B, and D sequentially. Proof 6.3.3 GH = (V , E) is implicitly present in H of Π. Any graph search algor… view at source ↗
Figure 6.6
Figure 6.6. Figure 6.6: Illustration of results in the example scenarios. [PITH_FULL_IMAGE:figures/full_fig_p165_6_6.png] view at source ↗
Figure 6.7
Figure 6.7. Figure 6.7: The city route network is depicted. Each node represents the important [PITH_FULL_IMAGE:figures/full_fig_p167_6_7.png] view at source ↗
Figure 6.8
Figure 6.8. Figure 6.8: Warehouse automation domain. obstacles through which the robot cannot move. The movement of the robot is restricted to one of its adjacent cells, and movement to diagonal cells is prohibited. The continuous dynamics capture the battery charge depletion rate of the robot within a cell. Within each cell, the robot follows the dynamics particular to that cell. When the robot makes a transition from one cell… view at source ↗
Figure 8.1
Figure 8.1. Figure 8.1: A hybrid automaton model of the generator-events domain for the planning problem instance 1. [PITH_FULL_IMAGE:figures/full_fig_p197_8_1.png] view at source ↗
read the original abstract

The recent advancement in artificial intelligence (AI) technologies facilitates a paradigm shift toward automation. Autonomous systems are fully or partially replacing manually crafted ones. At the core of these systems is automated planning. With the advent of powerful planners, automated planning is now applied to many complex and safety-critical domains, including smart energy grids, self-driving cars, warehouse automation, urban and air traffic control, search and rescue operations, surveillance, robotics, and healthcare. There is a growing need to generate explanations of AI-based systems, which is one of the major challenges the planning community faces today. The thesis presents a comprehensive study on explainable artificial intelligence planning (XAIP) for hybrid systems that capture a representation of real-world problems closely.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper presents a comprehensive study on explainable artificial intelligence planning (XAIP) for hybrid systems. It emphasizes the application of automated planning in complex, safety-critical domains such as smart energy grids, self-driving cars, warehouse automation, urban and air traffic control, search and rescue, surveillance, robotics, and healthcare, while addressing the growing need for explanations of AI-based systems in these areas.

Significance. If the XAIP approaches developed prove effective for hybrid systems without compromising planning performance, the work could advance explainability in automated planning for real-world applications. The emphasis on hybrid systems that closely model practical problems offers potential for improved trust and safety in autonomous systems, provided concrete methods and evaluations are demonstrated.

major comments (1)
  1. [Abstract] Abstract: The central claim of a 'comprehensive study' on XAIP methods for hybrid systems cannot be evaluated, as no specific approaches, algorithms, derivations, experimental results, or performance metrics are provided to support assertions of effectiveness and applicability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their review of our manuscript on explainable planning for hybrid systems. We address the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim of a 'comprehensive study' on XAIP methods for hybrid systems cannot be evaluated, as no specific approaches, algorithms, derivations, experimental results, or performance metrics are provided to support assertions of effectiveness and applicability.

    Authors: The abstract is intentionally concise to summarize the thesis scope. The full manuscript details the specific XAIP approaches for hybrid systems, including algorithms for explanation generation, formal derivations of the methods, and experimental results with performance metrics on domains such as smart energy grids, robotics, and traffic control. The 'comprehensive study' claim refers to the breadth of the work presented in the body of the paper. We can revise the abstract to briefly reference key methods and evaluation outcomes if this improves clarity. revision: partial

Circularity Check

0 steps flagged

No circularity detected; derivation chain not present in available text

full rationale

The provided abstract and context describe a comprehensive study on XAIP methods for hybrid systems without any equations, derivations, fitted parameters, predictions, or self-citations that could reduce to inputs by construction. No load-bearing steps of the enumerated kinds are identifiable, so the work is treated as self-contained conceptual research rather than a closed mathematical chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no technical details on parameters, axioms, or entities; no free parameters, axioms, or invented entities can be identified.

pith-pipeline@v0.9.0 · 5403 in / 1018 out tokens · 58816 ms · 2026-05-15T19:35:02.782686+00:00 · methodology

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Reference graph

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