Smarter Robot Paths: Balancing Goals and Preferences

Author: Denis Avetisyan

This research introduces a new path planning algorithm that allows robots to intelligently navigate complex tasks while accommodating user-defined priorities when perfect solutions aren’t possible.

Trajectories demonstrate that the proposed heuristic achieves minimally relaxed subspecifications-indicated by green circles-while avoiding the suboptimal relaxation denoted by a red circle, suggesting an improved approach to trajectory optimization.

A heuristic A* search approach to temporal logic path planning incorporates relaxed task satisfaction based on user preferences and weighted transition systems.

Achieving full compliance with complex, temporally-defined robotic tasks is often impractical in large, dynamic environments. This paper addresses this challenge with ‘A-based Temporal Logic Path Planning with User Preferences on Relaxed Task Satisfaction’, introducing a novel A search framework capable of efficiently generating near-optimal robot trajectories. By integrating user-defined preferences for relaxing task constraints, the proposed approach effectively balances mission objectives with feasibility, leveraging automata-based representations and a computationally inexpensive heuristic. Could this framework enable robots to navigate complex scenarios with greater autonomy and adaptability, even when faced with imperfect information or unforeseen obstacles?

Navigating Complexity: The Rise of Adaptive Robotics

Contemporary robotics is rapidly extending beyond the controlled settings of factory floors and into the unpredictable realities of human-populated environments. This transition necessitates a shift in capabilities, as robots are now expected to perform increasingly intricate operations – from surgical assistance and in-home care to search and rescue missions in disaster zones – all while navigating dynamic surroundings filled with unforeseen obstacles and changing conditions. These environments present significant challenges, demanding that robotic systems not only execute pre-programmed instructions but also perceive, interpret, and react to the world around them in real-time. Consequently, research is focused on developing robots capable of robust perception, adaptable planning, and safe interaction with humans and unstructured spaces, marking a move towards truly versatile and autonomous machines.

Conventional robotic planning relies heavily on pre-programmed sequences and meticulously mapped environments, methods quickly overwhelmed by the computational demands of genuinely complex tasks. As robots venture beyond controlled factory floors and into unpredictable real-world scenarios, the limitations of these approaches become starkly apparent. The sheer number of possible actions and potential environmental variations creates a “combinatorial explosion,” rendering exhaustive planning impractical. Furthermore, static plans lack the necessary flexibility to respond to unforeseen obstacles or dynamic changes, necessitating constant re-planning which further strains computational resources. Researchers are therefore investigating methods that prioritize efficient approximations and real-time adaptation, allowing robots to learn from experience and adjust their strategies on the fly, rather than relying on complete, pre-calculated solutions.

The pursuit of reliable robotic autonomy hinges on the ability to define task requirements with mathematical precision, a practice known as formal methods. However, this approach frequently encounters difficulties when applied to real-world scenarios. Environments are rarely static or perfectly predictable, and human instructions are often inherently ambiguous – a request to “pick up the red block” doesn’t specify how, with what force, or what to do if it’s obstructed. Bridging this gap between the clarity demanded by robotic control systems and the imprecision of natural language, or even nuanced human demonstration, remains a significant challenge. Researchers are actively exploring techniques like probabilistic reasoning and machine learning to allow robots to interpret incomplete or uncertain specifications, effectively translating ambiguous goals into actionable plans while managing the inherent risks of operating in unpredictable contexts.

The proposed heuristic consistently estimates costs with a low relative error compared to the optimal cost.

Formalizing Intent: Precise Specification with Temporal Logic

Syntactically co-safe Linear Temporal Logic (scLTL) is employed as a formal specification language to define robot task requirements due to its ability to express temporal properties with guaranteed completeness and safety. Unlike standard Linear Temporal Logic (LTL), scLTL restricts the use of universal quantifiers to ensure that all possible execution paths satisfy the specified requirements, preventing undefined behavior or incomplete tasks. Specifically, scLTL formulas are constructed using Boolean operators, atomic propositions representing robot actions or sensor readings, and temporal operators such as $X$ (next), $F$ (eventually), $G$ (always), and $U$ (until). This formalism allows for the precise and unambiguous description of desired robot behavior, enabling automated verification and planning processes within the $Planning Framework$.

Syntactically co-safe Linear Temporal Logic (scLTL) enables the specification of robot task requirements beyond simple atomic propositions. It allows for the expression of temporal properties including sequences of actions – for example, requiring a robot to “pick up object A before placing it on surface B” – and conditional constraints. These constraints can relate actions to specific states; for instance, a robot might be required to “only activate effector C if sensor D reports a value greater than 10”. Formally, scLTL utilizes operators like $X$ (next), $F$ (eventually), $G$ (always), and $U$ (until) to construct these complex temporal relationships between states and actions, providing a precise language for defining desired robot behavior.

The Planning Framework serves as the central component for translating high-level task specifications into executable robot actions. It operates by accepting formally defined goals expressed in syntactically co-safe Linear Temporal Logic (scLTL), and then generating plans that satisfy these temporal properties. This process involves a search algorithm that explores possible action sequences, evaluating each against the scLTL constraints to ensure adherence to the specified requirements – such as action ordering, conditional execution, and eventual fulfillment of desired states. The framework’s architecture enables the robot to not only achieve a goal state, but also to demonstrably satisfy the way in which the goal must be achieved, as defined by the scLTL specification.

Embracing Imperfection: Relaxation and Preference Integration

The system addresses scenarios where strict adherence to initial task specifications is impossible or results in suboptimal outcomes by integrating user-defined preferences for relaxation. These preferences allow the framework to intelligently modify task requirements when faced with infeasibility or undesirable results, effectively broadening the solution space. Rather than simply failing when constraints cannot be met, the system leverages user input to prioritize which aspects of the task are most critical, and which can be adjusted to achieve a feasible and satisfactory solution. This is distinct from automated constraint relaxation which lacks user-specific value judgments, and ensures the resulting solution aligns with user expectations even when perfect fulfillment of the original request is not possible.

Relaxation techniques within the framework address infeasibility or undesirability in task specifications by systematically altering requirements. This process doesn’t involve random modification; instead, it utilizes a defined methodology to adjust constraints, aiming to minimize the degree of violation across all altered parameters. Importantly, these techniques are not applied uniformly; user-defined priorities dictate which requirements can be relaxed and the relative cost associated with each relaxation, ensuring that the resulting solution aligns with the user’s preferences even if it deviates from the original, strict specification. The system actively seeks solutions that satisfy the highest-priority requirements while intelligently compromising on lower-priority ones.

The system utilizes a Weighted Finite State Edit System (WFSE) to quantify the impact of modifying task requirements. The WFSE represents possible relaxations as transitions between states, with each transition associated with a cost reflecting the degree of deviation from the original specification. These costs are determined by user-defined priorities, allowing the system to explore relaxation options and select those that minimize overall cost while satisfying as many original constraints as possible. The weighting scheme within the WFSE enables a granular assessment of relaxation impacts, considering factors such as the type of constraint violated and the magnitude of the modification. This allows for the generation of feasible plans even when strict adherence to all initial requirements is impossible.

Efficient Trajectory Planning with Informed Search

Informed search algorithms, specifically implementations of the $A^$ Search Algorithm and ARA, are employed to efficiently navigate the relaxed state space and determine optimal paths. These algorithms differ from uninformed search methods by incorporating heuristic functions to estimate the cost to reach the goal state, allowing them to prioritize exploration of more promising paths. This prioritization reduces the search space and improves computational efficiency, as the algorithms focus on nodes deemed more likely to be part of the optimal solution. The relaxed state space represents a simplified version of the problem, allowing for faster heuristic evaluation while still providing a valid, albeit potentially sub-optimal, solution path.

The heuristic function is integral to informed search algorithms by providing an estimate of the remaining cost, or “Distance to Satisfaction”, from a given node to the goal state. This estimate allows the search algorithm to prioritize exploration of nodes deemed more likely to lead to an optimal solution, effectively guiding the search process. The accuracy of this heuristic directly impacts performance; a more accurate heuristic reduces the number of nodes expanded, leading to faster pathfinding and reduced memory consumption. In our implementation, the heuristic cost is empirically bounded by a factor of 1.5 times the optimal cost, ensuring a controlled trade-off between heuristic accuracy and computational efficiency.

In a 20×20 grid environment, implementation of a heuristic-based A* search algorithm resulted in substantial performance gains when contrasted with a baseline uninformed search. Specifically, the heuristic-based approach demonstrated a reduction in runtime of up to 93.5% and a corresponding decrease in memory usage of up to 93.2%. These improvements indicate a significant increase in computational efficiency attributable to the informed search strategy, allowing for faster pathfinding and reduced resource consumption in the tested environment.

To address scalability for large state spaces, our system incorporates both Contraction Hierarchies and Stylus path planning techniques. Contraction Hierarchies pre-process the graph by iteratively contracting nodes based on their degree, creating a multi-level representation that facilitates rapid shortest path queries. Stylus utilizes a shortcut-based approach, identifying and storing edges that represent significant reductions in path length, allowing the algorithm to bypass large portions of the graph during search. These techniques, implemented in conjunction with informed search, enable efficient pathfinding in complex environments such as the New York City motorway network, consisting of 378,040 nodes and 1,131,664 edges.

Testing of the implemented heuristic function indicates a cost no greater than 1.5 times the cost of the optimal path. This performance has been validated through application to a large-scale dataset representing the New York City motorway network, which consists of 378,040 nodes and 1,131,664 edges. Successful operation on this network demonstrates the scalability and practical applicability of the heuristic within complex, real-world routing scenarios.

The proposed heuristic successfully guides trajectories to nodes containing key atomic propositions, as demonstrated by the resulting paths compared to the baseline.

Towards Robust and Adaptive Robotic Systems

Robotic systems are increasingly designed with integrated architectures that prioritize resilience and flexibility in dynamic settings. Rather than rigidly executing pre-programmed instructions, these robots leverage sensor fusion, predictive modeling, and real-time adaptation algorithms to navigate and respond to unexpected events. This approach allows for graceful degradation of performance, rather than catastrophic failure, when encountering disturbances like slippery surfaces, moving obstacles, or incomplete information. The system continuously assesses its environment, forecasts potential issues, and dynamically adjusts its actions – be it modifying a trajectory, re-planning a task, or requesting human assistance – ensuring continued operation and minimizing disruptions. Such adaptability is crucial for deploying robots beyond controlled laboratory environments and into the unpredictable complexity of real-world applications.

Robotic systems are increasingly designed to operate alongside humans, necessitating an ability to understand and respond to individual needs. This is achieved through explicit modeling of user preferences – a process where the robot learns not just what a task is, but how a user prefers it to be completed. By incorporating these preferences, the system moves beyond simple task execution and can prioritize actions intelligently, even when faced with ambiguous or incomplete instructions. For instance, a robotic assistant might discern that a user prefers objects placed gently versus quickly, or that certain tasks should be completed in a specific order, allowing it to make informed decisions and adapt its behavior without explicit reprogramming. This nuanced understanding fosters more natural and effective human-robot interaction, ultimately leading to systems that are not only capable but also considerate of individual user expectations.

The architecture’s inherent scalability and computational efficiency are poised to unlock robotics in diverse, practical settings. Beyond simulated environments, this framework facilitates the deployment of robots capable of navigating dynamic spaces – envisioning autonomous vehicles adapting to unpredictable traffic, or delivery robots traversing complex urban landscapes. Equally promising is the advancement of robotic manipulation; the system allows for intricate assembly tasks, precision agriculture, and even surgical assistance, all while maintaining robustness in the face of environmental variations and unexpected obstacles. This combination of adaptability and processing speed signifies a crucial step towards realizing truly versatile robots capable of seamlessly integrating into, and enhancing, everyday life.

The pursuit of robotic autonomy, as detailed in this work, often necessitates navigating complex constraints. The presented A* algorithm, by accommodating user-defined relaxation preferences, exemplifies a pragmatic approach to problem-solving. This mirrors the sentiment expressed by John McCarthy: “It is better to deliver a program that does a few things well than a program that attempts to do everything.” The research prioritizes feasible solutions, even if it means adjusting task satisfaction levels, reflecting a preference for functional clarity over exhaustive, yet unattainable, perfection. This aligns with the core idea of prioritizing a working system-even a simplified one-over an overly ambitious, incomplete endeavor, embracing a similar philosophy of focused implementation.

Further Refinements

The presented work addresses a specific locus of robotic autonomy-planning under softened constraints. Yet, the inherent complexity of temporal logic, even when relaxed, remains. Future iterations must confront the scalability of this approach. Current methods, while demonstrating efficacy, still rely on heuristic estimations within the A* framework. Refinement of these heuristics-perhaps leveraging learned models of task feasibility-offers a direct path toward handling more intricate, real-world scenarios. Clarity is the minimum viable kindness.

A salient limitation lies in the static nature of user preference weighting. Environments are rarely static. Adaptation-allowing the system to learn and refine preference models based on observed task execution and environmental feedback-constitutes a logical progression. This necessitates exploration of reinforcement learning paradigms, integrated with the automata-based planning framework.

Ultimately, the pursuit of ‘intelligent’ autonomy demands a reduction, not an accumulation, of complexity. The goal is not simply to satisfy temporal logic, but to understand the underlying constraints, and to operate effectively within their boundaries. A perfect solution will not be feature-rich; it will be elegantly minimal.

Original article: https://arxiv.org/pdf/2511.16844.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/