Interval-Based Localization Techniques for Mobile Robotics

Interval-based localisation techniques employ mathematical intervals to represent uncertainties in sensor measurements, model parameters and environmental interactions. By operating on sets of possible values rather than single estimates, these methods guarantee that the true state of a mobile robot—its position and orientation—lies within the computed bounds. Central to this approach is the formulation of the localisation problem as an Interval Constraint Satisfaction Problem, which systematically narrows intervals through constraint propagation and optimisation. This yields consistent and reliable localisation even in the presence of non-Gaussian noise, sensor drift or map inaccuracies. Compared with probabilistic filters, interval methods avoid inconsistency and overconfidence by acknowledging bounded errors explicitly. Applications span autonomous vehicles navigating urban canyons and indoor service robots operating without GPS, where robust position estimates are crucial. Recent advances have enhanced computational efficiency through graph-based optimisation and adaptive partitioning, while integration with inertial and odometric measurements has improved latency and resilience to outliers. The global significance of this work lies in its potential to underpin safety-critical navigation in unstructured environments and to support emerging systems in search and rescue, planetary exploration and precision agriculture.

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Research from all publishers

Recent developments have refined interval-based methods for practical deployment. One study introduced a dynamic graph-based optimisation framework for car-like robots in outdoor settings, constructing an interval map during a GPS-supported teaching phase and applying interval constraint propagation on a two-stage graph to achieve consistent ego-localisation during autonomous repeats. Another investigation proposed a low-cost vehicle localisation scheme that fuses monocular camera data and dead-reckoning within an interval constraint framework, demonstrating that vehicles with minimal sensors can attain reliable pose estimates by solving the ICSP with guaranteed error bounds. A more recent work implemented an interval-based inertial navigation system onboard an autonomous boat, showing that the fusion of inertial measurements with interval analysis naturally handles outliers and maintains fast, reliable state estimation under real-world disturbances. Together, these studies underscore the versatility of interval techniques across domains and highlight ongoing strides in computational efficiency and sensor integration.

Interval-Based Localization Techniques for Mobile Robotics publication trend

The graph below shows the total number of articles in interval-based localization techniques for mobile robotics across all publications each year (not limited to Nature Index journals).

Technical terms

Interval analysis: A mathematical framework representing uncertain values as ranges, ensuring that true values lie within specified bounds.

Interval constraint propagation: A process of iteratively narrowing intervals by applying mathematical constraints to eliminate infeasible values.

Interval Constraint Satisfaction Problem (ICSP): A formulation in which the localisation problem is cast as a network of interval variables and constraints to be satisfied simultaneously.

Bounded error estimation: An approach that models measurement and process inaccuracies as known limits rather than probabilistic distributions.

Sensor fusion: The combination of data from multiple sensors to improve the accuracy and robustness of state estimation.

References

1. Dynamic ICSP Graph Optimization Approach for Car-Like Robot Localization in Outdoor Environments †. Computers (2019).
2. A Low‐Cost Consistent Vehicle Localization Based on Interval Constraint Propagation. Journal of Advanced Transportation (2018).
3. An Online Interval-Based Inertial Navigation System for Control Purposes of Autonomous Boats. Frontiers in Control Engineering (2022).