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Daniel E. Koditschek

Publications and source records attributed to Daniel E. Koditschek.

At least 19 recordsLinked to original sources
arXiv2026

Legged Autonomous Surface Science In Analogue Environments (LASSIE): Making Every Robotic Step Count in Planetary Exploration

The ability to efficiently and effectively explore planetary surfaces is currently limited by the capability of wheeled rovers to traverse challenging terrains, and by pre-programmed data acquisition plans with limited in-situ flexibility. In this paper, we present two novel approaches to address these limitations: (i) high-mobility legged robots that use direct surface interactions to collect rich information about the terrain's mechanics to guide exploration; (ii) human-inspired data acquisition algorithms that enable robots to reason about scientific hypotheses and adapt exploration priorities based on incoming ground-sensing measurements. We successfully verify our approach through lab work and field deployments in two planetary analog environments. The new capability for legged robots to measure soil mechanical properties is shown to enable effective traversal of challenging terrains. When coupled with other geologic properties (e.g., composition, thermal properties, and grain size data etc), soil mechanical measurements reveal key factors governing the formation and development of geologic environments. We then demonstrate how human-inspired algorithms turn terrain-sensing robots into teammates, by supporting more flexible and adaptive data collection decisions with human scientists. Our approach therefore enables exploration of a wider range of planetary environments and new substrate investigation opportunities through integrated human-robot systems that support maximum scientific return.

cs.RO↗
arXiv2026

Scout-Rover cooperation: online terrain strength mapping and traversal risk estimation for planetary-analog explorations

Robot-aided exploration of planetary surfaces is essential for understanding geologic processes, yet many scientifically valuable regions, such as Martian dunes and lunar craters, remain hazardous due to loose, deformable regolith. We present a scout-rover cooperation framework that expands safe access to such terrain using a hybrid team of legged and wheeled robots. In our approach, a high-mobility legged robot serves as a mobile scout, using proprioceptive leg-terrain interactions to estimate regolith strength during locomotion and construct spatially resolved terrain maps. These maps are integrated with rover locomotion models to estimate traversal risk and inform path planning. We validate the framework through analogue missions at the NASA Ames Lunar Simulant Testbed and the White Sands Dune Field. Experiments demonstrate (1) online terrain strength mapping from legged locomotion and (2) rover-specific traversal-risk estimation enabling safe navigation to scientific targets. Results show that scout-generated terrain maps reliably capture spatial variability and predict mobility failure modes, allowing risk-aware path planning that avoids hazardous regions. By combining embodied terrain sensing with heterogeneous rover cooperation, this framework enhances operational robustness and expands the reachable science workspace in deformable planetary environments.

cs.RO↗
arXiv2026

Global dynamical structures from infinitesimal data

Scientists and engineers alike target modeling of complex, high dimensional, and nonlinear dynamical systems as a central goal. Machine learning breakthroughs alongside mounting computation and data advance the efficacy of learning from trajectory measurements. However scientifically interpreting data-driven models, e.g., localizing attracting sets and their basins, remains elusive. Such limitations particularly afflict identification of system-level regulatory mechanisms characteristic of living systems, e.g., stabilizing control for whole-body locomotion, where discontinuous, transient, and multiscale phenomena are common and prior models are rare. As a next step towards theory-grounded discovery of behavioral mechanisms in biology and beyond, we introduce VERT, a framework for discovering attracting sets from trajectories without recourse to any global model. Our infinitesimal-local-global (ILG) pipeline estimates the proximity of any sampled state to an attracting set, if one exists, with formal accuracy guarantees. We demonstrate our approach on phenomenological and physical oscillators with hierarchical and impulsive dynamics, finding sensitivity to both global and intermediate attractors composed in sequence and parallel. Application of VERT to human running kinematics data reveals insight into control modules that stabilize task-level dynamics, supporting a longstanding neuromechanical control hypothesis. The VERT framework promotes rigorous inference of underlying dynamical structure even for systems where learning a global dynamics model is impractical or impossible.

q-bio.QM↗
arXiv2023

Technical Report on: Tripedal Dynamic Gaits for a Quadruped Robot

A vast number of applications for legged robots entail tasks in complex, dynamic environments. But these environments put legged robots at high risk for limb damage. This paper presents an empirical study of fault tolerant dynamic gaits designed for a quadrupedal robot suffering from a single, known "missing" limb. Preliminary data suggests that the featured gait controller successfully anchors a previously developed planar monopedal hopping template in the three-legged spatial machine. This compositional approach offers a useful and generalizable guide to the development of a wider range of tripedal recovery gaits for damaged quadrupedal machines.

cs.RO↗
arXiv2022

Necessary conditions for feedback stabilization and safety

Brockett's necessary condition yields a test to determine whether a system can be made to stabilize about some operating point via continuous, purely state-dependent feedback. For many real-world systems, however, one wants to stabilize sets which are more general than a single point. One also wants to control such systems to operate safely by making obstacles and other "dangerous" sets repelling. We generalize Brockett's necessary condition to the case of stabilizing general compact subsets having a nonzero Euler characteristic in general ambient state spaces (smooth manifolds). Using this generalization, we also formulate a necessary condition for the existence of "safe" control laws. We illustrate the theory in concrete examples and for some general classes of systems including a broad class of nonholonomically constrained Lagrangian systems. We also show that, for the special case of stabilizing a point, the specialization of our general stabilizability test is stronger than Brockett's.

math.OC↗
arXiv2022

Technical Report: A Hierarchical Deliberative-Reactive System Architecture for Task and Motion Planning in Partially Known Environments

We describe a task and motion planning architecture for highly dynamic systems that combines a domain-independent sampling-based deliberative planning algorithm with a global reactive planner. We leverage the recent development of a reactive, vector field planner that provides guarantees of reachability to large regions of the environment even in the face of unknown or unforeseen obstacles. The reachability guarantees can be formalized using contracts that allow a deliberative planner to reason purely in terms of those contracts and synthesize a plan by choosing a sequence of reactive behaviors and their target configurations, without evaluating specific motion plans between targets. This reduces both the search depth at which plans will be found, and the number of samples required to ensure a plan exists, while crucially preserving correctness guarantees. The result is reduced computational cost of synthesizing plans, and increased robustness of generated plans to actuator noise, model misspecification, or unknown obstacles. Simulation studies show that our hierarchical planning and execution architecture can solve complex navigation and rearrangement tasks, even when faced with narrow passageways or incomplete world information.

cs.RO↗
arXiv2021

Reactive Navigation in Partially Familiar Planar Environments Using Semantic Perceptual Feedback

This paper solves the planar navigation problem by recourse to an online reactive scheme that exploits recent advances in SLAM and visual object recognition to recast prior geometric knowledge in terms of an offline catalogue of familiar objects. The resulting vector field planner guarantees convergence to an arbitrarily specified goal, avoiding collisions along the way with fixed but arbitrarily placed instances from the catalogue as well as completely unknown fixed obstacles so long as they are strongly convex and well separated. We illustrate the generic robustness properties of such deterministic reactive planners as well as the relatively modest computational cost of this algorithm by supplementing an extensive numerical study with physical implementation on both a wheeled and legged platform in different settings.

cs.RO↗
arXiv2021

Hybrid dynamical type theories for navigation

We present a hybrid dynamical type theory equipped with useful primitives for organizing and proving safety of navigational control algorithms. This type theory combines the framework of Fu--Kishida--Selinger for constructing linear dependent type theories from state-parameter fibrations with previous work on categories of hybrid systems under sequential composition. We also define a conjectural embedding of a fragment of linear-time temporal logic within our type theory, with the goal of obtaining interoperability with existing state-of-the-art tools for automatic controller synthesis from formal task specifications. As a case study, we use the type theory to organize and prove safety properties for an obstacle-avoiding navigation algorithm of Arslan--Koditschek as implemented by Vasilopoulos. Finally, we speculate on extensions of the type theory to deal with conjugacies between model and physical spaces, as well as hierarchical template-anchor relationships.

cs.LO↗
arXiv2021

Technical Report: Reactive Planning for Mobile Manipulation Tasks in Unexplored Semantic Environments

Complex manipulation tasks, such as rearrangement planning of numerous objects, are combinatorially hard problems. Existing algorithms either do not scale well or assume a great deal of prior knowledge about the environment, and few offer any rigorous guarantees. In this paper, we propose a novel hybrid control architecture for achieving such tasks with mobile manipulators. On the discrete side, we enrich a temporal logic specification with mobile manipulation primitives such as moving to a point, and grasping or moving an object. Such specifications are translated to an automaton representation, which orchestrates the physical grounding of the task to mobility or manipulation controllers. The grounding from the discrete to the continuous reactive controller is online and can respond to the discovery of unknown obstacles or decide to push out of the way movable objects that prohibit task accomplishment. Despite the problem complexity, we prove that, under specific conditions, our architecture enjoys provable completeness on the discrete side, provable termination on the continuous side, and avoids all obstacles in the environment. Simulations illustrate the efficiency of our architecture that can handle tasks of increased complexity while also responding to unknown obstacles or unanticipated adverse configurations.

cs.RO↗
arXiv2020

Conley's fundamental theorem for a class of hybrid systems

We establish versions of Conley's (i) fundamental theorem and (ii) decomposition theorem for a broad class of hybrid dynamical systems. The hybrid version of (i) asserts that a globally-defined "hybrid complete Lyapunov function" exists for every hybrid system in this class. Motivated by mechanics and control settings where physical or engineered events cause abrupt changes in a system's governing dynamics, our results apply to a large class of Lagrangian hybrid systems (with impacts) studied extensively in the robotics literature. Viewed formally, these results generalize those of Conley and Franks for continuous-time and discrete-time dynamical systems, respectively, on metric spaces. However, we furnish specific examples illustrating how our statement of sufficient conditions represents merely an early step in the longer project of establishing what formal assumptions can and cannot endow hybrid systems models with the topologically well characterized partitions of limit behavior that make Conley's theory so valuable in those classical settings.

math.DS↗
arXiv2020

Technical Report: A New Hopping Controller for Highly Dynamical Bipeds

We present angle of attack control, a novel control strategy for a hip energized Penn Jerboa. The energetic losses from damping are counteracted by aligning most of the velocity at touchdown in the radial direction and the fore-aft velocity is controlled by using the hip torque to control to a target angular momentum. The control strategy results in highly asymmetric leg angle trajectories, thus avoiding the traction issues that plague hip actuated SLIP. Using a series of assumptions we find an analytical expression for the fixed points of an approximation to the hopping return map relating the design parameters to steady state gait performance. The hardware robot demonstrates stable locomotion with speeds ranging from 0.4 m/s to 2.5 m/s (2 leg lengths/s to 12.5 leg lengths/s) and heights ranging from 0.21 m to 0.27 m (1.05 leg lengths to 1.35 leg lengths). The performance of the empirical trials is well approximated by the analytical predictions.

cs.RO↗
arXiv2020

Formal composition of hybrid systems

We develop a compositional framework for formal synthesis of hybrid systems using the language of category theory. More specifically, we provide mutually compatible tools for hierarchical, sequential, and independent parallel composition. In our framework, hierarchies of hybrid systems correspond to template-anchor pairs, which we model as spans of subdividing and embedding semiconjugacies. Hierarchical composition of template-anchor pairs corresponds to the composition of spans via pullback. To model sequential composition, we introduce "directed hybrid systems," each of which flows from an initial subsystem to a final subsystem in a Conley-theoretic sense. Sequential composition of directed systems is given by a pushout of graph embeddings, rewriting the continuous dynamics of the overlapping subsystem to prioritize the second directed system. Independent parallel composition corresponds to a categorical product with respect to semiconjugacy. To formalize the compatibility of these three types of composition, we construct a vertically cartesian double category of hybrid systems where the vertical morphisms are semiconjugacies, and the horizontal morphisms are directed hybrid systems.

math.CT↗
arXiv2020

A Hybrid Systems Model for Simple Manipulation and Self-Manipulation Systems

Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs individually. In concert, it is well known that the interaction of such idealized approximations can lead to conflicting and even paradoxical results. As robotics modeling moves from the consideration of isolated behaviors to the analysis of tasks requiring their composition, a mathematically tractable framework for building models that combine these simple approximations yet achieve reliable results is overdue. In this paper we present a formal hybrid dynamical system model that introduces suitably restricted compositions of these familiar abstractions with the guarantee of consistency analogous to global existence and uniqueness in classical dynamical systems. The hybrid system developed here provides a discontinuous but self-consistent approximation to the continuous (though possibly very stiff and fast) dynamics of a physical robot undergoing intermittent impacts. The modeling choices sacrifice some quantitative numerical efficiencies while maintaining qualitatively correct and analytically tractable results with consistency guarantees promoting their use in formal reasoning about mechanism, feedback control, and behavior design in robots that make and break contact with their environment.

cs.RO↗
arXiv2020

Technical Report: Reactive Semantic Planning in Unexplored Semantic Environments Using Deep Perceptual Feedback

This paper presents a reactive planning system that enriches the topological representation of an environment with a tightly integrated semantic representation, achieved by incorporating and exploiting advances in deep perceptual learning and probabilistic semantic reasoning. Our architecture combines object detection with semantic SLAM, affording robust, reactive logical as well as geometric planning in unexplored environments. Moreover, by incorporating a human mesh estimation algorithm, our system is capable of reacting and responding in real time to semantically labeled human motions and gestures. New formal results allow tracking of suitably non-adversarial moving targets, while maintaining the same collision avoidance guarantees. We suggest the empirical utility of the proposed control architecture with a numerical study including comparisons with a state-of-the-art dynamic replanning algorithm, and physical implementation on both a wheeled and legged platform in different settings with both geometric and semantic goals.

cs.RO↗
arXiv2019

Towards a terramechanics for bio-inspired locomotion in granular environments

Granular media (GM) present locomotor challenges for terrestrial and extraterrestrial devices because they can flow and solidify in response to localized intrusion of wheels, limbs, and bodies. While the development of airplanes and submarines is aided by understanding of hydrodynamics, fundamental theory does not yet exist to describe the complex interactions of locomotors with GM. In this paper, we use experimental, computational, and theoretical approaches to develop a terramechanics for bio-inspired locomotion in granular environments. We use a fluidized bed to prepare GM with a desired global packing fraction, and use empirical force measurements and the Discrete Element Method (DEM) to elucidate interaction mechanics during locomotion-relevant intrusions in GM such as vertical penetration and horizontal drag. We develop a resistive force theory (RFT) to account for more complex intrusions. We use these force models to understand the locomotor performance of two bio-inspired robots moving on and within GM.

physics.bio-ph↗
arXiv2019

A Tunably Compliant Origami Mechanism for Dynamically Dexterous Robots

We present an approach to overcoming challenges in dynamical dexterity for robots through tunable origami structures. Our work leverages a one-parameter family of flat sheet crease patterns that folds into origami bellows, whose axial compliance can be tuned to select desired stiffness. Concentrically arranged cylinder pairs reliably manifest additive stiffness, extending the tunable range by nearly an order of magnitude and achieving bulk axial stiffness spanning 200-1500 N/m using 8 mil thick polyester-coated paper. Accordingly, we design origami energy-storing springs with a stiffness of 1035 N/m each and incorporate them into a three degree-of-freedom (DOF) tendon-driven spatial pointing mechanism that exhibits trajectory tracking accuracy less than 15% rms error within a ~2 cm^3 volume. The origami springs can sustain high power throughput, enabling the robot to achieve asymptotically stable juggling for both highly elastic (1~kg resilient shot put ball) and highly damped ("medicine ball") collisions in the vertical direction with apex heights approaching 10 cm. The results demonstrate that "soft" robotic mechanisms are able to perform a controlled, dynamically actuated task.

cs.RO↗
arXiv2018

Iterated Belief Revision Under Resource Constraints: Logic as Geometry

We propose a variant of iterated belief revision designed for settings with limited computational resources, such as mobile autonomous robots. The proposed memory architecture---called the {\em universal memory architecture} (UMA)---maintains an epistemic state in the form of a system of default rules similar to those studied by Pearl and by Goldszmidt and Pearl (systems $Z$ and $Z^+$). A duality between the category of UMA representations and the category of the corresponding model spaces, extending the Sageev-Roller duality between discrete poc sets and discrete median algebras provides a two-way dictionary from inference to geometry, leading to immense savings in computation, at a cost in the quality of representation that can be quantified in terms of topological invariants. Moreover, the same framework naturally enables comparisons between different model spaces, making it possible to analyze the deficiencies of one model space in comparison to others. This paper develops the formalism underlying UMA, analyzes the complexity of maintenance and inference operations in UMA, and presents some learning guarantees for different UMA-based learners. Finally, we present simulation results to illustrate the viability of the approach, and close with a discussion of the strengths, weaknesses, and potential development of UMA-based learners.

cs.AI↗