Contact-Aided Navigation (CAN)

• Contact-Aided Navigation (CAN) is a framework that treats physical contact events, like footfalls and wheel slips, as structured measurements to improve navigation accuracy.
• It integrates techniques such as pseudo-measurements, invariant filtering, and contact-aware planning to enhance observability and reduce filter divergence in dynamic settings.
• CAN finds applications in legged robots, continuum devices, crowd navigation, medical endoscopy, and underwater missions, expanding reachable sets while managing uncertainty.

Contact-Aided Navigation (CAN) denotes navigation and estimation approaches in which physical contact events or environmental interaction cues are treated as usable information or control resources rather than solely as disturbances. Within information-aided navigation, contact events such as footfalls, wheel slippage, or contact with the environment act as anchoring points for the navigation solution; in motion-planning settings, robots may intentionally allow and manage safe contacts, or exploit contact with rigid or deformable boundaries, to reach target poses that would otherwise be inaccessible or difficult to realize (Engelsman et al., 2023, Hartley et al., 2018, Morgenstein et al., 2023, Rao et al., 2024, Ng et al., 30 Aug 2025). The literature represented here spans pseudo-measurement-based inertial aiding, invariant filtering for legged robots, search-based planning for continuum robots, crowd navigation with safe human contact, flexible endoscope navigation in a dynamic stomach, and cooperative underwater path planning with intermittent aiding contacts (Wolek, 2024).

1. Conceptual scope and taxonomy

Within the review literature on information aided navigation, CAN is most naturally situated in direct information aiding, where known physical or operational constraints are imposed as pseudo-measurements to the navigation filter. The same review also identifies indirect information aiding, which derives aided information from relationships between existing sensor data, and model-based aiding, which embeds constraints into a vehicle or environment model. In this framing, contact events are not incidental: they are the occasions on which zero velocity, nonholonomic, zero angular rate, zero down velocity, or slip-related constraints become valid and informative (Engelsman et al., 2023).

A central organizing idea is that the navigation benefit of contact depends on matching the constraint to the operational scenario. The review states that choosing constraints that appropriately describe the physics of the actual operational scenario maximizes observability and minimizes filter divergence. This makes CAN less a single algorithm than a family of estimation and planning strategies whose common feature is the operationalization of interaction events as structured information (Engelsman et al., 2023).

Domain	Contact signal or resource	Representative papers
Pedestrian and legged navigation	Stance phase, zero velocity, point contact	(Engelsman et al., 2023, Hartley et al., 2018)
Wheeled and vehicle navigation	Zero velocity, nonholonomic constraints, slip detection	(Engelsman et al., 2023)
Crowd navigation	Safe, minimally disruptive human contact	(Morgenstein et al., 2023)
Continuum and soft robots	Contact-induced curvature, wall guidance, force feedback	(Rao et al., 2024, Ng et al., 30 Aug 2025)
Underwater cooperative aiding	Co-located aiding events and surfacing resets	(Wolek, 2024)

This taxonomy also clarifies a recurring misconception. CAN is not restricted to “collision recovery” after nominal planning fails. In the cited works, contact may be the primary source of filter updates, the mechanism that expands a robot’s reachable set, or the means by which navigation remains feasible in environments where zero-contact motion is impossible (Engelsman et al., 2023, Morgenstein et al., 2023, Rao et al., 2024).

2. Pseudo-measurements, observability, and invariant filtering

The canonical information-aided form of CAN appears in inertial navigation. The review gives the zero-velocity update in navigation frame as

$$\delta \mathbf{z}_{ZVN} = v^n_{\text{INS}} - 0_{3\times 1} = H_{ZVN}\, \delta\mathbf{x} + \boldsymbol{\nu}_{ZVN},$$

and the nonholonomic body-frame constraint as

$$v^b_{yz} = \begin{bmatrix} v^b_y \ v^b_z \end{bmatrix} = 0_{2\times 1}.$$

These pseudo-measurements anchor the inertial solution and reset integrated errors whenever a valid contact event occurs, such as foot-ground stance or a vehicle stop (Engelsman et al., 2023).

For legged robots, the contact-aided invariant extended Kalman filter makes this structure explicit. The state lies on

$X_t \in SE_{N+2}(3),$

and, for a single contact point, includes the IMU orientation, velocity, and position together with the world-frame position of the contact point. The filter uses the right-invariant error

$\eta_t^r = \hat{X}_t X_t^{-1},$

and exploits the fact that the point contact-inertial system is group-affine, so the error follows a log-linear autonomous differential equation,

$\frac{d\xi_t}{dt} = A_t \xi_t.$

Because of this log-linear form, the observable state variables can be rendered convergent with a domain of attraction that is independent of the system’s trajectory, and one can directly infer that absolute position and a rotation about the gravity vector (yaw) are unobservable when only an IMU and contact sensors are used (Hartley et al., 2018).

The filter models contact points as additional state variables, assumes that a contact point is stationary in the world frame up to Gaussian slippage noise, and augments or marginalizes the state and covariance when contacts are made or broken. Joint encoders provide forward-kinematics corrections analogous to leg odometry. The authors further extend the filter with IMU biases as random walks; this “Imperfect InEKF” no longer strictly preserves the full group-affine property, but remains more robust than a naive EKF in the reported evaluations (Hartley et al., 2018).

The reported empirical picture is consistent with the theory. In Monte Carlo simulation on a Cassie-series bipedal robot, the InEKF converged significantly faster and more robustly than a quaternion-based EKF across observable states, and in hardware experiments on a real Cassie biped it outperformed the quaternion-based EKF in all 100 trials, converging more quickly and reliably for all observable states (Hartley et al., 2018). A common misconception is that contact alone resolves all state ambiguity; the cited observability result shows that it does not.

3. Contact as a motion-planning primitive in cluttered environments

A second major line of CAN research treats contact as a planning primitive rather than solely as an estimation aid. The tendon-driven continuum robot study is exemplary: it considers a single-segment long TDCR, the mechanically simplest topology, and argues that by leveraging contact with the environment the robot can achieve multiple curvatures without mechanical alterations to the robot. The planner is search-based, discretizes the configuration space, and employs a best-first search guided by a specially designed heuristic that estimates cost-to-go while respecting kinematic constraints and environmental interactions (Rao et al., 2024).

The heuristic is built around constant-curvature arcs, since an unconstrained single-segment TDCR moves along such arcs. Contact is approximated as allowing curvature changes at valid contact points on obstacle boundaries. Precomputation on an $SE(2)$ grid yields a heuristic map, and the online value for a node $n$ is

$h(n) = \min \{ h(c_n), h(c_n^+), h(c_n^-) \},$

where $c_n$ is the grid cell containing the tip pose and $c_n^\pm$ are adjacent orientation cells. The forward kinematics are contact-aware and path-dependent, so the planner tracks the history of actions and contacts, and duplicate detection requires both equal joint-space coordinates and sufficiently close tip positions (Rao et al., 2024).

The kinematic model is optimization-based. It minimizes backbone strain energy,

$$v^b_{yz} = \begin{bmatrix} v^b_y \ v^b_z \end{bmatrix} = 0_{2\times 1}.$$0

subject to actuation consistency and obstacle avoidance:

$$v^b_{yz} = \begin{bmatrix} v^b_y \ v^b_z \end{bmatrix} = 0_{2\times 1}.$$1

This formulation reflects the fact that, in contact-rich regimes, the mapping from control to shape is not purely geometric but constrained by passive interaction with obstacles (Rao et al., 2024).

The empirical results establish the practical effect of contact-aware search. Over 525 queries in environments with both convex and non-convex obstacles, the planner achieved a success rate of about 80%, while the baselines were not able to obtain a success rate higher than 30%. The detailed success rates reported for the three benchmark environments were $$v^b_{yz} = \begin{bmatrix} v^b_y \ v^b_z \end{bmatrix} = 0_{2\times 1}.$$2, $$v^b_{yz} = \begin{bmatrix} v^b_y \ v^b_z \end{bmatrix} = 0_{2\times 1}.$$3, and $$v^b_{yz} = \begin{bmatrix} v^b_y \ v^b_z \end{bmatrix} = 0_{2\times 1}.$$4 for the proposed method, compared with $$v^b_{yz} = \begin{bmatrix} v^b_y \ v^b_z \end{bmatrix} = 0_{2\times 1}.$$5–$$v^b_{yz} = \begin{bmatrix} v^b_y \ v^b_z \end{bmatrix} = 0_{2\times 1}.$$6 for the contactless planner and $$v^b_{yz} = \begin{bmatrix} v^b_y \ v^b_z \end{bmatrix} = 0_{2\times 1}.$$7–$$v^b_{yz} = \begin{bmatrix} v^b_y \ v^b_z \end{bmatrix} = 0_{2\times 1}.$$8 for CAN with a simple heuristic (Rao et al., 2024). The paper further reports that the proposed planner expands over an order of magnitude fewer nodes than BFS, especially for queries requiring multiple contacts. This suggests that, in underactuated continuum systems, contact-aware heuristics are not a secondary optimization but the principal mechanism by which planning remains tractable.

4. Safe contact in human crowds and deformable organs

In dense human crowds, the cited literature rejects the premise that meaningful navigation is equivalent to collision avoidance. The crowd-navigation paper states that traditional social navigation frameworks require the robot to stop suddenly or “freeze” whenever a collision is imminent, and identifies two problems: freezing while navigating a crowd may cause people to trip and fall over the robot, and in very dense social environments where collisions are unavoidable such a control scheme renders the robot unable to move (Morgenstein et al., 2023). The proposed alternative is a learning-based motion planner and control scheme for an omnidirectional mobile robot that allows safe, minimally disruptive contact subject to human safety thresholds according to ISO 15066:2016.

The policy is trained with Proximal Policy Optimization and fuses waypoint information from a global planner, robot state, contact force readings, and a history of depth camera images. It outputs desired speed, motion heading, and camera heading, while auxiliary outputs estimate distances to lateral walls and the nearest human in the depth-camera field of view. A simple PD controller stabilizes velocity and heading. The planner is evaluated in simulation over 360 trials with crowd densities varying between $$v^b_{yz} = \begin{bmatrix} v^b_y \ v^b_z \end{bmatrix} = 0_{2\times 1}.$$9 and $X_t \in SE_{N+2}(3),$0 people per square meter; the reported success rates are $X_t \in SE_{N+2}(3),$1 for density $X_t \in SE_{N+2}(3),$2, $X_t \in SE_{N+2}(3),$3 for density $X_t \in SE_{N+2}(3),$4, and $X_t \in SE_{N+2}(3),$5 for density $X_t \in SE_{N+2}(3),$6, with mean times to completion of $X_t \in SE_{N+2}(3),$7 s, $X_t \in SE_{N+2}(3),$8 s, and $X_t \in SE_{N+2}(3),$9 s respectively (Morgenstein et al., 2023). The same study identifies two failure modes: sensor limitation, especially for feet or lower legs outside the robot’s sensory field of view, and mechanical limitation when the robot cannot stop or reverse fast enough.

In a medical setting, CAN takes a different but structurally related form. The flexible robotic endoscope study addresses navigation in a dynamic stomach, where the robot must learn to effectively use contact with the deformable stomach walls to reach target locations. The proposed deep reinforcement learning-based CAN strategy uses contact force feedback as part of the state, together with tip-to-target relative position, end-effector velocity, cable lengths, and a binary contact indicator, and controls a cable-driven FRE with a 5-dimensional continuous action space (Ng et al., 30 Aug 2025).

Training occurs in a physics-based finite element simulation of a deformable stomach built in SOFA, with geometry imported from Blender and meshed using Gmsh. The deformation dynamics are modeled as

$\eta_t^r = \hat{X}_t X_t^{-1},$0

contact is handled by Lagrange multipliers through

$\eta_t^r = \hat{X}_t X_t^{-1},$1

and periodic external forces simulate breathing or peristalsis. PPO trains a 4-layer network with $\eta_t^r = \hat{X}_t X_t^{-1},$2 units, with each episode ending if the target is reached within $\eta_t^r = \hat{X}_t X_t^{-1},$3, the FRE leaves the stomach, or steps exceed $\eta_t^r = \hat{X}_t X_t^{-1},$4 (Ng et al., 30 Aug 2025).

The reported performance is stringent. In both static and dynamic stomach environments, the CAN agent achieved a $\eta_t^r = \hat{X}_t X_t^{-1},$5 success rate with $\eta_t^r = \hat{X}_t X_t^{-1},$6 mm average error, and it maintained an $\eta_t^r = \hat{X}_t X_t^{-1},$7 success rate in challenging unseen scenarios with stronger external disturbances. The paper also reports that policies trained without force or contact observation fail catastrophically in contact-rich or dynamic environments, whereas policies with contact adaptation and force feedback achieve perfect or near-perfect performance in the training environments (Ng et al., 30 Aug 2025). Across these two application classes, contact is not merely tolerated; it is encoded as an actionable feedback channel whose regulation determines whether navigation remains safe or precise.

5. Cooperative aiding and uncertainty control in underwater missions

The underwater cooperative navigation aid literature extends CAN from local interaction to sequential multi-agent task allocation. The problem is to plan a path for a single underwater cooperative navigation aid vehicle that intermittently aids multiple agents with lower navigation capabilities so as to minimize their average navigation uncertainty. Both the CNA and the agents are modeled as planar, constant-velocity vehicles in discrete time with Gaussian process noise, and agent aiding is modeled through a scalar discrete time Kalman filter (Wolek, 2024).

Without a measurement, the agent covariance evolves as

$\eta_t^r = \hat{X}_t X_t^{-1},$8

When an agent receives an absolute position update from the CNA while co-located, the covariance is reduced according to the update rule

$\eta_t^r = \hat{X}_t X_t^{-1},$9

where the effective measurement noise includes the CNA’s own navigation error and sensor noise. The CNA may also surface at a time $\frac{d\xi_t}{dt} = A_t \xi_t.$0 for $\frac{d\xi_t}{dt} = A_t \xi_t.$1 time steps, during which it does not move or aid agents, after which its own navigation variance is reset to $\frac{d\xi_t}{dt} = A_t \xi_t.$2, reflecting a GPS update (Wolek, 2024).

The mission objective is the average navigation uncertainty

$\frac{d\xi_t}{dt} = A_t \xi_t.$3

defined over all agents and the mission duration. Planning requires computing the minimum interception time $\frac{d\xi_t}{dt} = A_t \xi_t.$4 to a moving agent and reasoning about each agent’s optimal time-to-aid $\frac{d\xi_t}{dt} = A_t \xi_t.$5, the time when receiving CNA assistance yields minimal average navigation uncertainty over the mission (Wolek, 2024).

Two algorithmic strategies are reported. The exhaustive method enumerates all possible task sequences and surfacing insertion points for manageable problem sizes. The greedy method uses a heuristic reward function combining expected cost reduction from aiding an agent, closeness to the agent’s optimal aiding time, and travel time required. In Monte Carlo experiments with randomized agent trajectories and initial navigation uncertainty, the greedy heuristic algorithm, particularly when all three reward terms were blended, performed nearly as well as the optimal exhaustive search for up to 10–14 agents. The optimal approach increases exponentially with the number of agents, while the greedy algorithm remains fast, including sub-second computation time, and scenarios with allowed CNA surfacing produced significantly improved outcomes with lower average uncertainty (Wolek, 2024).

This underwater line of work broadens CAN beyond a single platform. Contact-like aiding events become schedulable resources in a fleet-level optimization, and surfacing plays the role of self-calibration for the aiding vehicle itself.

6. Terminological breadth, adjacent usages, and unresolved issues

The acronym CAN is not fully stable across the navigation literature. In the vehicle-navigation paper “GNSS Measurement-Based Context Recognition for Vehicle Navigation using Gated Recurrent Unit,” CAN denotes context-adaptive navigation, where seamless performance in complex environments depends on fast, reliable, and robust navigational context recognition. That paper proposes a seven-class context categorization framework—open sky, tree-lined avenue, semi-outdoor, urban canyon, viaduct-down, shallow indoor, and deep indoor—together with a $\frac{d\xi_t}{dt} = A_t \xi_t.$6-dimensional GNSS feature vector and a GRU-based classifier. It reports $\frac{d\xi_t}{dt} = A_t \xi_t.$7 overall recognition accuracy for isolated scenarios, $\frac{d\xi_t}{dt} = A_t \xi_t.$8 for transition scenarios, and an average transition delay of $\frac{d\xi_t}{dt} = A_t \xi_t.$9 seconds on a dataset containing $SE(2)$0 samples (Liu et al., 2024).

A related adjacent usage appears in “CropNav,” which presents a hybrid navigation system that autonomously switches between exteroceptive sensing based navigation such as LiDAR row-following and waypoints path tracking in real farms, detects failure, and recovers automatically. The abstract reports an improvement of about $SE(2)$1 m per intervention over GNSS-based navigation and $SE(2)$2 m over row following navigation (Gasparino et al., 2024). This suggests that some recent literature uses CAN-adjacent terminology to denote adaptive or seamless navigation architectures rather than literal exploitation of physical contact.

That ambiguity matters because the physically grounded CAN literature makes stronger, and narrower, claims. First, contact does not eliminate all unobservability: with IMU and contact sensors, absolute position and yaw remain unobservable in the legged InEKF setting (Hartley et al., 2018). Second, contact-aware navigation is not synonymous with unconstrained contact. The crowd-navigation study explicitly regulates force with respect to ISO 15066:2016 thresholds and still reports failures due to sensory field-of-view limits and braking dynamics (Morgenstein et al., 2023). Third, exploiting contact often increases algorithmic complexity rather than reducing it: TDCR planning is path-dependent because the same joint-space position can induce different backbone shapes under different contact histories, and exhaustive underwater task sequencing grows exponentially with the number of agents (Rao et al., 2024, Wolek, 2024).

Across these works, a consistent technical theme emerges. CAN is most effective when contact is represented neither as a binary failure event nor as an abstract regularizer, but as a structured source of state information, reachable-set expansion, or uncertainty reduction. A plausible implication is that future convergence across subfields will depend less on a shared acronym than on a shared formal treatment of interaction events: as pseudo-measurements in filters, admissible transitions in planners, regulated forces in human environments, and schedulable aiding opportunities in multi-agent systems.