Contact-Aware Planning and Control of Continuum Robots in Highly Constrained Environments

Abstract: Continuum robots are well suited for navigating confined and fragile environments, such as vascular or endoluminal anatomy, where contact with surrounding structures is often unavoidable. While controlled contact can assist motion, unfavorable contact can degrade controllability, induce kinematic singularities, or introduce safety risks. We present a contact-aware planning approach that evaluates contact quality, penalizing hazardous interactions, while permitting benign contact. The planner produces kinematically feasible trajectories and contact-aware Jacobians which can be used for closed-loop control in hardware experiments. We validate the approach by testing the integrated system (planning, control, and mechanical design) on anatomical models from patient scans. The planner generates effective plans for three common anatomical environments, and, in all hardware trials, the continuum robot was able to reach the target while avoiding dangerous tip contact (100% success). Mean tracking errors were 1.9 +/- 0.5 mm, 1.2 +/- 0.1 mm, and 1.7 +/- 0.2 mm across the three different environments. Ablation studies showed that penalizing end-of-continuum-segment (ECS) contact improved manipulability and prevented hardware failures. Overall, this work enables reliable, contact-aware navigation in highly constrained environments.

• The paper demonstrates a contact-aware planning and control method that discriminates between benign and hazardous contacts to ensure safe navigation in constrained anatomical environments.
• It employs a search-based algorithm with task-space partitioning and contact quality evaluation, achieving low tracking errors (e.g., 1.2±0.1 mm) in aortic arch models.
• The results highlight the critical role of hybrid feedback control in preserving manipulability and preventing unsafe tip contacts during autonomous surgical procedures.

Contact-Aware Planning and Control for Continuum Robots Navigating Highly Constrained Anatomical Environments

Introduction

This paper addresses the dual challenge of motion planning and control for continuum robots tasked with navigation in highly constrained and fragile anatomical environments, such as the aortic arch during neurovascular procedures. The proposed framework centers on contact-aware planning that discriminates between benign and hazardous robot-environment interactions, ensuring kinematic feasibility and preserving manipulability while minimizing safety risks. Rigorous hardware validation is conducted across multiple patient-derived anatomical environments, demonstrating robust autonomous navigation with minimal tracking error and strict avoidance of unfavorable tip contact.

Figure 1: Overview of the proposed contact-aware planning and control system, integrating anatomical imaging inputs, contact-aware motion planning, and feedback-based execution.

Contact-Aware Planning Methodology

The planning framework employs a search-based algorithm operating over a discretized configuration space, leveraging a contact-aware motion model that enforces actuation consistency and environmental constraints. Key elements include:

• Task-space partitioning: The workspace is divided based on the minimal control complexity required to reach the anatomical goal, allowing dynamic adaptation of the planner's action space and cost structure for improved efficiency (Figure 2).
• Contact quality evaluation: Interaction with the environment is scored, penalizing tip and end-of-continuum-segment (ECS) contacts—most susceptible to inducing singularities and safety-critical failures—while permitting benign body contact where advantageous for navigation.
• Partition-dependent action sets: The planner adapts motion primitives based on workspace partition, notably restricting available actions until the robot approaches the target vessel origin.

  Figure 2: Task-space partitions encode workspace regions based on required motion complexity to reach the goal, informing planner action sets and contact cost.

The cost function combines joint motion penalties proportional to expected tip displacement and contact penalties weighted by anatomical risk. Favorable robot-environment interaction permits compliant movement, but unfavorable contact—particularly distal tip contact—is strictly prohibited at all stages except controlled entry into the target vessel.

The planner utilizes analytic derivatives to accelerate optimization in the high-dimensional curvature space and caches function evaluations. Planning times are consistently achievable within anatomically relevant time windows.

Figure 3: Heuristic fields generated via backward Dijkstra search efficiently prioritize feasible paths and penalize lateral approaches at vascular bifurcations.

Contact-Aware Motion Model and Robot Design

The robot architecture features antagonistically-actuated proximal and distal continuum segments. Shape modeling leverages a piecewise constant curvature kinematic parameterization, with constraints enforced for tendon length consistency and minimum clearance from anatomical boundaries. Transformation chains propagate gradients, enabling efficient analytical differentiation in optimization.

Figure 4: Piecewise constant curvature robot model with environmental contact points and segment transformations.

Control Framework

Execution employs a hybrid trajectory tracking controller combining feedforward inputs derived from the planner and feedback correction via a contact-aware Jacobian estimated offline for each plan step. The Jacobian is computed numerically by perturbing joint parameters and measuring local tip pose variations under contact constraints.

• PD control with a damped pseudoinverse Jacobian compensates real-world errors from tendon friction, environment misalignment, and hardware inaccuracies.
• Closed-loop feedback is critical for maintaining safety and accuracy, as open-loop approaches fail in environments with significant uncertainty or model mismatch.

  Figure 5: Controller schematic tracking planned tip pose trajectory, utilizing minimal sensing and contact-aware Jacobians for real-time correction.

Experimental Evaluation

Hardware experiments employ a custom-fabricated continuum robot and a set of 3D printed anatomical models reconstructed from patient CTA data. The framework was tested across three aortic arch types (I, II, III), reflecting increasing navigation difficulty observed in clinical practice.

• Numerical results: Across all trials (three per environment), the robot reached the target vessel with 100% success while avoiding distal tip contact.
• Mean tracking errors: $1.9 \pm 0.5$ mm (type I), $1.2 \pm 0.1$ mm (type II), $1.7 \pm 0.2$ mm (type III).
• Planning times: All plans converge within clinically relevant durations (type III: 21.1 min total, including 839 s planning).
• Ablation studies: Penalizing ECS contact substantially improves manipulability (reduced Jacobian condition number) and prevents hardware failures; introducing body contact penalties reduces completion time and enhances agreement between planned and actual kinematics.

  Figure 6: Hardware trials in three anatomical environments; robot successfully reaches targets, avoiding critical contacts.

  

  Figure 7: Comparative analysis—plans allowing ECS contact (red) induce loss of manipulability and result in robotic failures; penalty (green) preserves control.

  

  Figure 8: Robust navigation in type III arch with reduced body contact, validating planner's impact on contact minimization.

  

  Figure 9: Closed-loop feedback demonstrates superior tracking; open-loop execution yields large errors and unsafe tip contact.

Implications and Future Directions

Practically, the framework enables reliable and safe autonomous continuum robot navigation through highly complex anatomical environments, minimizing procedural risk and potentially shortening intervention times—critical for neurovascular emergencies. The approach generalizes to other constrained domains demanding compliant, contact-aware navigation.

Theoretically, this methodology advances motion planning for soft robots by integrating task-space complexity partitioning, anatomy-specific contact assessment, and analytic motion modeling within a unified framework. The results highlight the necessity of both favorable trajectory generation and robust feedback control for successful hardware deployment.

Future work includes transitioning from 2D to full 3D anatomical planning, further accelerating computation, enhancing execution speed, and incorporating advanced state estimation to infer interaction forces or tissue properties. Integration with learning-based approaches and adaptive controllers could further extend performance in real-world surgical scenarios.

Conclusion

This paper presents a unified, contact-aware planning and control framework for continuum robotic navigation in anatomically constrained environments. Experimental results validate consistent target reaching, low tracking error, and safety preservation in patient-derived aortic arch models. Avoiding ECS contact and minimizing body contact are essential for maintaining manipulability and hardware reliability. The framework represents a technically rigorous advance in continuum robot autonomy, with significant clinical and theoretical implications for future intelligent robotic systems.