Trajectory Generation for Underactuated Soft Robot Manipulators using Discrete Elastic Rod Dynamics

Soft robots are well suited for contact-rich tasks due to their compliance, yet this property makes accurate and tractable modeling challenging. Planning motions with dynamically-feasible trajectories requires models that capture arbitrary deformations, remain computationally efficient, and are compatible with underactuation. However, existing approaches balance these properties unevenly: continuum rod models provide physical accuracy but are computationally demanding, while reduced-order approximations improve efficiency at the cost of modeling fidelity. To address this, our work introduces a control-oriented reformulation of Discrete Elastic Rod (DER) dynamics for soft robots, and a method to generate trajectories with these dynamics. The proposed formulation yields a control-affine representation while preserving certain first-principles force-deformation relationships. As a result, the generated trajectories are both dynamically feasible and consistent with the underlying actuation assumptions. We present our trajectory generation framework and validate it experimentally on a pneumatic soft robotic limb. Hardware results demonstrate consistently improved trajectory tracking performance over a constant-curvature-based baseline, particularly under complex actuation conditions.

Force-Safe Environment Maps and Real-Time Detection for Soft Robot Manipulators

Soft robot manipulators have the potential for deployment in delicate environments to perform complex manipulation tasks. However, existing obstacle detection and avoidance methods do not consider limits on the forces that manipulators may exert upon contact with delicate obstacles. This work introduces a framework that maps force safety criteria from task space (i.e. positions along the robot's body) to configuration space (i.e. the robot's joint angles) and enables real-time force safety detection. We incorporate limits on allowable environmental contact forces for given task-space obstacles, and map them into configuration space (C-space) through the manipulator's forward kinematics. This formulation ensures that configurations classified as safe are provably below the maximum force thresholds, thereby allowing us to determine force-safe configurations of the soft robot manipulator in real-time. We validate our approach in simulation and hardware experiments on a two-segment pneumatic soft robot manipulator. Results demonstrate that the proposed method accurately detects force safety during interactions with deformable obstacles, thereby laying the foundation for real-time safe planning of soft manipulators in delicate, cluttered environments.

Safe Autonomous Environmental Contact for Soft Robots using Control Barrier Functions

Robots built from soft materials will inherently apply lower environmental forces than their rigid counterparts, and therefore may be more suitable in sensitive settings with unintended contact. However, these robots' applied forces result from both their design and their control system in closed-loop, and therefore, ensuring bounds on these forces requires controller synthesis for safety as well. This article introduces the first feedback controller for a soft manipulator that formally meets a safety specification with respect to environmental contact. In our proof-of-concept setting, the robot's environment has known geometry and is deformable with a known elastic modulus. Our approach maps a bound on applied forces to a safe set of positions of the robot's tip via predicted deformations of the environment. Then, a quadratic program with Control Barrier Functions in its constraints is used to supervise a nominal feedback signal, verifiably maintaining the robot's tip within this safe set. Hardware experiments on a multi-segment soft pneumatic robot demonstrate that the proposed framework successfully constrains its environmental contact forces. This framework represents a fundamental shift in perspective on control and safety for soft robots, defining and implementing a formally verifiable logic specification on their pose and contact forces.