A Closed-Form CLF-CBF Controller for Whole-Body Continuum Soft Robot Collision Avoidance

The safety problem in soft robotics has always had two layers. The first is mechanical: silicone and rubber give way where rigid steel would puncture. The second is harder — if the robot can flex around an obstacle, it still needs to know when to flex, in real time, without crashing its own math. A preprint posted March 19 to arXiv by a team at MIT's Computer Science and Artificial Intelligence Laboratory (CSAIL) takes a clean shot at that second problem, and their main result is a little unusual: they made the hard part disappear.

The standard approach to formal safety in robot control is the Control Barrier Function, or CBF — a mathematical condition that, when satisfied, guarantees the system stays in a safe region of state space. Pair it with a Control Lyapunov Function (CLF) to steer the robot toward a goal, and you get a CLF-CBF framework that simultaneously chases objectives and avoids danger. The catch: actually solving for a control input that satisfies both conditions at each timestep typically requires an online quadratic program, a small optimization problem that runs continuously. For fast robots in cluttered environments, that QP is the bottleneck. The solver runs, the robot waits.

Kiwan Wong, a PhD student in MIT's mechanical engineering department funded by the Hong Kong Jockey Club Graduate Scholarship, took a different route. Working with Maximilian Stölzle, a doctoral student simultaneously at Delft University of Technology and Disney Research; Wei Xiao, a former MIT CSAIL postdoc now running the Safe Autonomy and Intelligence Lab (SAIL) at Worcester Polytechnic Institute; and Daniela Rus, the director of MIT CSAIL — the team derived a closed-form expression for the control input that analytically embeds both the stability and safety constraints, with no online optimization required.

The speedup is substantial. According to the paper, the controller runs up to 10 times faster than standard QP-based CLF-CBF implementations and up to 100 times faster than traditional sampling-based planners like RRT*, the kind of motion planner common in industrial robotics. They tested it on a two-segment tendon-driven soft manipulator in simulation and hardware, demonstrating obstacle avoidance in cluttered three-dimensional environments. The paper has been accepted at IEEE RoboSoft 2026, scheduled for April 7–9 in Kanazawa, Japan.

This is a direct progression from an October 2025 result by the same group. That earlier paper — published in IEEE Robotics and Automation Letters and covered by MIT News in December 2025 — introduced a high-order CBF and CLF framework for contact-aware safety in soft robots, but it still relied on the QP solver. The new paper closes that gap. The arc of the research is: first, prove you can have formal safety guarantees; then, make the controller fast enough to actually use.

The caveats matter. The safety guarantees are conditional on the accuracy of the Piecewise Constant Strain (PCS) kinematic model, which approximates how a continuum soft robot deforms. Real tendon-driven manipulators deviate from that model under load, at speed, or when the material properties drift — and the paper doesn't characterize how much model error the guarantees can absorb. The obstacle representation is also limited to spherical primitives, which handles demonstrations in open lab environments but will need extension before it's useful in the kind of dense, irregularly shaped spaces where soft robots are most compelling. And the hardware experiments relied on external motion capture for sensing — reflective markers and a lab tracking system — not onboard perception.

None of those caveats are unusual for a methods paper at this stage, and they don't undercut what's actually novel here. Closed-form solutions to CLF-CBF problems in manipulation contexts are rare; most of the field has accepted that you just run the QP and optimize your solver. What Wong and his co-authors showed is that for the specific kinematic structure of soft continuum robots — where the state space has particular geometric properties — you can write down the answer analytically. That's not a small result.

For the soft robot field, the practical implication is real-time whole-body collision avoidance on hardware that wasn't fast enough to do it the old way. Xiao's research agenda at WPI, described in his faculty profile, applies CBF methods across legged robots, drone swarms, and manipulation — the soft robot paper is one entry in a broader program for bringing formal safety certificates to embodied systems that actually move around people. The code will be released publicly on GitHub before the conference in April.

Soft manipulators are a natural fit for shared workspace with humans — they don't break fingers if they collide, they can reach into confined spaces, they're useful anywhere you'd prefer not to put a rigid arm near a person. The gap between that promise and deployment has always included the safety and control challenge. A controller that can run fast enough to matter, with formal guarantees, is a step in a direction worth tracking.