Imagine a soft robotic arm flexing around a bunch of grapes or broccoli and adjusting its grip in real time as it picks up the object. Unlike traditional rigid robots, which generally try to avoid as much contact with their surroundings as possible and stay away from people for safety reasons, this arm senses subtle forces, stretching and bending in a way that more closely mimics the compliance of a human arm. His every move is calculated to avoid excessive force and at the same time perform the task effectively. At MIT's Computer Science and Artificial Intelligence Laboratory (CSAIL) and Laboratory for Information and Decision Systems (LIDS), these seemingly simple movements are the culmination of complex mathematics, careful engineering, and a vision for robots that can safely interact with humans and delicate objects.
Soft robots with their deformable bodies promise a future in which machines move more fluidly alongside humans, assist with care, or handle delicate objects in industrial settings. However, it is this flexibility that makes them difficult to control. Small bends or twists can create unpredictable forces, increasing the risk of damage or injury. This motivates the need to develop safe control strategies for soft robots.
“Inspired by advances in safe control and formal methods for rigid robots, our goal is to adapt these ideas to soft robotics — modeling their complex behavior and embracing rather than avoiding contact — to enable designs with higher performance (e.g., greater payload and precision) without sacrificing safety or embodied intelligence,” says lead author and MIT assistant professor Gioele Zardini, principal investigator at LIDS and the Department of Civil and Environmental Engineering, and an affiliate with the Institute for Data, Systems and Society (IDSS). “This vision is shared by recent and parallel work by other groups.”
Safety first
The team developed a new framework that combines nonlinear control theory (control systems requiring highly complex dynamics) with advanced physical modeling techniques and effective real-time optimization to provide what it calls “contact-aware safety.” The basis of this approach are high-order control barrier functions (HOCBF) and high-order Lyapunov control functions (HOCLF). HOCBFs establish safe operating limits, ensuring that the robot does not exert unsafe forces. HOCLFs effectively guide the robot to task goals, balancing safety and efficiency.
“We are essentially teaching the robot to know its own limits when interacting with the environment while still achieving its goals,” says MIT Department of Mechanical Engineering graduate student Kiwan Wong, lead author of the new paper describing the structure. “This approach involves complex derivation of soft robot dynamics, contact models, and control constraints, but the specification of control objectives and safety barriers is rather straightforward for the practitioner, and the results are very tangible as the robot can be seen to move smoothly, respond to contact, and never result in unsafe situations.”
“Compared to traditional kinematic CBFs – where it is difficult to determine safe forward-invariant sets – the HOCBF structure simplifies barrier design, and its optimization formula takes system dynamics (e.g. inertia) into account, ensuring that the soft robot stops early enough to avoid dangerous contact forces,” says Worcester Polytechnic Institute assistant professor and former CSAIL PhD student Wei Xiao.
“Since the advent of soft robots, the field has highlighted their embodied intelligence and greater inherent safety compared to rigid robots, thanks to the passive compatibility of materials and structures. However, their cognitive intelligence – especially safety systems – lags behind that of rigid serial link manipulators,” says co-author Maximilian Stölzle, a research intern at Disney Research and previously a PhD student at Delft University of Technology and a visiting researcher at MIT LIDS and CSAIL. “This work helps fill this gap by adapting proven algorithms for soft robots and fine-tuning them for safe contact and soft continuum dynamics.”
The LIDS and CSAIL team tested the system in a series of experiments to test the robot's safety and adaptability. In one test, the arm gently pressed against a compliant surface, maintaining precise force without exceeding the limit. In another, he traced the contours of a curved object, adjusting his grip to avoid slipping. In another demonstration, the robot manipulated delicate objects with the operator, reacting in real time to unexpected nudges or movements. “These experiments show that our system is able to generalize to a variety of tasks and goals, and that the robot can detect, adapt and act in complex scenarios, always respecting clearly defined safety boundaries,” says Zardini.
Soft robots with contact-sensitive protection could of course add real value in places where the stakes are high. In healthcare, they could aid in surgery by ensuring precise manipulation while reducing risk to patients. In industry, they may handle delicate goods without constant supervision. In home settings, robots could assist with household chores or caregiving tasks by interacting safely with children and the elderly, a key step towards making soft robots reliable partners in real-world environments.
“Soft robots have incredible potential,” says co-lead senior author Daniela Rus, director of CSAIL and professor in the Department of Electrical Engineering and Computer Science. “However, ensuring safety and motion coding with relatively simple targets has always been a major challenge. We wanted to create a system in which the robot was flexible and responsive, while mathematically ensuring that it did not exceed safe force limits.”
Combining soft robot models, differentiable simulation and control theory
At the heart of the control strategy is a differentiable implementation of the so-called Piecewise Cosserat-Segment (PCS) dynamics model, which predicts how the soft robot deforms and where forces accumulate. This model allows the system to predict how the robot's body will react to actuation and complex interactions with the environment. “The aspect that I like most about this work is the combination of the integration of new and old tools from different fields, such as advanced soft robot models, differentiable simulation, Lyapunov theory, convex optimization and safety constraints based on injury severity. All of this is nicely combined into a real-time controller, fully based on first principles,” says co-author Cosimo Della Santina, associate professor at Delft University of Technology.
This is complemented by the differentially conservative separation axis theorem (DCSAT), which estimates the distances between the soft robot and obstacles in the environment, which can be approximated by a chain of convex polygons in a differential manner. “Previous differentiable distance metrics for convex polygons either did not allow the calculation of penetration depth – necessary for estimating contact forces – or produced unconservative estimates that could compromise safety,” says Wong. “Instead, the DCSAT metric returns strictly conservative and therefore safe estimates, while still enabling fast and differential calculations.” Together, PCS and DCSAT give the robot a predictable sense of its surroundings, allowing for more proactive and safe interactions.
Looking to the future, the team plans to extend their methods to 3D soft robots and explore integration with learning-based strategies. By combining contact-based safety with adaptive learning, soft robots can cope with even more complex, unpredictable environments.
“That's what makes our job so exciting,” Rus says. “We see that the robot behaves in a human and cautious manner, but behind this charm lies a rigorous control framework to ensure that it never oversteps its limits.”
“Soft robots are inherently safer to interact with than rigid-bodied robots due to the compliance and energy-absorbing properties of their bodies,” says University of Michigan assistant professor Daniel Bruder, who was not involved in the study. “However, as soft robots become faster, stronger and more efficient, this may no longer be enough to ensure safety. This work is a key step towards ensuring the safe operation of soft robots by offering a method to reduce contact forces across the body.”
The team's work was supported in part by scholarships from The Hong Kong Jockey Club, the European Union's Horizon Europe program, Cultuurfonds Wetenschapsbeurzen, and the Rudge (1948) and Nancy Allen Chair. Their work was published earlier this month in the journal of the Institute of Electrical and Electronics Engineers Letters in robotics and automation.
