Safe yet Precise Soft Robots

Abstract

As we increasingly strive to integrate robots into human-centric environments, safety is a top priority. Traditionally, rigid collaborative robots have relied on safety-aware computational control policies, which are susceptible to perception errors and often lead to overly cautious behavior that limits performance. In contrast, soft robotics offers a promising alternative by ensuring passive compliance throughout the robot’s structure via material softness. This mechanical compliance inherently mitigates safety issues arising from perception or control errors, although this has been paid with a substantial drop in precision. In recent years, significant advances have been seen in soft robotics, with exciting new developments in design, smart materials, actuators, sensors, models, and control strategies. However, the modeling and control of continuum soft robots continue to pose major challenges due to their infinite degrees of freedom, complex nonlinear dynamics, and time-dependent behaviors like hysteresis. As a result, soft robots often lack the necessary capability and motion precision, leading to a tradeoff where performance is sacrificed for safety. With this thesis, we argue that this tradeoff can be overcome by developing more advanced algorithms that can reason on the physics of the soft robot. More specifically, we propose combining powerful learned models with efficient and effective model-based control approaches that allow for interpretability into the actions and admit stability guarantees.

Currently, two main approaches exist for controlling soft robots. The first employs model-based control using approximated physics-based models derived from first principles. The second directly learns control policies, primarily through reinforcement learning. Both strategies face notable limitations. Existing model-based controllers are unable to fully manage and eventually exploit the dynamics of soft robots because their underlying models inadequately capture complex behaviors, particularly how actuation and external interactions affect the robot’s deformation. Moreover, deriving these models requires extensive expert knowledge. Additionally, the combined complexity and uncertainty of the dynamics between a soft robot and its environment make it currently infeasible to develop comprehensive world models from first principles alone, thereby motivating the integration of machine learning approaches that can effectively leverage data-driven insights. Conversely, directly learning the controller — such as via reinforcement learning — lacks interpretability and stability guarantees while being highly sample inefficient, a significant drawback given the time-dependent material properties and limited lifespan of current soft robots.

In this thesis, we contend that combining learned models with model-based controllers presents a promising alternative that brings together the advantages of both approaches: expressive, data-driven models that require less expert knowledge paired with controllers that are both interpretable and provably stable. Although recent years have seen increased interest in leveraging learned models for control, most work in this area depends on computationally intensive optimal control methods, such as MPC, to optimize the actuation sequence with the learned model. However, the high computational cost of solving these optimal control problems limits the maximum control frequency during deployment, preventing us from fully exploiting the dynamic capabilities of soft robots. Instead, this thesis pursues closed-form controllers that utilize the physical structure of learned models within an energy-shaping framework. The main challenge here is to develop approaches that integrate such physical structures—specifically, kinetic and potential energy terms—into the learning of dynamical models for soft robots. Before addressing this main challenge, we first had to advance physics-based models derived from first principles and identify novel techniques to leverage them for control. On one hand, this clarified which physical priors were available for learning, while on the other hand, it inspired new ways to integrate model-based controllers with learned models. The thesis addresses this topic through several interconnected key contributions.

First, we argue that quantifying the safety of soft robots is crucial for designing and controlling them to ensure that the closed-loop system meets the specific safety requirements of their intended applications. To this end, we present the first safety metric for continuum soft robots, which assesses the safety of an integrated soft robot design by accounting for both its embodied and computational intelligence.

Secondly, this thesis enhances shape sensing for soft robots by leveraging insights from kinematic models. We accomplish this by formulating and solving nonlinear optimization problems that align sensor measurements with the backbone shapes predicted by the kinematic model. We present two distinct approaches that integrate commercial sensors—namely visual and magnetic—with SLAM algorithms and a learned sensor measurement model, respectively, to accurately estimate the soft robot’s state, a key requirement for effective feedback control.

Thirdly, this thesis introduces advanced physics-based actuation models, including those for robots actuated by auxetic metamaterials - referred to as HSA robots—and models that capture the actuation dynamics of piston-driven pneumatic soft robots. We then leverage the acquired model insights to design provably stable nonlinear controllers—specifically, an integral-saturated PID combined with potential shaping and Cartesian-space impedance control for planar GSA robots, as well as a backstepping controller for pneumatic piston-driven soft robots. This contribution deepens our understanding of actuation, a critical aspect of soft robot behavior, and demonstrates how such insights can be incorporated into model-based control strategies. Moreover, experiments with HSA robots have highlighted the limitations of purely physics-based models in capturing complex phenomena like hysteresis, thereby motivating the exploration of learning-based approaches. In the future, the developed actuation models can serve as valuable physical priors for learned models.

Fourthly, the thesis presents techniques for learning soft robot models that incorporate physical structures while ensuring stability. We accomplish this by embedding physics-based dynamical models into the learning algorithm, which determines the free parameters of the dynamics and optionally optimizes a coordinate transformation—such as encoding into latent space. Two notable approaches are introduced: (1) an algorithm that extracts low-dimensional soft robot strain models from samples of the robot backbone’s shape evolution, and (2) a network of coupled harmonic oscillators for learning latent dynamics from high-dimensional observations like images. The explicit inclusion of kinematic and potential energy terms in these models allows for stability analysis using standard nonlinear system theory tools, such as Lyapunov methods. For instance, we prove that the coupled oscillator network is both globally asymptotically stable and input-to-state stable.

Fifthly, we exploit the physical structure of the learned models from contribution four to design closed-form setpoint regulators. The controller contains two key components: (1) a potential shaping feedforward term that positions the local/global minimum of the closed-loop potential energy at the setpoint by leveraging the learned model knowledge, and (2) an integral-saturated PID feedback term that rejects disturbances and compensates for modeling errors to prevent steady-state errors. The stability of the closed-loop system can then be analyzed using Lyapunov arguments.

Finally, the thesis explores methods for generating compliant motion behaviors in soft robots beyond low-level control. One approach focuses on assisting users, particularly elderly individuals, with activities of daily living by guiding the low-level controller with brain signals. This is achieved by combining motor imagery classification from wearable EEG devices with compliant impedance control in operational space. The second approach combines an orbitally stable dynamical system in latent space with a bijective neural network parametrized encoder to learn periodic motions from demonstrations. By avoiding reliance on time references, this learned motion policy enables natural and compliant tracking of demonstrated periodic motions. This contribution ensures that not just the robot structure and low-level controller are compliant, but also the high-level motion strategy.