Payload generalization on feedforward control actions for trajectory tracking in robots with rigid and elastic joints

Model-based control can achieve reliable task performance, but its effectiveness depends on the accuracy of the underlying model. Robots operating under model uncertainty must often adapt to previously unseen payloads, objects, and interaction dynamics to complete a task successfully. Conventional approaches typically rely on a dedicated task- and control-agnostic excitation phase for estimating physics parameters, delaying task execution and collecting potentially irrelevant data. In this paper, we instead consider zero-shot task execution under parametric uncertainty, where online model learning and control proceed concurrently during task execution. Our approach formulates reference generation within a dual control framework to produce task-relevant, informative trajectories that reduce parameter uncertainty in directions critical to task success. We predefine a feedback policy with an explicit parameter adaptation law and optimize the reference through the resulting adaptive closed-loop dynamics. We propose two formulations: 1) minimizing expected task cost under parameter uncertainty, and 2) minimizing optimality loss, which quantifies the degradation in task performance caused by planning with an incorrect parameter estimate. By actively optimizing for informative trajectories via a natural Fisher information measure, we tightly approach a lower bound on task-relevant parameter uncertainty while simultaneously achieving reliable task execution. Across diverse tasks, controllers, and adaptation laws, targeted exploration enables the identification required for successful task execution, allowing robots to learn relevant physical parameters while completing the task in a single attempt.

Trajectory tracking for compliant robots is challenging due to nonlinear dynamics and modeling uncertainties, often requiring learning-based methods to avoid explicit parameter identification. Iterative Learning Control (ILC) ensures theoretically high precision and preserves the passive compliance of the robot. However, traditional ILC requires a separate learning phase for each new trajectory. Conversely, Reinforcement Learning (RL) generalizes to new trajectories, but practically suffers from high sample complexity and limited tracking precision. This work proposes Reinforced Iterative Learning Control (RILC) that combines the strengths of both approaches to achieve fast adaptation and guaranteed tracking convergence across diverse trajectories. By establishing a concurrent coupling between the two controllers, RILC overcomes the high initial errors and slow adaptation of traditional ILC, enabling high-performance tracking from the very first trials. In this architecture, ILC provides high-quality samples, while RL contributes as a generalizing best-effort policy across iterations. Additionally, a theoretical proof is presented to show that the RL component preserves ILC stability and, under specific conditions, can also reduce the error bound asymptotically. The efficacy of this framework is demonstrated through simulation and experiments on an underactuated 4-degree-of-freedom serial elastic robot using different trajectories and modeling mismatches.

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.