Continuum soft robots present significant opportunities for advancing robotics, but they also introduce substantial technical challenges. These systems are highly nonlinear, infinite-dimensional, and severely underactuated, making control particularly difficult. While recent advancements in model-based control have addressed some of these issues for soft robotics, numerical optimal control has shown strong potential, especially given its success in other severely underactuated domains such as bipedal and quadrupedal locomotion.

However, the application of optimal control in soft robotics has largely relied on simplified models, and its use with more accurate and geometrically consistent formulations remains underexplored, particularly for explicitly tackling underactuation. This thesis investigates the use of Differential Dynamic Programming (DDP) to control continuum soft robots modeled using the Geometric Variable Strain (GVS) framework. The focus is on the Soft Inverted Pendulum (SIP) as a template system to evaluate DDP’s feasibility, robustness, and performance in underactuated settings, including low-stiffness regimes where collocated feedback strategies break down. The implementation leverages the use of analytical gradients computed via the Recursive Newton-Euler Algorithm (RNEA) to improve convergence and computational efficiency.

The results show that DDP outperforms traditional Partial Feedback Linearization (PFL) methods, both collocated and non-collocated, especially across challenging mass-stiffness combinations. This effectively extends control authority and stability into regimes previously considered difficult to handle. This thesis extends the method to more complex hybrid soft–rigid systems, examining real-time feasibility and practical implementation, thereby laying the foundation for a generalizable optimal control framework for soft robots.