Maximilian Raff

Iskandar Khemakhem, Dominik Tschemernjak, Maximilian Raff et al.

In the fields of robotics and biomechanics, the integration of elastic elements such as springs and tendons in legged systems has long been recognized for enabling energy-efficient locomotion. Yet, a significant challenge persists: designing a robotic leg that perform consistently across diverse operating conditions, especially varying average forward speeds. It remains unclear whether, for such a range of operating conditions, the stiffness of the elastic elements needs to be varied or if a similar performance can be obtained by changing the motion and actuation while keeping the stiffness fixed. This work explores the influence of the leg stiffness on the energy efficiency of a monopedal robot through an extensive parametric study of its periodic hopping motion. To this end, we formulate an optimal control problem parameterized by average forward speed and leg stiffness, solving it numerically using direct collocation. Our findings indicate that, compared to the use of a fixed stiffness, employing variable stiffness in legged systems improves energy efficiency by 20 % maximally and by 6.8 % on average across a range of speeds.

Maximilian Raff, Kathrin Flaßkamp, C. David Remy

Trajectory optimization is an essential tool for generating efficient, dynamically consistent gaits in legged locomotion. This paper explores the indirect method of trajectory optimization, emphasizing its application in creating optimal periodic gaits for legged systems and contrasting it with the more common direct method. While the direct method provides flexibility in implementation, it is limited by its need for an input space parameterization. In contrast, the indirect method improves accuracy by computing the control input from states and costates obtained along the optimal trajectory. In this work, we tackle the convergence challenges associated with indirect shooting methods by utilizing numerical continuation methods. This is particularly useful for the systematic development of gait libraries. Our contributions include: (1) the formalization of a general periodic trajectory optimization problem that extends existing first-order necessary conditions to a broader range of cost functions and operating conditions; (2) a methodology for efficiently generating libraries of optimal trajectories (gaits) utilizing a single shooting approach combined with numerical continuation methods; (3) a novel approach for reconstructing Lagrange multipliers and costates from passive gaits; (4) a comparative analysis of the indirect and direct shooting methods using a compass-gait walker as a case study, demonstrating the improved accuracy of the indirect method in generating optimal gaits; and (5) demonstrating applicability to the more complex legged robot RABBIT, with ten dynamic states and four inputs. The findings underscore the potential of the indirect method for generating families of optimal gaits, thereby advancing the field of trajectory optimization in legged robotics.

Kristin M. de Payrebrune, Kathrin Flaßkamp, Tom Ströhla et al.

Artificial intelligence (AI) is driving transformative changes across numerous fields, revolutionizing conventional processes and creating new opportunities for innovation. The development of mechatronic systems is undergoing a similar transformation. Over the past decade, modeling, simulation, and optimization techniques have become integral to the design process, paving the way for the adoption of AI-based methods. In this paper, we examine the potential for integrating AI into the engineering design process, using the V-model from the VDI guideline 2206, considered the state-of-the-art in product design, as a foundation. We identify and classify AI methods based on their suitability for specific stages within the engineering product design workflow. Furthermore, we present a series of application examples where AI-assisted design has been successfully implemented by the authors. These examples, drawn from research projects within the DFG Priority Program \emph{SPP~2353: Daring More Intelligence - Design Assistants in Mechanics and Dynamics}, showcase a diverse range of applications across mechanics and mechatronics, including areas such as acoustics and robotics.

Maximilian Raff, Nelson Rosa, C. David Remy

In this work, we present a nonlinear dynamics perspective on generating and connecting gaits for energetically conservative models of legged systems. In particular, we show that the set of conservative gaits constitutes a connected space of locally defined 1D submanifolds in the gait space. These manifolds are coordinate-free parameterized by energy level. We present algorithms for identifying such families of gaits through the use of numerical continuation methods, generating sets and bifurcation points. To this end, we also introduce several details for the numerical implementation. Most importantly, we establish the necessary condition for the Delassus' matrix to preserve energy across impacts. An important application of our work is with simple models of legged locomotion that are often able to capture the complexity of legged locomotion with just a few degrees of freedom and a small number of physical parameters. We demonstrate the efficacy of our framework on a one-legged hopper with four degrees of freedom.