In this paper, we present an efficient Dynamic Programing framework for optimal planning and control of legged robots. First we formulate this problem as an optimal control problem for switched systems. Then we propose a multi-level optimization approach to find the optimal switching times and the optimal continuous control inputs. Through this scheme, the decomposed optimization can potentially be done more efficiently than the combined approach. Finally, we present a continuous-time constrained LQR algorithm which simultaneously optimizes the feedforward and feedback controller with O(n) time-complexity. In order to validate our approach, we show the performance of our framework on a quadrupedal robot. We choose the Center of Mass dynamics and the full kinematic formulation as the switched system model where the switching times as well as the contact forces and the joint velocities are optimized for different locomotion tasks such as gap crossing, walking and trotting.

Despite the recent advances in, and the adoption of robotic technologies in the construction industry, the architectural processes which demand a high degree of geometric freedom still remain largely labour intensive and manual. This is due to the inherent difficulties in robotizing the current implementation of such processes coupled with the lack of alternate robotic technologies. A specific example, which is also the focus of this paper, is that of building a steel reinforced concrete structure, with varying curvature or cross-section. This process still remains rather manual and requires extensive support of customized form-work. In this paper, first we describe an alternate novel robotic fabrication process for building steel wire meshes which act as both reinforcement and formwork. The robotization of such a process is discussed with the use of a previously developed mobile robotic system. Based on the specifications derived from the process, design of a novel custom designed robotic end-effector, enabling this process, is detailed. Automation of the full robotic system comprising the mobile robotic system and the robotic end-effector is discussed from simulation to control. Through experimental evaluation of the robotic system, we demonstrate the ability to fully automate the construction of non-standard steel reinforced steel meshes of varying curvature and cell sizes.