In paper [“Reduced locomotion dynamics with passive internal DoFs: Application to nonholonomic and soft robotics,” IEEE Trans. Robot., vol. 30, no. 3, pp. 578–592, Jun. 2014; Boyer, F. and Belkhiri, A.], we proposed a general modeling framework to address locomotion systems containing internal passive degrees of freedom. Unfortunately, we committed an error in illustrating the approach on the 3-D model of the bicycle. In this erratum, we correct this error which concerns the kinematic model of the bicycle.

The paper deals with the dynamic modeling of bio-inspired robots with soft appendages such as flying insect-like or swimming fish-like robots. In order to model such soft systems, we propose to use the Mobile Multibody System framework introduced in [1], [2], [3]. In such a framework, the robot is considered as a tree-like structure of rigid bodies where the evolution of the position of the joints is governed by stress-strain laws or control torques. Based on the Newton-Euler formulation of these systems, we propose a new algorithm able to compute at each step of a time loop both the net and passive joint accelerations along with the control torques supplied by the motors. To illustrate, based on previous work [4], the proposed algorithm is applied to the simulation of the hovering flight of a soft flapping-wing insect-like robot (see the attached video).

This paper proposes a general modeling approach for locomotion dynamics of mobile multibody systems containing passive internal degrees of freedom concentrated into (ideal or not) joints and/or distributed along deformable bodies of the system. The approach embraces the case of nonholonomic mobile multibody systems with passive wheels, the pendular climbers, and the locomotion systems bioinspired by animals that exploit the advantages of soft appendages such as fish swimming with their caudal fin or moths that use the softness of their flapping wings to improve flight performance. The paper proposes a general structured modeling approach of MMS with tree-like structures along with efficient computational algorithms of the resulting equations. The approach is illustrated through nontrivial examples such as the 3-D bicycle and a compliant version of the snake-board.