Abstract
Derivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.
Highlights
Rigid body dynamics algorithms for evaluating the equations of motion (EOM) and their derivatives find numerous applications in the design optimization and control of modern robotic systems
Time derivatives of EOM are required for the model-based control and motion planning of robots with higher-order continuity [27], since for highly dynamic applications the actuation forces and their derivatives must be bounded in order to ensure feasibility
While O (n)-formulations are deemed computationally advantageous when dealing with large systems, formulating and evaluating the EOM in closed form remains an efficient alternative for many robotic systems and provides insights into the structure of the problem
Summary
Rigid body dynamics algorithms for evaluating the equations of motion (EOM) and their derivatives find numerous applications in the design optimization and control of modern robotic systems. The equations of motion can be differentiated with respect to state variables, control output (generalized forces), time and physical parameters of the robot (see [8] for an overview). While O (n)-formulations are deemed computationally advantageous when dealing with large systems, formulating and evaluating the EOM in closed form remains an efficient alternative for many robotic systems and provides insights into the structure of the problem Such closed-form formulations were not reported in the literature, with the exception of [13] where first-order time derivatives of the EOM were presented within the so-called spatial operator framework. 4 presents the first- and second-order time derivatives of the equations of motion in closed form, respectively. Closed-form time derivatives of the equations of motion of rigid body
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