A unifying framework for robot control with redundant DOFs

Abstract

Recently, Udwadia (Proc. R. Soc. Lond. A 2003Lond. A :1783Lond. A -1800Lond. A , 2003 suggested to derive tracking controllers for mechanical systems with redundant degrees-offreedom (DOFs) using a generalization of Gauss' principle of least constraint. This method allows reformulating control problems as a special class of optimal controllers. In this paper, we take this line of reasoning one step further and demonstrate that several well-known and also novel nonlinear robot control laws can be derived from this generic methodology. We show experimental verifications on a Sarcos Master Arm robot for some of the derived controllers. The suggested approach offers a promising unification and simplification of nonlinear control law design for robots obeying rigid body dynamics equations, both with or without external constraints, with over-actuation or underactuation, as well as open-chain and closed-chain kinematics.

A probabilistic approach to robot trajectory generation

“…Such a linear model is also used to represent the robot's dynamics in DMPs approach. It is a valid model given the assumption that the inverse dynamics model is sufficiently precise for controlling the robot [9], [13]. The state of the linear system is given by the joint angle q t and velocityq t and the control output u t =q t by the desired acceleration.…”

Towards Motor Skill Learning for Robotics

“…Its potential for dynamically consistent control, compliant control, force control, and hierarchical control has not been exhausted to date. Applications of OSC range from basic end-effector control of manipulators [18] to balancing and gait execution for humanoid robots [23]. If the robot model is accurately known, operational space control is well-understood and a variety of different solution alternatives are available.…”

“…However, the first important insight for this paper is that a physically correct solution to the inverse problem with redundant degrees-of-freedom does exist when learning of the inverse map is performed in a suitable piecewise linear way [19,20]. The second crucial component for our work is based on the insight that many operational space controllers can be understood in terms of a constrained optimal control problem [18]. The cost function associated with this optimal control problem allows us to formulate a learning algorithm that automatically synthesizes a globally consistent desired resolution of redundancy while learning the operational space controller.…”

A novel method for learning policies from constrained motion

“…Constraints of the form (2) commonly appear in scenarios where manipulators interact with solid objects, for example when grasping a tool or turning a crank or a pedal. Such constraints are also common in the control of redundant degrees of freedom in high-dimensional manipulators [7], [6], [10], where policies such as (3) are used, for example, to aid joint stabilisation under task constraints. As an example: Setting A to the Jacobian that maps from joint-space to end-effector position coordinates would allow any motion in the joint space provided that the end-effector remained stationary.…”