Learning Singularity Avoidance

Abstract

With the increase in complexity of robotic systems and the rise in non-expert users, it can be assumed that task constraints are not explicitly known. In tasks where avoiding singularity is critical to its success, this paper provides an approach, especially for non-expert users, for the system to learn the constraints contained in a set of demonstrations, such that they can be used to optimise an autonomous controller to avoid singularity, without having to explicitly know the task constraints. The proposed approach avoids singularity, and thereby unpredictable behaviour when carrying out a task, by maximising the learnt manipulability throughout the motion of the constrained system, and is not limited to kinematic systems. Its benefits are demonstrated through comparisons with other control policies which show that the constrained manipulability of a system learnt through demonstration can be used to avoid singularities in cases where these other policies would fail. In the absence of the systems manipulability subject to a tasks constraints, the proposed approach can be used instead to infer these with results showing errors less than 10 −5 in 3DOF simulated systems as well as 10 −2 using a 7DOF real world robotic system.

A library for constraint consistent learning

“…where x ∈ R P represents state and u ∈ R Q represents the action. A(x) ∈ R S×Q is the constraint matrix which projects the task space policy onto the relevant part of the The task space can refer to the DoF (Degree of Freedom) required to perform the primary task such as reaching towards a target point, and the null space controls a second lower priority objective in a way where it doesn't interfere with the main task such as avoiding joint-limits, self-collision or kinematic singularities [23,24]. This formalism is generic and works for a wide variety of systems, it not only applies to kinematics, but also to redundant actuation [25], and redundancy in dynamics [26].…”

Exploiting Ergonomic Priors in Human-to-Robot Task Transfer

“…where ψ is a (possibly, state-dependent) redundancy resolution policy for the robot. For instance, ψ could be chosen so as to avoid robot-specific joint limits or singularities [13].…”

“…Specifically, the example chosen uses Λ = Λ x,y , w derived from the policy (18), r * = (−9.12, 3.89) and q = (8.67 • , 94.18 • , −2.32 • ) . This movement is retargeted by using the learnt à to derive b, and then applying (13) with a replacement null space control policy.…”

“…correspondence is drawn between these and the equivalent quantities for the new arm (e.g., if the first row of J relates to the Jacobian for the r x coordinate, the corresponding row of the Jacobian J r for the imitator is selected), and A r is constructed accordingly. Substituting into (13) gives the controller…”

“…Specifically, it presents a new method for programming by demonstration whereby explicit use of the underlying null space control policyas determined by the stereotypical or ergonomic featuresis used to learn the task and null spaces involved in the behaviour and their underlying constraints [11], [12]. The latter allows the original behaviour to be retargeted to an imitator robot that has a different kinematic embodiment, by optimising movement according to the robot's own structure without causing any interference with the task goal [13]. Numerical and physical evaluations are reported in which the proposed approach is applied to learn constraints in a toy experiment where performance on varying data lengths and noise are evaluated, a simulated 3DoF experiment where the approach is compared to the state-of-the-art approach, a demonstration on the benefits of retargeting the system to resolve redundancy for obstacle avoidance, task reproduction from a demonstrator system to an imitator of a different embodiment and finally a real world experiment where demonstrations from a human are used to learn and reproduce the task space motions with a Sawyer, a 7DoF physical robot.…”