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Technical Brief

Passive Compliance Control of Redundant Serial Manipulators

[+] Author and Article Information
Jacob J. Rice

Department of Mechanical Engineering,
Marquette University,
Milwaukee, WI 53233
e-mail: jacob.rice@marquette.edu

Joseph M. Schimmels

Department of Mechanical Engineering,
Marquette University,
Milwaukee, WI 53233
e-mail: joseph.schimmels@marquette.edu

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received July 25, 2017; final manuscript received January 31, 2018; published online May 31, 2018. Assoc. Editor: Hai-Jun Su.

J. Mechanisms Robotics 10(4), 044507 (May 31, 2018) (8 pages) Paper No: JMR-17-1225; doi: 10.1115/1.4039591 History: Received July 25, 2017; Revised January 31, 2018

Passive compliance control is an approach for controlling the contact forces between a robotic manipulator and a stiff environment. This paper considers passive compliance control using redundant serial manipulators with real-time adjustable joint stiffness. Such manipulators can control the elastic behavior of the end-effector by adjusting the manipulator configuration and by adjusting the intrinsic joint stiffness. The end-effector's time-varying elastic behavior is a beneficial quality for constrained manipulation tasks such as opening doors, turning cranks, and assembling parts. The challenge in passive compliance control is finding suitable joint commands for producing the desired time-varying end-effector position and compliance (task manipulation plan). This problem is addressed by extending the redundant inverse kinematics (RIK) problem to include compliance. This paper presents an effective method for simultaneously attaining the desired end-effector position and end-effector elastic behavior by tracking a desired variation in both the position and the compliance. The set of suitable joint commands is not unique; the method resolves the redundancy by minimizing the actuator velocity norm. The method also compensates for joint deflection due to known external loads, e.g., gravity.

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Figures

Grahic Jump Location
Fig. 1

Joint coordinates of an np-R serial manipulator with adjustable compliance. The kinematic position of each joint is given by qpi and the compliance of each joint is given by qci.

Grahic Jump Location
Fig. 2

Actuator coordinates of joint i. The kinematic actuator position ϕpi is the no-load joint position. External loads cause a joint displacement Δi resulting in the static equilibrium joint position qpi. The amount of displacement depends on the joint compliance qci that is determined by the compliance actuator position ϕci.

Grahic Jump Location
Fig. 3

Local IK resolution of redundant manipulators with elastic joints using the weighted pseudoinverse J at a single instant in time. User-provided input is x(t) and procedure output is ϕ(t). Thick straight arrows show the integration cycle to generate the joint plan q(t). Solid straight arrows show necessary calculations. Solid curved arrows represent mappings between spaces, whereas dashed curved arrows with a × indicate non-existent mappings between spaces.

Grahic Jump Location
Fig. 4

Planar 3R manipulator and manipulation plan. Four equally spaced instants in time illustrate the continuous end-effector motion plan xp(t) and the continuous compliance manipulation plan xc(t).

Grahic Jump Location
Fig. 5

Locally resolved manipulation plan starting at q0. (a) Stroboscopic image of the manipulator performing the task. The color of each joint indicates the compliance actuator position. The compliance ellipse is shown at each snap-shot. (b) Position profiles of each joint's kinematic and compliance actuator.

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