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Research Papers

Using Dynamics to Consider Torque Constraints in Manipulator Planning With Heavy Loads

[+] Author and Article Information
Oscar Y. Chuy,, Jr.

Department of Electrical and Computer
Engineering,
University of West Florida,
Pensacola, FL 32514
e-mail: ochuy@uwf.edu

Emmanuel G. Collins,, Jr.

Department of Mechanical Engineering,
Florida A&M University—Florida State
University College of Engineering,
Tallahassee, FL 32310
e-mail: ecollins@eng.fsu.edu

Aneesh Sharma

Department of Mechanical Engineering,
Florida A&M University—Florida State
University College of Engineering
Tallahassee, FL 32310
e-mail: as10ae@my.fsu.edu

Ryan Kopinsky

Department of Mechanical Engineering,
Florida A&M University—Florida State
University College of Engineering
Tallahassee, FL 32310
e-mail: rkopinsky@fsu.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 24, 2015; final manuscript received October 26, 2016; published online March 1, 2017. Assoc. Editor: Heikki Handroos.

J. Dyn. Sys., Meas., Control 139(5), 051001 (Mar 01, 2017) (12 pages) Paper No: DS-15-1646; doi: 10.1115/1.4035168 History: Received December 24, 2015; Revised October 26, 2016

Input constraints are active in robot trajectory planning when a mobile robot traverses mobility challenges such as steep hills that limit the acceleration of the robot due to the torque constraints of the motor or engine or in manipulator lifting tasks when the load is sufficiently heavy that the torque constraints of the robot's motor prevent it from statically supporting the load in regions of the robot's workspace. This paper presents a general methodology for solving these planning tasks using a minimum-time cost function and applies it to the problem of a multiple degrees-of-freedom (DOF) manipulator lifting a heavy load. Planning for these types of problems requires use of the robot's dynamic model. Here, we plan using sampling-based model predictive optimization (SBMPO), which is only practical if the planning can be done quickly. Hence, substantial attention is given to efficient computations by: (1) using the dynamic model without integrating it, (2) using optimal control theory to develop an “optimistic A* estimate of cost-to-goal,” which is in this case a rigorous lower bound on the minimum time from a current state to a goal state, and (3) using prior experience to speed up the computation of a new trajectory. The methodology is experimentally verified for heavy lifting using a two-link manipulator.

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References

Chuy, O. , Collins, E. , Dunlap, D. , and Sharma, A. , 2013, “ Sampling-Based Direct Trajectory Generation Using the Minimum Time Cost Function,” Experimental Robotics (Springer Tracts in Advanced Robotics, Vol. 88), J. P. Desai , G. Dudek , O. Khatib , and V. Kumar , eds., Springer International Publishing, Switzerland, pp. 651–666.
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Figures

Grahic Jump Location
Fig. 1

(a) This figure shows the reachable region for a 2DOF manipulator due to its kinematic constraints. (b) An illustration of disjoint reachable region due to dynamic constraints. The manipulator has a payload greater than its capacity.

Grahic Jump Location
Fig. 2

Trajectory planning using SBMPO [1]

Grahic Jump Location
Fig. 3

Extended kinematic model [1]

Grahic Jump Location
Fig. 4

Illustration of bang–bang minimum-time optimal control which yields the minimum-time solution t¯f of Eq. (8) [1]

Grahic Jump Location
Fig. 5

The 2DOF manipulator used in this study was designed and built at the Center for Intelligent Systems, Controls, and Robotics (CISCOR)

Grahic Jump Location
Fig. 6

Quasi-static reachable region of the 2DOF manipulator: (a) no load, (b) 2.27 kg (5 lb) load, and (c) 5.54 kg (10 lb) load

Grahic Jump Location
Fig. 7

For the no-load case, SBMPO produced these commanded angular accelerations, which are the inputs to the manipulator system

Grahic Jump Location
Fig. 8

End effector's path of the 2DOF manipulator with no load. The task was to move from rest at (0 m, −0.675 m), where the end effector is vertically down, to rest at a goal position (0.0 m, 0.65 m). The planning time was 0.57 s.

Grahic Jump Location
Fig. 9

Simulation results: trajectory planning and tracking results for the no-load case. The desired and actual angular positions were virtually identical.

Grahic Jump Location
Fig. 10

Simulation results: trajectory planning and tracking results for the no-load case. The desired and actual angular velocities were virtually identical.

Grahic Jump Location
Fig. 11

Experimental results: trajectory planning and tracking results for the no-load case. The desired and actual angular positions closely coincide. The average tracking error for joint one is 0.032 rad and joint two is 0.021 rad.

Grahic Jump Location
Fig. 12

For the 2.27 kg (5 lb) load, SBMPO produced these commanded angular accelerations, which are the inputs to the manipulator system

Grahic Jump Location
Fig. 13

End effector's path of the 2DOF manipulator with 2.27 kg (5 lb) load. The task was to move from (0 m, −0.675 m), where the end effector is vertically down, to rest at a goal position (0.0 m, 0.65 m). The planning time was 22.8 s.

Grahic Jump Location
Fig. 14

Simulation results: trajectory planning and tracking results for 2.27 kg (5 lb) load. The desired and actual angular positions were virtually identical.

Grahic Jump Location
Fig. 15

Simulation results: Trajectory planning and tracking results for 2.27 kg (5 lb) load. The desired and actual angular velocities were virtually identical.

Grahic Jump Location
Fig. 16

Experimental results: Trajectory planning and tracking results for 2.27 kg (5 lb) load. The desired and actual angular positions closely coincide. The average tracking error for joint one is 0.065 rad and joint two is 0.028 rad.

Grahic Jump Location
Fig. 17

End effector's path of the 2DOF manipulator with 4.54 kg (10 lb) load. The task was to move from (0 m, −0.675 m), where the end effector is vertically down, to rest at a goal position (0.0 m, 0.65 m). The planning time was 16.0 s.

Grahic Jump Location
Fig. 18

Angular position: planning results of Ref. [19] and SBMPO for 1DOF of the PUMA 762 robot

Grahic Jump Location
Fig. 19

Angular velocity: planning results of Ref. [19] and SBMPO for 1DOF of the PUMA 762 robot

Grahic Jump Location
Fig. 20

Joint torque: planning results of Ref. [19] and SBMPO for 1DOF of the PUMA 762 robot

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