Optimization of the computational load of a hypercube supercomputer onboard a mobile robot

Jacob Barhen; N. Toomarian; V. Protopopescu

doi:10.1364/AO.26.005007

Applied Optics
Vol. 26,
Issue 23,
pp. 5007-5014
(1987)
•https://doi.org/10.1364/AO.26.005007

Optimization of the computational load of a hypercube supercomputer onboard a mobile robot

Jacob Barhen, N. Toomarian, and V. Protopopescu

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Jacob Barhen, N. Toomarian, and V. Protopopescu, "Optimization of the computational load of a hypercube supercomputer onboard a mobile robot," Appl. Opt. 26, 5007-5014 (1987)

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Abstract

A combinatorial optimization methodology is developed, which enables the efficient use of hypercube multiprocessors onboard mobile intelligent robots dedicated to time-critical missions. The methodology is implemented in terms of large-scale concurrent algorithms based either on fast simulated annealing, or on nonlinear asynchronous neural networks. In particular, analytic expressions are given for the effect of single-neuron perturbations on the systems' configuration energy. Compact neuromorphic data structures are used to model effects such as precedence constraints, processor idling times, and task-schedule overlaps. Results for a typical robot-dynamics benchmark are presented.

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Equations (44)

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Task No.	Rotational link	Prismatic link
1–6	$w_{i} = A_{i}^{-} (w_{i - 1} + z_{i - 1} {\dot{q}}_{i})$	$w_{i} = A_{i}^{-} w_{i - 1}$
7–12	$ẇ_{i} = A_{i}^{-} (ẇ_{i - 1} + z_{i - 1} {\ddot{q}}_{i} + w_{i - 1} \times z_{i - 1} {\dot{q}}_{i})$	$ẇ_{i} = A_{i}^{-} ẇ_{i - 1}$
13–18	$V_{i}^{(1)} = w_{i} \times (w_{i} \times p_{i}^{*})$	$V_{i}^{(1)} = w_{i} \times (2 A_{i}^{-} z_{i - 1} {\dot{q}}_{i} + w_{i} \times p_{i}^{*})$
19–24	${\ddot{p}}_{i} = A_{i}^{-} {\ddot{p}}_{i - 1} + ẇ_{i} \times p_{i}^{*} + V_{i}^{(1)}$	${\ddot{p}}_{i} = V_{i}^{-} + A_{i}^{-} ({\ddot{p}}_{i - 1} + z_{i - 1} {\ddot{q}}_{i}) + ẇ \times p_{i}^{*}$
25–30	$V_{i}^{(2)} = w_{i} \times [w_{i} \times r_{i}^{*}]$
30–36	$F_{i} = m_{i} [V_{i}^{(2)} + ẇ_{i} \times r_{i}^{*} + {\ddot{p}}_{i}]$
37–42	$Γ_{i} = J_{i} ẇ_{i} + w_{i} \times (J_{i} w_{i})$
43–48	$V_{i}^{(3)} = Γ_{i} + (p_{i}^{} + r_{i}^{}) \times F_{i}$
49–54	$f_{i} = F_{i} + A_{i}^{+} f_{i + 1}$
55–60	$V_{i}^{(4)} = p_{i}^{*} \times (f_{i} - F_{i})$
60–66	$γ_{i} = A_{i}^{+} γ_{i + 1} + V_{i}^{(3)} + V_{i}^{(4)}$

Number of processors	Luh and Lin27 ms	Kasahara and Narita26 ms	ROSES2 (determin) ms	CSA24^b ms	This work^c ms
1	24.80	24.83	24.80	24.83	24.83
2	—	12.42	12.43	12.41	—
3	—	8.43	8.49	—	—
4	—	6.59	6.67	6.63	6.38
5^a	—	5.86	5.88	—
6	9.70	5.73	5.78	—	—
7	—	5.69	5.67	—
8	—	—	5.67	—	—

Task No.	Rotational link	Prismatic link
1–6	$w_{i} = A_{i}^{-} (w_{i - 1} + z_{i - 1} {\dot{q}}_{i})$	$w_{i} = A_{i}^{-} w_{i - 1}$
7–12	$ẇ_{i} = A_{i}^{-} (ẇ_{i - 1} + z_{i - 1} {\ddot{q}}_{i} + w_{i - 1} \times z_{i - 1} {\dot{q}}_{i})$	$ẇ_{i} = A_{i}^{-} ẇ_{i - 1}$
13–18	$V_{i}^{(1)} = w_{i} \times (w_{i} \times p_{i}^{*})$	$V_{i}^{(1)} = w_{i} \times (2 A_{i}^{-} z_{i - 1} {\dot{q}}_{i} + w_{i} \times p_{i}^{*})$
19–24	${\ddot{p}}_{i} = A_{i}^{-} {\ddot{p}}_{i - 1} + ẇ_{i} \times p_{i}^{*} + V_{i}^{(1)}$	${\ddot{p}}_{i} = V_{i}^{-} + A_{i}^{-} ({\ddot{p}}_{i - 1} + z_{i - 1} {\ddot{q}}_{i}) + ẇ \times p_{i}^{*}$
25–30	$V_{i}^{(2)} = w_{i} \times [w_{i} \times r_{i}^{*}]$
30–36	$F_{i} = m_{i} [V_{i}^{(2)} + ẇ_{i} \times r_{i}^{*} + {\ddot{p}}_{i}]$
37–42	$Γ_{i} = J_{i} ẇ_{i} + w_{i} \times (J_{i} w_{i})$
43–48	$V_{i}^{(3)} = Γ_{i} + (p_{i}^{} + r_{i}^{}) \times F_{i}$
49–54	$f_{i} = F_{i} + A_{i}^{+} f_{i + 1}$
55–60	$V_{i}^{(4)} = p_{i}^{*} \times (f_{i} - F_{i})$
60–66	$γ_{i} = A_{i}^{+} γ_{i + 1} + V_{i}^{(3)} + V_{i}^{(4)}$

Number of processors	Luh and Lin27 ms	Kasahara and Narita26 ms	ROSES2 (determin) ms	CSA24^b ms	This work^c ms
1	24.80	24.83	24.80	24.83	24.83
2	—	12.42	12.43	12.41	—
3	—	8.43	8.49	—	—
4	—	6.59	6.67	6.63	6.38
5^a	—	5.86	5.88	—
6	9.70	5.73	5.78	—	—
7	—	5.69	5.67	—
8	—	—	5.67	—	—

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