Efficient and Accurate CORDIC Pipelined Architecture Chip Design Based on Binomial Approximation for Biped Robot
Abstract
:1. Introduction
2. Biped Robot Model and CORIDC Algorithm
2.1. Biped Robot Model
2.2. CORDIC Algorithm
2.3. Binomial Approximation for Scale Factor
3. Hardware Architecture
3.1. CV-Mode Hardware Sharing Machine
3.2. HV1-/HV2-Mode Hardware Sharing Machine
3.3. Whole Hardware Architecture of the Proposed Efficient CORDIC Design with Hardware Sharing Machine
4. Hardware Simulation Result
5. Results and Discussion
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Chung, R.-L.; Zhang, Y.-Q.; Chen, S.-L. Fully pipelined CORDIC-based inverse kinematics FPGA design for biped robots. Electron. Lett. 2015, 51, 1241–1243. [Google Scholar] [CrossRef]
- Lin, J.-L.; Hwang, K.-S.; Jiang, W.-C.; Chen, Y.-J. Gait balance and acceleration of a biped robot based on Q-Learning. IEEE Access 2016, 4, 2439–2449. [Google Scholar] [CrossRef]
- Kim, J.-H. Multi-axis force-torque sensors for measuring zero-moment point in humanoid robots: A review. IEEE Sens. J. 2020, 20, 1126–1141. [Google Scholar] [CrossRef]
- Vyas, P.; Vachhani, L.; Sridharan, K.; Pudi, V. CORDIC-based azimuth calculation and obstacle tracing via optimal sensor placement on a mobile robot. IEEE/ASME Trans. Mechatron. 2016, 21, 2317–2329. [Google Scholar] [CrossRef]
- Vachhani, L.; Sridharan, K.; Meher, P.K. Efficient FPGA realization of CORDIC with application to robotic exploration. IEEE Trans. Ind. Electron. 2009, 56, 4915–4929. [Google Scholar] [CrossRef]
- Meher, P.K.; Valls, J.; Juang, T.-B.; Sridharan, K.; Maharatna, K. 50 years of CORDIC: Algorithms, architectures, and applications. IEEE Trans. Circuits Syst. I 2009, 56, 1893–1906. [Google Scholar] [CrossRef] [Green Version]
- Phamila, Y.A.V.; Amutha, R. Low complexity energy efficient very low bit-rate image compression scheme for wireless sensor network. Inf. Processing Lett. 2013, 113, 672–676. [Google Scholar] [CrossRef]
- Satyanarayana, V.; Ramasubramanian, N. Energy efficient modular exponentiation for public-key cryptography based on bit forwarding techniques. Inf. Processing Lett. 2017, 119, 25–38. [Google Scholar]
- Aggarwal, S.; Meher, P.K.; Khare, K. Concept, design, and implementation of reconfigurable CORDIC. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 2016, 24, 1588–1592. [Google Scholar] [CrossRef]
- Wang, D.; Ercegovac, M.D.; Zheng, N. Design of high-throughput fixed-point complex reciprocal/square-root unit. IEEE Trans. Circuits Syst. II 2010, 57, 627–631. [Google Scholar] [CrossRef]
- Nguyen, H.N.; Khan, S.A.; Kim, C.-H.; Kim, J.-M. A pipelined FFT Processor using an optimal hybrid rotation scheme for complex multiplication: Design, FPGA implementation and analysis. Electronics 2018, 7, 137. [Google Scholar] [CrossRef] [Green Version]
- Vadlamani, S.; Mahmoud, W. Comparison of CORDIC algorithm implementations on FPGA families. In Proceedings of the IEEE International Symposium on System Theory (SSST-2002), Huntsville, AL, USA, 19 March 2002; pp. 192–196. [Google Scholar]
- Chung, R.-L.; Chen, C.-W.; Chen, C.-A.; Abu, P.A.R.; Chen, S.-L. VLSI implementation of a Cost-Efficient Loeffler DCT algorithm with recursive CORDIC for DCT-based encoder. Electronics 2021, 10, 862. [Google Scholar] [CrossRef]
- Sun, L.; Wu, B.; Ye, T. Design and VLSI implementation of a reduced-complexity sorted QR decomposition for high-speed MIMO systems. Electronics 2020, 9, 1657. [Google Scholar] [CrossRef]
- Pilato, L.; Fanucci, L.; Saponara, S. Real-time and high-accuracy arctangent computation using CORDIC and fast magnitude estimation. Electronics 2017, 6, 22. [Google Scholar] [CrossRef] [Green Version]
- Hobart, C.G.; Mazumdar, A.; Spencer, S.J.; Quigley, M.; Smith, J.P.; Bertrand, S.; Pratt, J.; Kuehl, M.; Buerger, S.P. Achieving versatile energy efficiency with the WANDERER biped robot. IEEE Trans. Robot. 2020, 36, 959–966. [Google Scholar] [CrossRef]
- Wong, C.-C.; Liu, C.-C.; Xiao, S.R.; Yang, H.-Y.; Lau, M.-C. Q-learning of straightforward gait pattern for humanoid robot based on automatic training platform. Electronics 2019, 8, 615. [Google Scholar] [CrossRef] [Green Version]
- Wong, C.C.; Liu, C.C. FPGA realisation of inverse kinematics for biped robot based on CORDIC. Electron. Lett. 2013, 49, 332–334. [Google Scholar] [CrossRef]
- Volder, J.E. The CORDIC trigonometric computing technique. IRE Trans. Electron. Comput. 1959, EC-8, 330–334. [Google Scholar] [CrossRef]
- Kajur, R.; Prasad, K.V. Hardware realization of GMSK system using pipelined CORDIC module on FPGA. Appl. Inform. Cybern. Intell. Syst. 2020, 21–31. [Google Scholar] [CrossRef]
θ1(θ3) | θ2(θ4) | θ5(θ8) | θ6(θ9) | θ7(θ10) | Average | |
---|---|---|---|---|---|---|
[18] | 5.7 × 10−4 | 8.75 × 10−4 | 1.924 × 10−2 | 3.8 × 10−2 | 2.715 × 10−2 | 1.717 × 10−2 |
[1] | 1.98 × 10−5 | 5.36 × 10−7 | 2.39 × 10−2 | 1.9 × 10−3 | 2.3 × 10−3 | 5.624 × 10−3 |
This work | 2.45 × 10−6 | 5.63 × 10−6 | 7.79 × 10−4 | 7.54 × 10−4 | 1.13 × 10−5 | 3.11 × 10−4 |
θ1(θ3) | θ2(θ4) | θ5(θ8) | θ6(θ9) | θ7(θ10) | Average | |
---|---|---|---|---|---|---|
[18] | 0.12 | 0.13 | 0.43 | 0.42 | 0.44 | 0.308 |
[1] | 0.063 | 0.063 | 0.189 | 0.063 | 0.197 | 0.115 |
This work | 0.043 | 0.043 | 0.129 | 0.043 | 0.136 | 0.0788 |
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Chung, R.-L.; Hsueh, Y.; Chen, S.-L.; Abu, P.A.R. Efficient and Accurate CORDIC Pipelined Architecture Chip Design Based on Binomial Approximation for Biped Robot. Electronics 2022, 11, 1701. https://doi.org/10.3390/electronics11111701
Chung R-L, Hsueh Y, Chen S-L, Abu PAR. Efficient and Accurate CORDIC Pipelined Architecture Chip Design Based on Binomial Approximation for Biped Robot. Electronics. 2022; 11(11):1701. https://doi.org/10.3390/electronics11111701
Chicago/Turabian StyleChung, Rih-Lung, Yen Hsueh, Shih-Lun Chen, and Patricia Angela R. Abu. 2022. "Efficient and Accurate CORDIC Pipelined Architecture Chip Design Based on Binomial Approximation for Biped Robot" Electronics 11, no. 11: 1701. https://doi.org/10.3390/electronics11111701