This paper introduces the concept of motion planning of delivery robot in an autonomous driving mode using an inverted pendulum model that can effectively control disturbance. The inverted pendulum model exhibits the non-minimum phase characteristic caused by the right half-plane zero. An effective method of reducing this characteristic is examined. A motion platform with 3-degree-of-freedom motion and a touch sensor are installed on a wheeled omnidirectional mobile platform. A steel ball is placed on the touch sensor and controlled to be located at the center. As the autonomous delivery robot moves, the steel ball is subjected to various disturbances and goes off the center. The influence of disturbance can be predicted by measuring the distance the steel ball moves away from the center. In this paper, linear quadratic regulator, preview control, and model predictive control are applied to the inverted pendulum model for motion planning, and thus the reduction of the non-minimum phase characteristic can be comparatively analyzed via simulation. The decrease in the disturbance is experimentally compared according to motion planning. Consequently, this paper proposes an effective motion planning method for an autonomous delivery robot with non-minimum phase characteristic.
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Choi, D., & Oh, J. (2012). ZMP stabilization of rapid mobile manipulator. In Proceedings of the IEEE international conference on robotics and automation (ICRA) (pp. 883–888). IEEE.
García, P., Albertos, P., & Hägglund, T. (2016). Control of unstable non-minimum-phase delayed systems. Journal of Process Control, 16(10), 1099–1111.
Nakamura, R., & Amino, A. (2017). Perfect tracking control using a phase plane for a wheeled inverted pendulum under hardware constraints. In Proceedings of the IEEE international conference on robotics and automation (ICRA) (pp. 4377–4382). IEEE.
Dallali, H., Brown, M., & Vanderborght, B. (2009). Using the torso to compensate for non-minimum phase behaviour in ZMP bipedal walking. In T. Kröger & F. M. Wahl (Eds.), Advances in robotics research (pp. 191–202). Berlin: Springer.
Katayama, T., Ohki, T., Inoue, T., & Kato, T. (1985). Design of an optimal controller for a discrete-time system subject to previewable demand. International Journal of Control, 41(3), 677–699.
Akachi, K., Kaneko, K., Kanehira, N., Ota, S., Miyamori, G., Hirata, M., et al. (2005). Development of humanoid robot HRP-3P. In 5th IEEE-RAS international conference on humanoid robots (pp. 50–55). IEEE.
Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Harada, K., Yokoi, K., et al. (2003). Biped walking pattern generation by using preview control of zero-moment point. In 2003 IEEE international conference on robotics and automation (ICRA) (pp. 1620–1626). IEEE.
Cho, B.-K., & Kim, J.-Y. (2018). Dynamic posture stabilization of a biped robot SUBO-1 on slope-changing grounds. International Journal of Precision Engineering and Manufacturing, 19(7), 1003–1009.
Holkar, K. S., & Waghmare, L. M. (2010). An overview of model predictive control. International Journal of Control and Automation, 3(4), 47–63.
Pannocchia, G., & Rawlings, J. B. (2003). Disturbance models for offset-free model-predictive control. AIChE Journal, 49(2), 426–437.
Wieber, P.-B. B. (2006). Trajectory free linear model predictive control for stable walking in the presence of strong perturbations. In 2006 6th IEEE-RAS international conference on humanoid robots (pp. 137–142). IEEE.
Giselsson, P. (2009). Model predictive control in a pendulum system. In 2009 American control conference (pp. 2335–2340).
Lafaye, J., Collette, C., & Wieber, P. B. (2015). Model predictive control for tilt recovery of an omnidirectional wheeled humanoid robot. In 2015 IEEE international conference on robotics and automation (ICRA) (pp. 5134–5139). IEEE.
Lim, H., et al. (2014). Experimental verification of nonlinear model predictive tracking control for six-wheeled unmanned ground vehicles. International Journal of Precision Engineering and Manufacturing, 15(5), 831–840.
Choi, D., Kim, M., Kim, H., Choe, J., & Nah, M. C. (2018). Real-time motion planning of autonomous personal transporter using model predictive control for minimizing non-minimum phase motion. In 2018 15th international conference on ubiquitous robots (UR) (pp. 362–368). IEEE.
Zeeshan, A., Nauman, N., & Jawad Khan, M. (2012). Design, control and implementation of a ball on plate balancing system. In Proceedings of 2012 9th international Bhurban conference on applied sciences and technology (IBCAST) (pp. 22–26). IEEE.
Awtar, S., Bernard, C., Boklund, N., Master, A., Ueda, D., & Craig, K. (2002). Mechatronic design of a ball-on-plate balancing system. Mechatronics, 12(2), 217–228.
Fan, X., Zhang, N., & Teng, S. (2004). Trajectory planning and tracking of ball and plate system using hierarchical fuzzy control scheme. Fuzzy Sets and Systems, 144(2), 297–312.
Fabregas, E., Chacón, J., Dormido-Canto, S., Farias, G., & Dormido, S. (2015). Virtual laboratory of the ball and plate system. IFAC-PapersOnLine, 48(29), 152–157.
Jørgensen, V. (1974). A ball-balancing system for demonstration of basic concepts in the state-space control theory. International Journal of Electrical Engineering Education, 11(4), 367–376.
Choi, D., & Oh, J. (2008). Human-friendly motion control of a wheeled inverted pendulum by reduced-order disturbance observer. In 2008 IEEE international conference on robotics and automation (ICRA) (pp. 2521–2526). IEEE.
Choi, D., Oh, J. H. (2011). Four and two wheel transformable dynamic mobile platform. In 2011 IEEE international conference on robotics and automation (ICRA) (pp. 1–4). IEEE.
Kim, M., & Choi, D. (2019). Design and development of a variable configuration delivery robot platform. International Journal of Precision Engineering and Manufacturing, 20(10), 1757–1765.
Choi, D., & Oh, J. (2014). Motion planning for a rapid mobile manipulator using model-based ZMP stabilization. Robotica. https://doi.org/10.1017/S0263574714002501.
Choi, D., Kim, M., & Oh, J. H. (2012). Development of a rapid mobile robot with a multi-degree-of-freedom inverted pendulum using the model-based zero-moment point stabilization method. Advanced Robotics, 26(5–6), 515–535.
Kim, M., Choi, D., & Oh, J. H. J. (2010). Stabilization of a rapid four-wheeled mobile platform using the ZMP stabilization method. In 2010 IEEE/ASME international conference on advanced intelligent mechatronics (AIM) (pp. 317–322). IEEE.
Canete, L., & Takahashi, T. (2014). Development of a single controller for the compensation of several types of disturbances during task execution of a wheeled inverted pendulum assistant robot. In 2014 IEEE/RSJ international conference on intelligent robots and systems (IROS) (pp. 2414–2420). IEEE.
Kajita, S., Morisawa, M., Harada, K., Kaneko, K., Kanehiro, F., Fujiwara, K., et al. (2006). Biped walking pattern generator allowing auxiliary ZMP control. In 2006 IEEE/RSJ international conference on intelligent robots and systems (IROS) (pp. 2993–2999). IEEE.
[Experiment] Ball Plate Omni Robot. (2019). Retrieved December 5, 2019, from https://youtu.be/WEnwpPVgp6Q.
This work was supported by 2018 Research Fund of Myongji University.
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Choi, D. Model Predictive Control of Autonomous Delivery Robot with Non-minimum Phase Characteristic. Int. J. Precis. Eng. Manuf. 21, 883–894 (2020). https://doi.org/10.1007/s12541-019-00303-w
- Model predictive control
- Motion planning
- Autonomous robot