TechTalks from event: Technical session talks from ICRA 2012

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Underactuated Robots

  • Trajectory Generation for Underactuated Control of a Suspended Mass Authors: Schultz, Jarvis; Murphey, Todd
    The underactuated system under consideration is a magnetically-suspended, differential drive robot with a winch system articulating a suspended mass. A dynamic model of the system is first constructed, and then a nonlinear, infinite-dimensional optimization algorithm is presented. The Lagrangian mechanics based system model uses the principles of kinematic reduction to produce a mixed kinematic-dynamic model that isolates the modeling of the system actuators from the modeling of the rest of the system. In this framework, the inputs become generalized velocities instead of generalized forces facilitating real-world implementation in an embedded system. The optimization algorithm automatically deals with the complexities introduced by the nonlinear dynamics and underactuation to synthesize dynamically feasible system trajectories for a wide array of trajectory generation problems. Applying this algorithm to the mixed kinematic-dynamic model, several example problems are solved and the results are tested experimentally. The experimental results agree quite well with the theoretical showing promise in extending the capabilities of the system to utilize more advanced feedback techniques and to handle more complex, three-dimensional problems.
  • Planning in High-Dimensional Shape Space for a Single-Wheeled Balancing Mobile Robot with Arms Authors: Nagarajan, Umashankar; Kim, Byungjun; Hollis, Ralph
    The ballbot with arms is an underactuated balancing mobile robot that moves on a single ball. Achieving desired motions in position space is a challenging task for such systems due to their unstable zero dynamics. This paper presents a novel approach that uses the dynamic constraint equations to plan shape trajectories, which when tracked will result in optimal tracking of desired position trajectories. The ballbot with arms has shape space of higher dimension than its position space and therefore, the procedure uses a user-defined weight matrix to choose between the infinite number of possible combinations of shape trajectories to achieve a particular desired trajectory in position space. Experimental results are shown on the real robot where different motions in position space are achieved by tracking motions of either the body lean angles, or the arm angles or combinations of both.
  • Integrated Planning and Control for Graceful Navigation of Shape-Accelerated Underactuated Balancing Mobile Robots Authors: Nagarajan, Umashankar; Kantor, George; Hollis, Ralph
    This paper presents controllers called motion policies that achieve fast, graceful motions in small, collision-free domains of the position space for balancing mobile robots like the ballbot. The motion policies are designed such that their valid compositions will produce overall graceful motions. An automatic instantiation procedure deploys motion policies on a 2D map of the environment to form a library and the validity of their composition is given by a gracefully prepares graph. Dijsktra's algorithm is used to plan in the space of these motion policies to achieve the desired navigation task. A hybrid controller is used to switch between the motion policies. The results of successful experimental testing of two navigation tasks, namely, point-point and surveillance motions on the ballbot platform are presented.
  • Differentially Flat Design of a Closed-Chain Planar Under-Actuated 2 DOF System Authors: Zhang, Chengkun; Franch, Jaume; Agrawal, Sunil
    This paper investigates when a 2 degree-offreedom PRRRP closed-chain system with a single actuator is both strongly accessible and feedback linearizable. It is demonstrated that for certain choices of mass distribution and addition of springs, an under-actuated 2 DOF PRRRP system is static feedback linearizable, i.e., also differentially flat.
  • Design of Energy Efficient Walking Gaits for a Three-Link Planar Biped Walker with Two Unactuated Degrees of Freedom Authors: Ortiz Morales, Daniel; La Hera, Pedro
    We consider the example of a three-link planar biped walker with two passive links. The main objective is to design symmetric periodic gaits in flat ground, that can be exponentially stabilized by feedback control. To this end, we apply recent advances in nonlinear control, to propose a systematic procedure to the problems of gait synthesis and control design. The core of the method lays on a nontrivial coordinate transformation, in order to approach the problem in a state-dependent form. For gait synthesis, such procedure allows a reduction of the search space, with the feasibility of considering energetic performance for optimization. For control design, this allows to apply concepts of transverse linearization, to design a nonlinear feedback control law, which performance is studied by numerical simulations.
  • Biped Walking Stabilization Based on Gait Analysis Authors: Hashimoto, Kenji; Takezaki, Yuki; Motohashi, Hiromitsu; Lim, Hun-ok; Takanishi, Atsuo
    This paper describes a walking stabilization control based on gait analysis for a biped humanoid robot. We have developed a human-like foot mechanism mimicking the medial longitudinal arch to clarify the function of the foot arch structure. To evaluate the arch function through walking experiments using a robot, a walking stabilization control should also be designed based on gait analysis. Physiologists suggest the ankle, hip and stepping strategies, but these strategies are proposed by measuring human beings who are not "walking" but "standing" against force disturbances. Therefore, first we conducted gait analysis in this study, and we modeled human walking strategy enough to be implemented on humanoid robots. We obtained following two findings from gait analysis: i) a foot-landing point exists on the line joining the stance leg and the projected point of CoM on the ground, and ii) the distance between steps is modified to keep mechanical energy at the landing within a certain value. A walking stabilization control is designed based on the gait analysis. Verification of the proposed control is conducted through experiments with a human-sized humanoid robot WABIAN-2R. The experimental videos are supplemented.