Generating Trajectories for Wide Ditch Crossing of Biped Robots

Vistapalli, Janardhan and R, Prasanth Kumar (2018) Generating Trajectories for Wide Ditch Crossing of Biped Robots. PhD thesis, Indian Institute of Technology, Hyderabad.

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Abstract

Ditch crossing is one of the essential capabilities required for a biped robot in disaster management and search and rescue operations. This thesis presents di�erent approaches for trajectory generation of a planar biped robot crossing a wide ditch, which is de�ned as a ditch for which the ankle to ankle stretch required to cross the ditch is equal to or more than the leg length of the biped robot. Crossing a wide ditch can be considered as an application of long step walking. It is an extreme case walking demanding more attention than normal walking. In crossing a wide ditch the di�culty lies in generating trajectories considering friction and impact. With the proposed approaches in this work trajectories are generated for crossing wide ditch considering a least friction coe�cient of 0.15 also. With the analysis carried out in this work, some of the key issues to be considered in crossing a wide ditch are identi�ed. The thesis starts with proposing an o�ine approach for �nding feasible trajectories for dynamically crossing a wide ditch in ideal conditions. Later an online approach for the same task is proposed using the concept control constraints. The e�orts have been extended further to propose a real time approach for �nding joint trajectories crossing a wide ditch with uncertainties and also to �nd optimal solutions with Genetic Algorithm (GA). In generating feasible trajectories o�ine for a biped robot to dynamically cross a wide ditch, the dynamic balance of the biped robot, friction between the robot foot and ground, impact on the foot, limitations on the joint actuator torques and angular velocities are considered. The biped robot is modeled as a seven link planar robot with the ditch crossing task consisting of two single support phases and a double support phase. An algorithm is developed to �nd the joint trajectories and the joint torques in each phase of ditch crossing by formulating the ditch crossing task as a constrained nonlinear optimization problem. In order to make the algorithm converge fast and to give feasible solutions, additional constraints called Adopted Constraints (ACs) are incorporated into the system of constraints. With time being one of the parameters, the developed algorithm adaptively adjusts the time for crossing a wide ditch. The signi�cance of ground reaction force constraints in obtaining feasible solutions for crossing the wide ditch is shown through simulations. Feasible solutions obtained from simulation results provide not only the feasible joint angle trajectories, but also the joint torques required for the selection of actuators for a biped robot crossing the wide ditch. From the results obtained it is felt that an approach for �nding faster solutions (trajectories) is essential for studying the behavior of the biped robot with various initial postures. Ful�lling the above requirement this work also proposes a multibody dynamics approach to generate online trajectories. Trajectories are generated using control constraints that depend on the horizontal distance traveled by the center of mass and are not explicitly dependent on time. Behavior of the biped robot for various initial postures is studied considering dynamic balance, friction, and impact in order to �nd the preferred initial postures considering the net energy consumption and peak power requirements at various joints. Several cases of friction, zero moment point location, and the center of mass height variation are considered in the study. Using the proposed approach, feasible trajectories for an adult sized biped robot could be generated for a wide ditch of 1.05 m width at coe�cients of friction as low as 0.2. The results obtained are useful for designing reference trajectories and actuation systems for biped robots that need to cross wide ditches or take large steps. Time needed for trajectory generation is found to be su�ciently low for online implementation. The work has been extended for generating trajectories for wide ditch crossing with uncertainties. viii Wide ditch crossing with landing uncertainties by a planar biped robot demands real-time solutions, at the same time it has to ful�ll the necessary criteria mentioned before. Besides using the timeindependent control constraints, considering the impact, dynamic balance and friction, to generate real time solutions, a novel concept called the point of feasibility is introduced, for bringing the biped robot to complete rest at the end of ditch crossing. With the proposed approach real-time solutions are found for various initial postures of the biped robot at di�erent friction coe�cients to give the feasible regions for crossing a wide ditch with landing uncertainties. A study on the in uence of initial posture on landing impact and net energy consumption is presented. Through simulations, the best initial postures to e�ciently cross a wide ditch of width 1.05 m, with less impact and without singularities are found. Finally, the advantage of the proposed approach to cross a wide ditch when the surface friction is not same on both sides of the ditch is demonstrated. Using the model with control constraints an approach is proposed for �nding optimal solutions for wide ditch crossing with GA multiobjective optimization. With the proposed approach optimal solutions with GA can be obtained without any additional constraints. Finally optimal initial postures for the biped robot to cross a wide ditch are given along with the peak torque, peak rotational speed and the peak power rating of the actuators required at various joints of the biped robot.

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