پايداري ژيروسكوپي حركت غلتشي يك ربات كروي

Gyroscopic Stability Analysis of a Rolling Robot

در اين مطالعه پايداري دوراني يك نمونه ربات كرويِ داراي حركت غلتشي و مجهز به روتورهاي داخلي بررسي و تحليل مي‌شود. بدين‌منظور ابتدا يك مطالعه‌ي اغتشاشي انجام مي پذيرد تا شرايط رسيدن به آستانه‌ي ناپايداري براي حركت غلتشي مشخص ‌شود. با اتكا به نظريه‌ي فلوكه و قضيه‌ي هاپف، شرايط پايداري در حالت هاي غلتش پايا و توزيع جرم متقارن محوري مورد مطالعه قرار مي گيرد. با استخراج ثابت هاي حركت حاكم بر اين سيستم، معياري براي پايداري و مطالعه‌ي دوشاخگي رفتار غلتشي در حالت كره مجهز به چرخ اينرسي داخلي تعيين مي‌شود. همانند جسم معلق فضايي، اين ربات در حين دوران حول محور اينرسي مياني تمايل به انحراف دارد. با تعبيه‌ي يك پايداركننده‌ي داخلي، ساختار اينرسي كره به‌صورت ديناميكي تغيير مي يابد تا به سيستمي ذاتاً پايدار بدل ‌شود. كنترل پذيري برگرفته از اين سازوكار داخلي، طرح ريزي حركت در فضاي مفاصل روتورها را چنان ممكن مي‌سازد كه حركت اين ربات بر سطوح شيب دار نيز امكان پذير ‌شود.

The rotational stability of a spherical shaped system equipped with internal rotors, and constrained to roll on floors, is investigated in multiple cases. The spinning masses produce the momentum, which, in turn, actuates robot motion through the slip-free contact constraint. Understanding this coupling between dynamics and kinematics is crucial in exploring novel mechanical locomotive designs. Possible applications of the aforementioned system may consist of their use as sentinels in large industrial domains and the exploration of unsecured areas when equipped with cameras and multiple sensors. Because such a system exhibits symmetry, or invariance under certain actions, the equations describing the system motion will conserve some physical properties that are quantified by constant values for the integrals of motion. These constants of motion permit determination of conditions of parametric stability of rolling, spinning, or precession motions, leading to a bifurcation analysis investigation. As shown, internal spinning disks can be employed as active stabilizers by appropriate feedbacks, dynamically transforming the inertia distribution of the whole system into a stable one. The controllability acquired by implementing at least two rotors is sufficient to permit motion planning in the joint space, conducting the system to track predetermined paths, even on inclined surfaces. This research focused on a locomotion technique that uses dynamically coupled actuation that is different from other direct means of locomotion, profiting by the interplay between dynamics conservation laws and kinematics constraints. Actually, studying the dynamics of nonholonomic systems finds applications in modern technologies, from plane landing gears to satellite applications. The present study reveals that standard approaches for the systematic stability analysis of nonholonomic systems have not yet been fully developed. Although considerable efforts have been made to this end, the realm can still be considered unexplored in comparison to its holonomic homologue. It is also undeniable that inquiries regarding a conventional solution to the stability question would have been much more challenging without considering the physical aspect underlying the problem.