The problem of planning a safe trajectory for a free-flying robot to approach an uncontrolled spinning satellite is addressed. First, a heuristic plan is presented for a simple planar case, which constructs a collision-free path within realistic system constraints. Second, a general numerical optimization technique for planning a safe spatial trajectory is presented. In it, the approach path is parameterized and a cost function based on performance metrics is minimized in order to find the optimal path. The results are analyzed, and it is shown that optimization techniques can be used to produce a far safer approach trajectory than the heuristic method.

Travelling Direction Earth Target V-bar Approach R-bar Approach Fly-by Approach Radius Direction Fig. 1 V-bar, R-bar and Fly-by ApproachExisting orbital transfer vehicles such as US Space Shuttles, Progress and Japanese H-IIA Transfer Vehicle (HTV) use a straight path approach to the International Space Station (ISS). The straight path approach has many advantages and is suitable for stable targets such as ISS and three-axis attitude-controlled satellites. However, for satellite capture missions, we cannot assume that the target satellite is in a stable attitude or that the docking or grasp point is on the straight path. We therefore developed a fly-by approach and capture method for uncontrolled satellite capture, in which a space robot approaches a target on a non-collision path subject to orbital mechanics and executes capturing task using its manipulator if everything goes well. This approach method can be used for arbitrary target positions and velocities in three-dimensional space. By choosing an appropriate initial position and velocity to utilize orbital mechanics, a space robot can approach a target position and velocity without any active trajectory control. This paper focuses on a fly-by approach method for uncontrolled rotating satellite capture considering collision avoidance between space robots and the target satellite, discusses the relative motion behavior during the fly-by approach, and develops planning and guidance algorithms for the fly-by approach.

Nuclear medicine has been widely applied as a diagnostic tool for orthopedic foot and ankle pathology. Although its indications have diminished with improvements in and the availability of magnetic resonance imaging, nuclear medicine still has a significant and valuable role. The present article offers a comprehensive and current review of the most common nuclear imaging modalities for the orthopedic foot and ankle surgeon. Methods discussed include bone scintigraphy, gallium citrate scintigraphy, labeled-leukocyte scintigraphy, and single-photon emission computed tomography (SPECT). We review the indications and utility of these techniques as they pertain to specific foot and ankle conditions, including osteomyelitis, stress fractures, talar osteochondral lesions, complex regional pain syndrome, oncology, plantar fasciitis, and the painful total ankle arthroplasty. We conclude with a discussion of our approach to nuclear medicine with illustrative cases. Level of Evidence: Level V, expert opinion.

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Background: Shortening and dorsiflexion of the first metatarsal are known potential side effects of metatarsal osteotomies for hallux valgus (HV) with the potential to cause transfer metatarsalgia. We compared the effect of the first tarsometatarsal joint arthrodesis (Lapidus procedure), proximal lateral closing wedge osteotomy (PLCWO), and intermetatarsal suture button fixation procedures on the length and dorsiflexion of the first ray. Methods: We retrospectively evaluated 105 feet in 99 patients with 30 weeks of follow-up. The average age was 54 years. Seventy-four feet had a Lapidus procedure, 12 had a PLCWO, and 19 had intermetatarsal suture button fixation. Digital radiographic measurements were made for the pre- and postoperative hallux valgus angle (HVA) and intermetatarsal angle (IMA), absolute and relative shortening of the first ray, and dorsiflexion. Results: Preoperative HVA and IMA did not differ between treatment groups ( P > .05 for each). Similar corrections of HVA (30.5-13.5 degrees) were achieved between all groups ( P > .05). The IMA was improved more in the Lapidus group (14.3-6.5 degrees) compared with the suture button fixation group (14.2-8.1 degrees) ( P = .045). There were significant differences in the change in absolute first cuneiform–metatarsal length (FCML) between the Lapidus (–1.6 mm), PLCWO (–2.3 mm), and intermetatarsal suture button fixation (+1.9 mm) procedure ( P = .004). There were also significant differences in relative first metatarsal shortening between the Lapidus (0.1 mm relative shortening), PLCWO (1.1 mm relative shortening), and intermetatarsal suture button fixation (1.3 mm lengthening) procedure ( P < .001). The average dorsiflexion differed between the Lapidus (1.8 degrees) and suture button fixation (0.4 degrees) groups ( P = .004). Conclusion: Intermetatarsal suture button fixation relatively lengthened the first ray, the Lapidus procedure maintained length, and the PLCWO relatively and absolutely shortened it. Dorsiflexion may be higher with the Lapidus and osteotomy procedures. Level of Evidence: Level III, retrospective comparative series.