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The dynamic walking of the compass\u2010gait walker is modeled by an impulsive hybrid nonlinear system. This impulsive hybrid nature is considered very complex as it can generate unwanted phenomena such as chaos and bifurcations. We show first by means of bifurcation diagrams and by varying the slope angle of the walking surface and also the length of the lower leg segment that the passive dynamic walking exhibits successive period\u2010doubling bifurcations leading to chaos. Furthermore, in order to control chaos and hence obtain one\u2010periodic walking behavior, we propose two control approaches based on tracking a desired trajectory. The first method consists in tracking the one\u2010periodic passive dynamic walking generated by the compass model itself. The second control method lies in following a planned trajectory using the 4th\u2010order Spline function. An optimization method is also achieved to design the parameters of the desired trajectory. Some features of the period\u20101 passive gait are used in the design of such Spline trajectory. Finally, we show some simulation results revealing the efficiency of the two proposed control methods in the control of the chaotic passive gait of the compass\u2010gait walker. Moreover, we demonstrate the stabilization of the bipedal locomotion of the compass biped walker on different slopes: descending and ascending inclined planes and walking on a level ground. A comparison with the OGY\u2010based control method is also performed to further show the superiority of these two control approaches.<\/jats:p>","DOI":"10.1155\/2021\/5533451","type":"journal-article","created":{"date-parts":[[2021,10,5]],"date-time":"2021-10-05T00:17:02Z","timestamp":1633393022000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Further Analysis of the Passive Dynamics of the Compass Biped Walker and Control of Chaos via Two Trajectory Tracking Approaches"],"prefix":"10.1155","volume":"2021","author":[{"given":"Essia","family":"Added","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5643-134X","authenticated-orcid":false,"given":"Hass\u00e8ne","family":"Gritli","sequence":"additional","affiliation":[]},{"given":"Safya","family":"Belghith","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,10,4]]},"reference":[{"key":"e_1_2_12_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2014.04.021"},{"key":"e_1_2_12_2_2","doi-asserted-by":"publisher","DOI":"10.1201\/9781420053739"},{"key":"e_1_2_12_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-6046-2"},{"key":"e_1_2_12_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-2-287-87716-2"},{"key":"e_1_2_12_5_2","doi-asserted-by":"crossref","unstructured":"HongS. 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