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Q-Bert: walking for a bipedal robot
Thesis (MEng)--Stellenbosch University, 2024.
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Stellenbosch : Stellenbosch University
2025
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| _version_ | 1867613941833662464 |
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| access_status_str | Open Access |
| author | Van der Walt, Jean Louis |
| author2 | Fisher, Callen |
| author_browse | Fisher, Callen Van der Walt, Jean Louis |
| author_facet | Fisher, Callen Van der Walt, Jean Louis |
| author_sort | Van der Walt, Jean Louis |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description |
Thesis (MEng)--Stellenbosch University, 2024. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/131948 |
| institution | Stellenbosch University (South Africa) |
| last_indexed | 2026-06-10T12:44:08.546Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/131948 Q-Bert: walking for a bipedal robot Van der Walt, Jean Louis Fisher, Callen Stellenbosch University. Faculty of Engineering. Dept. of Electrical and Electronic Engineering. Robots -- Kinematics Bipedalism Predictive control UCTD Thesis (MEng)--Stellenbosch University, 2024. ENGLISH ABSRACT: Achieving robust walking for legged robots is considered a formidable challenge in the robotics community due to their intricate and non-linear system dynamics. Despite these complexities, there has been a significant surge in interest in developing legged robots, particularly bipedal ones, because of their ability to navigate rough terrain. However, the high cost of platforms capable of advanced locomotion often makes them inaccessible to underfunded research institutes. Consequently, utilising a low-cost, in-house developed bipedal robot further amplifies the challenges associated with achieving robust walking for legged robots. This thesis aims to implement real-time walking on a low-cost bipedal robot named Q-Bert. Q-Bert is a 10 degree-of-freedom (DoF) bipedal robot, specifically designed as a low-cost platform for testing locomotion manoeuvres. Due to its lack of abduction and adduction capabilities, Q-Bert cannot move its legs sideways and therefore requires support from an additional testing setup that stabilises the robot within the sagittal plane. This setup reduces the number of DoF to 6: 4 for the leg movement and 2 for the horizontal and vertical movement. The robot is actuated using 4 joint motors, 2 for the hips and 2 for the knees, all placed at the hips of the robot, with the knee torque transmitted via a belt situated inside the femur. Additionally, the robot is also equipped with point feet. First, trajectory optimisation methods were employed to generate an optimal reference walking trajectory for Q-Bert. This process used a mathematical model of Q-Bert to capture its dynamics and was implemented using Euler-Lagrange dynamics in the form of the manipulator equation. A direct method of optimisation, known as three-point orthogonal collocation, was applied along with several bounds and constraints to ensure the generation of an optimal walking trajectory. The optimisation problem was solved iteratively using epsilon-relaxation techniques to address the challenging complementarity constraints associated with the through-contact methods, which model the ground contacts during the walking gait. Once these constraints were solved with the highest accuracy, the generated trajectory was deemed optimal and ready for implementation on Q-Bert. A dual-controller architecture was designed and implemented to track the reference walking trajectories in real-time. The high-level online model predictive control (MPC) controller, formulated as a single, unconstrained optimisation problem, integrated the non-linear dynamics of a bipedal robot with standard MPC techniques. The solution to this optimisation problem was used to calculate the desired motor torques, which were then implemented on Q-Bert using an additional low-level motor controller. A standard proportional (P) controller with a feedforward reference term served as the joint-level controller, fine-tuning the reference torques received from the MPC controller to enhance the trajectory tracking accuracy and real-time responsiveness of the designed control architecture. The experimental results presented were from extensive walking experiments conducted with Q-Bert on smooth terrain. These experiments confirmed the successful implementation of the reference walking gait on Q-Bert. Despite the inherent challenges in modelling various aspects of the robot and its environment, the designed control architecture demonstrated remarkable success in tracking the reference trajectory, achieving an average trajectory tracking error of 8.65% across the four joint trajectories. As a result, Q-Bert managed to walk an average distance of 1.06m forward during the experiments, taking 10 steps in the process, 5 steps per leg. As the walking gait is periodic by nature, the trajectory can be extended to any desired number of steps, subsequently increasing the distance Q-Bert can walk. This work not only underscored the feasibility of using low-cost platforms for advanced locomotion research but also established a solid foundation for further exploration with Q-Bert. By refining the reference walking trajectory and enhancing the testing setup, Q-Bert can be evaluated on more challenging terrains. Additionally, this will enable the implementation of various other locomotion manoeuvres, such as jogging or running, on the bipedal platform, thereby broadening the scope of future research opportunities. AFRIKAANSE OPSOMMING: ’n Direkte metode van optimering, bekend as driepunt ortogonale kollokasie, is toegepas tesame met verskeie grense en beperkings om die generering van ’n optimale looptrajek te verseker. Die optimeringsprobleem is iteratief opgelos deur gebruik te maak van epsilon-ontspanningstegnieke om die uitdagende komplementariteitsbeperkings, wat met die deurkontakmetodes geassosieer word, aan te spreek. Hierdie metodes was gebruik om die grondkontakte tydens die loopgang te modelleer. Sodra hierdie beperkings met die hoogste akkuraatheid opgelos is, is die gegenereerde trajek as optimaal beskou en gereed vir implementering op Q-Bert. ’n Dubbelbeheerder-argitektuur is ontwerp en geïmplementeer om die verwysingstaptrajek intyd na te spoor. Die hoëvlak aanlyn MPC-beheerder, geformuleer as ’n enkele, onbeperkte optimaliseringsprobleem, integreer die nielineêre dinamika van ’n tweevoetige robot met standaard MPC tegnieke. Die oplossing vir hierdie optimaliseringsprobleem is gebruik om die verlangde motor wringkagte te bereken, wat toe op Q-Bert geïmplementeer is met ’n bykomende lae-vlak motor beheerder. ’n Standaard proporsionele (P) beheerder met ’n voorwaartse verwysing term het gedien as die laevlak beheerder, wat die verwysingswringkragte wat van die MPC-beheerder ontvang is, verfyn het om die trajeknasporing akkuraatheid en intydse responsiwiteit van die ontwerpte beheerargitektuur te verbeter. Die eksperimentele resultate wat aangebied is, was van stapeksperimente wat met Q-Bert op gladde terrein uitgevoer is. Hierdie eksperimente het die suksesvolle implementering van die verwysingsloopgang op Q-Bert bevestig. Ten spyte van die inherente uitdagings tydens die modellering van verskeie aspekte van die robot en sy omgewing, het die ontwerpte beheerargitektuur merkwaardige sukses getoon in die naspoor van die verwysingstrajek, wat ’n gemiddelde trajekvolgfout van 8.65% oor die vier gesamentlike verwysingslooptrajekte behaal het. As gevolg hiervan, het Q-Bert daarin geslaag om ’n gemiddelde afstand van 1.06m vorentoe te stap tydens die eksperimente, deur 10 treë in die proses te neem, 5 treë per been. Aangesien die loopgang periodiek van aard is, kan die trajek uitgebrei word na enige verlangde aantal treë, wat die afstand wat Q-Bert kan loop, vergroot. Hierdie werk beklemtoon nie net die uitvoerbaarheid van die gebruik van laekoste platforms vir gevorderde voortbewegingsnavorsing nie, maar lê ook ’n stewige grondslag vir verdere eksplorasie met Q-Bert neer. Deur die verwysingstaptrajek te verfyn en die toetsopstelling te verbeter, kan Q-Bert op meer uitdagende terreine geëvalueer word. Daarbenewens sal dit die implementering van verskeie ander bewegingsmaneuvers, soos draf of hardloop, op die tweevoetige platform moontlik maak, en sodoende die omvang van toekomstige navorsingsgeleenthede verbreed. Masters 2025-04-30T10:36:30Z 2025-04-30T10:36:30Z 2024-12 Thesis https://scholar.sun.ac.za/handle/10019.1/131948 Stellenbosch University xiii, 114 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Robots -- Kinematics Bipedalism Predictive control UCTD Van der Walt, Jean Louis Q-Bert: walking for a bipedal robot |
| title | Q-Bert: walking for a bipedal robot |
| title_full | Q-Bert: walking for a bipedal robot |
| title_fullStr | Q-Bert: walking for a bipedal robot |
| title_full_unstemmed | Q-Bert: walking for a bipedal robot |
| title_short | Q-Bert: walking for a bipedal robot |
| title_sort | q bert walking for a bipedal robot |
| topic | Robots -- Kinematics Bipedalism Predictive control UCTD |
| url | https://scholar.sun.ac.za/handle/10019.1/131948 |
| work_keys_str_mv | AT vanderwaltjeanlouis qbertwalkingforabipedalrobot |