Agile legged robot locomotion

  • Beichen Ding

Student thesis: Doctoral ThesisPhD


Running robots are legged machines with a dynamic capability, i.e. with sensing, actuation and control systems which enable operation outside the constraints of static balance. They also require passive dynamics which are carefully tuned to the required running motion. Such robots have the potential to reach many parts of the planet which are inaccessible by wheeled or tracked vehicles, and to venture into unstructured environments which are dangerous for humans. Hopping is particularly useful to study since it leads to a fundamental understanding of legged locomotion, which can be extended to multi-legged platforms. A springy leg interacts with body mass to give a natural hopping or running frequency. Servo hydraulics is highly suitable for robot leg actuation due to the high power density and quick response.
This thesis concerns several aspects of dynamics and control for hydraulically actuated bipedal hopping robots. The development of a hydraulically actuated bipedal hopping robot, named BBH1, is presented, including the design of a compliant leg to provide desirable passive characteristics. Using a hydraulic accumulator is a promising approach to provide the required compliance in a hydraulically-actuated leg. However, there is friction from the sealing around the piston, especially at a high working pressure, and this has a significantly negative effect on the actuator`s position tracking performance. In order to quantify this friction effect, a novel factor called the ‘error-time integral’ is introduced to link the friction effect with the system compliance and aids component selection for this application.
As a consequence of the friction investigation, the BBH2 was developed with a mechanical extension coil spring to provide leg compliance instead of an accumulator. Most hopping height controllers require explicit detection of the ground contact, plus several state variables usually need to be measured. A novel self-excited hopping controller is developed to address these challenges. This controller is composed of a positive force feedback loop plus a saturation limit dictating the hopping height, a conventional proportional-integral position feedback loop, and command velocity feedforward is used to improve the system response. A criterion for guaranteed self-excited hopping is theoretically derived using the describing function technique, and experimentally verified on the BBH2. A nonlinear simulation model is used to explain the main findings from the experimental results and provide a better understanding of the effects of practical nonlinearities.
A modified double inverted pendulum model is used to study the balancing control while the BBH2 is standing on the ground with point foot contact. The balancing controller is developed using the pole-placement method and investigated via simulation. The results indicate that high order motion derivatives need to be sensed or estimated, and the corresponding noise issue plays an important role in the performance of this controller.
A controller is developed to maintain balance while the BBH2 is hopping. It follows the well-established structure of the ‘Three-part Controller’. The three controlled parts are: hopping height control; longitudinal control by changing the leg angle during the flight phase to place the foot in the desired position; and body attitude correction during the stance phase. Simulation results from a detailed non-linear model indicate that this controller can successfully balance the hydraulic robot while hopping with different longitudinal velocities.
Date of Award19 Jun 2019
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorAndrew Plummer (Supervisor) & Pejman Iravani (Supervisor)


  • bipedal hopping robot
  • Hydraulic actuation
  • motion control

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