Compliant and Adaptive Control of a Planar Monopod Hopper in Rough Terrain


 AAlthough wheeled robots are widely used for different applications, legged robots have also their own advantages in locomotion. They can potentially perform much better on rough terrains and complex environments. These robots are being mostly inspired from animals, but with simpler structures. However, the complexity of structure, considerable number of actuators and degrees of freedom has made control problem a great challenge for the engineers. There are various intelligent approaches developed that control the robot for different tasks, but not so general to handle any kind of terrains or obstacles potentially existing in a complex environment. Each control method has its own advantages and disadvantages regarding task properties. Among them,

  • Virtual Model Control: uses virtual components to compensate existing redundancy in the robot.
  • Operational Space Control: tries to navigate the body through the environment using attractive and repulsive potential fields.
  • Impedance control: tries to solve the control problem by representing the manipulator, environment and control laws as impedances or admittances and then modulating these elements to obtain desired performance.
  • Inverse dynamics: optimally calculates actuator inputs considering the current dynamics of the robot and contact constraints.


Overall, the two ends of control approaches could be shown bellow. On left, the robot can walk down a sloop in a completely passive manner while on right side, the well known Assimo humanoid robot by Honda uses a lot of computations and consumes considerable amounts of energy to walk, but still doesn’t look as natural as humans themselves. However, the desired standing point is to use as less energy as possible while being capable of handling different tasks by incorporating more knowledge about robot’s static and dynamic properties into controllers. 


 At BioRob, a set of dynamics modelling is prepared for some legged robots including planar monopod, biped and quadruped (with rigid and flexible spine) and additionally a 3D quadruped model with flexible spine. Also for some of these models thanks to an optimization, a periodic optimal sequence (gait) is obtained for actuator inputs. The extracted gaits are obtained so far to optimize locomotion performance metrics such as speed, energy efficiency and stability rather than producing the desired movement patterns such as running at a certain speed or jumping height. So previous works done in BioRob are:

  • Mathematical dynamics modelling for the legged robots (2D monopod and 2D and 3D Quadrupeds).
  • Open loop optimal trajectories for the periodic and energy-optimized solutions (gaits).
  • State feedback control loops (LQR) to stabilize the gaits.

Making use of these previous developments, a new complementary approach is needed to improve the controllability of the robot. Moreover, to replicate the off-line extracted trajectories on the real robot, one needs to design feedback controllers to sustain the desired trajectories against the model uncertainties. So the goal of this project was to design a control method to help the robot follow the optimal trajectories robustly. In addition, we wanted to take advantage of this knowledge in our proposed method to make the robot more flexible for some different scenarios. The main advantage of incorporating a model into the control loop is to achieve better nominal tracking of desired trajectories for a specific task knowing the dynamics of the robot. Environmental interactions could be improved also using this knowledge. 


In this project, first of all we had a review on above-mentioned approaches and described their roles and places in the whole control loop together with comparing their advantages and disadvantages. Regarding our goal, the best method was chosen for this project. Then to get better familiar with simulator platform and mathematical models, the algorithm was simulated for a monopod robot. The idea was to investigate the methodologies both for implementation and analysis on this simpler setup to provide good insights and knowledge for more complicated models. Since the goal of this project was to control a quadruped robot eventually, the algorithm was extended to such a robot as much as possible. 


The part of monopod robot is summerized in the form of a conference paper accepted in ICRA-2013. You can find video links bellow. The quadruped part is going to be developed more and published togther with monopod one as a uniform approach in a journal paper. 

Midterm presentation: here

Final presentation: here

Final report: here




In this paper, a method is proposed for controlling a hopping monopod. It takes dynamics of the robot into account to have better nominal tracking of desired trajectories and more compliant environmental interactions at the same time. We have incorporated also natural dynamics of the robot into the system by using off-line gaits extracted from optimizations on energy. The main control loop consists of the projected inverse dynamics that generates actuator torques given desired trajectories and also a feedback loop designed and tuned specifically for the structure of the robot. A trajectory generator uses known optimal trajectories together with some stabilizing control laws that modify these trajectories to have better robustness in different situations. The average speed of the robot is also regulated by means of a self-organizing controller. We apply soft transitions in trajectories from phase to phase to avoid sharp actuator input profiles. Our method is successfully tested on a monopod hopper robot in simulation. It can handle slightly rough or sloped terrains while maintaining a given average speed. Simulation results suggest that our method is a promising candidate to control a real robot under construction.