---
# System prepended metadata

title: Controls
tags: [Controls, Reconfigurable Robotics]

---

# Controls
###### tags: `Reconfigurable Robotics` `Controls`

[TOC]

| Paper                                                                                            | Understood |
|:-------------------------------------------------------------------------------------------------------:|:---:|
| [1](#trajectory-optimization-for-a-wheel-legged-system-for-dynamic-maneuvers-that-allow-for-wheel-slip) | 50% |
| [2](#On the Hardware Feasibility of Nonlinear Trajectory Optimization for Legged Locomotion based on a Simplified Dynamics) | 50% |
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# Trajectory Optimization for a Wheel-Legged System for Dynamic Maneuvers that Allow for Wheel Slip
## Brief Outline
In this paper, the authors present a trajectory optimization framework for a skating system on passive unactuated wheels, which has no means to locomote itself without exploiting tangential frictional forces.
![](https://i.imgur.com/Mr6B85y.png) ![](https://i.imgur.com/Vrm9Zw4.png)
## Research Questions 
### What did the authors try to accomplish ?
* In this work, authors show that by directly accounting for friction at wheel contact points, dynamic and realistic motions are found by their trajectory optimization framework.
* To show the versatility of their framework and the sorts of dynamic trajectories it can generate, they consider the results from 3 desired tasks:
    1) Skating forwards from rest optimally with respect to speed and efficiency ![](https://i.imgur.com/0cFRSsx.png)
    3) A dynamic skidding parking maneuver, showing the main strengths of their approach ![](https://i.imgur.com/K5zecX4.png) ![](https://i.imgur.com/8sUWybW.png)
    4) Hybrid gaits for walk-skating with 2-3 wheels remaining in contact with the ground ![](https://i.imgur.com/Fn1KfRJ.png) ![](https://i.imgur.com/kBMtH7r.png)
### What were the key elements of the approach ?
* Shown the benefit of not only accounting for, but also optimizing over frictional forces in wheel-legged systems to produce intuitive and dynamic motion primitives. As the system has passive wheels with no sensing, the only way for the system to locomote itself is to reconfigure its internal degrees of freedom to produce the required forces at each of its contact points.
* The no slip and no skid conditions are frequently violated throughout any wheeled motion, especially over terrain with low coefficients of friction such as slippery and icy roads. As soon as some skid/slip occurs, the entire model and constraints are already violated a priori before running the aforementioned trajectory optimizations, which do not model such behavior. By explicitly modeling the frictional forces at the contact point and treating the wheel as an ice skate, dynamic and realistic motions that take advantage of this phenomena are discovered naturally by their trajectory optimization framework.
### What can you use yourself ?
* Apply wheels on Rebis/QuadraSnake to traverse easily on different terrains by exploiting the dynamics of the environment
* Most research for wheel-legged systems until now has considered only static stability of the system, with fewer examples of dynamic or agile behaviors.
### What can be improved ?
* Future work of the authors includes porting the framework to C++ for computational efficiency and speed
* Developing a better whole-body controller for the full system to accurately track the desired trajectory that is not just a PD controller over the trajectory states.
* In particular, due to Robosimian’s heavy limbs, the trajectories requiring lifting a skate off the ground inadequately simplifies the true dynamics. This mismatch in dynamics also causes drift between the desired trajectory and actual robot states in MuJoCo.
* Additionally, the authors would like to increase the modeled dimensions to include pitch and roll for each body, to take advantage of Robosimian’s overactuated limbs, which may result in even more dynamic motions. We hypothesize these could include motions such as banking on turns to avoid slip and maintain.
### What other references do you want to follow ?
* Study JPL’s Robosimian quadruped.
* "Training in Task Space to Speed Up and Guide Reinforcement Learning"
    * In this work the authors used a model-free reinforcement learning algorithm, Proximal Policy Optimization (PPO),which means the agent indirectly learned properties about the environment through choosing actions in task space in the simulation environment, without explicitly learning or modeling friction or terrain. Thus the agent learns a policy that may or may not be taking advantage of wheel slip or skid to maximize rewards, without an explicit model or observation of these phenomena.
* "Trajectory optimization for wheeled-legged quadrupedal robots using linearized zmp constraints"
    * There the authors study a wheel-legged dynamic system with actuated wheels, and can generate agile motions combining walking and driving, including full flight modes. However, this framework enforces the no slip and no skid conditions, which will be frequently violated when driving in the real world.
* "Introducing Handle, by Boston Dynamics" [[video]](https://www.youtube.com/watch?v=-7xvqQeoA8c)
    * Handle has actuated wheels and can perform a variety of impressive motions quickly and agilely. However since there is no publication to accompany this work, so the authors could not be sure if wheel slipping or skidding are directly accounted for in their framework.

# On the Hardware Feasibility of Nonlinear Trajectory Optimization for Legged Locomotion based on a Simplified Dynamics
## Brief Outline
Authors propose two feasibility constraints to be included in a Single Rigid Body Dynamics based trajectory optimizer in order to obtain robust motions in challenging terrain

The paper is basically an implementation of winkler's end effector method on real hardware with 2 new novel constraints to get feasible results

![](https://i.imgur.com/jwrL6zB.png) ![](https://i.imgur.com/W5fpvC4.png) ![](https://i.imgur.com/mN6duR6.png)

## Research Questions 
### What did the authors try to accomplish ?
### What were the key elements of the approach ?
### What can you use yourself ?
### What can be improved ?
### What other references do you want to follow ?

# h1
## Brief Outline
## Research Questions 
### What did the authors try to accomplish ?
### What were the key elements of the approach ?
### What can you use yourself ?
### What can be improved ?
### What other references do you want to follow ?









