Periodic Reporting for period 1 - LP-NORM (Leveraging Precision in Numerical Optimization for Robotic Motions)
Reporting period: 2022-08-01 to 2024-07-31
Robotic systems are expected to take a large place in tomorrow’s society, from self-driving vehicles to humanoid robots, far beyond current industrial robots in tightly controlled factory environments. Disruptive domains include autonomous cars or buses for transportation, robotic arms in collaboration with workers, quadruped robots for inspection or as companion workers, humanoid robots to help fragile people or to relieve operators from tedious, MSD-inducing or low-added value tasks… and even landing-capable rockets. These widely different robotic systems all share a common approach when it comes to algorithms controlling their motion: these motions are designed by specifying numerical objectives and constraints on what these robotic systems must do, and within which limits. These specifications often conflict, and actual motor controls must then be computed to satisfy all these objectives and constraints in the best possible way. This is naturally achieved by solving a numerical optimization problem.
Optimization-base control is a very effective and popular solution. The problem arising in robotics are small enough that they can be solved exactly in theory and to the extent permitted by the computer precision in practice. Yet these problems (whether solved online or offline – e.g. in learning-based approach) relies on models, which imperfectly reflects the reality. The control is also based on inputs from sensors with a limited precision and the robot actuators can not exactly follow the command computed. So, do we really need exact, or even precise, numerical solutions?
The goal of the project was to explore two hypotheses:
- (H1) We can obtain the exact same performance with imprecise numerical solutions
- (H2) We can obtain these imprecise numerical solutions using less costly numerical methods
Three objectives were defined to explore them:
- (O1) Provide a diverse benchmark for optimization-based control of robotic systems
- (O2) Provide a detailed impact analysis of numerical precision in models and solutions
- (O3) Provide an efficient solver tailored for inexact computations
Additionally, the project looks at the environmental impacts of robotics, in particular to see how the findings can accompanied to reduce the overall computational footprint of robots rather than help more robots being built as a result of a cheaper operational cost.
Optimization-base control is a very effective and popular solution. The problem arising in robotics are small enough that they can be solved exactly in theory and to the extent permitted by the computer precision in practice. Yet these problems (whether solved online or offline – e.g. in learning-based approach) relies on models, which imperfectly reflects the reality. The control is also based on inputs from sensors with a limited precision and the robot actuators can not exactly follow the command computed. So, do we really need exact, or even precise, numerical solutions?
The goal of the project was to explore two hypotheses:
- (H1) We can obtain the exact same performance with imprecise numerical solutions
- (H2) We can obtain these imprecise numerical solutions using less costly numerical methods
Three objectives were defined to explore them:
- (O1) Provide a diverse benchmark for optimization-based control of robotic systems
- (O2) Provide a detailed impact analysis of numerical precision in models and solutions
- (O3) Provide an efficient solver tailored for inexact computations
Additionally, the project looks at the environmental impacts of robotics, in particular to see how the findings can accompanied to reduce the overall computational footprint of robots rather than help more robots being built as a result of a cheaper operational cost.
For (O1), a set of benchmarks was developed with several tasks for a robotic arm and a humanoid robot for instantaneous control at the kinematic level, and a few cases of dynamic whole-body control, two type of controllers widely used and with mature formulation. For humanoid robots, this has been coupled with a walking controller. These benchmarks were integrated to an existing suite of benchmarks for QP solvers.
For (O2), we kept the frame of the whole-body dynamic control with robotic arms or (non-walking) humanoid robots and studied the precision at two levels: in the solution found by the controller and in the inputs of the controller, with an emphasize on not recomputing all inputs at each control cycle, what can be considered as having low-precision inputs. We study this over a small number of scenario and found that (H1) was verified in these cases: even with large degradations (on the scale of the motors maximum acceleration) of the control outputs or low-frequency refreshment of some input data (typically up to 20 times lower frequency), the quality of tracking of the robots could be kept within the required precision of the task to be done.
For (O3), we mostly worked on leveraging the findings of (O2) to reduce the overall computation of the controller. In particular, we used the fact that input data could be updated less often to reduce the computations done by the underlying QP solver. This was done by adapting a solver (JRL-QP) previously developed by the researcher to avoid computation made unnecessary by the input data rate. This allowed to reduce the average computation time of the controller by more than 25 in the case of the humanoid robot, showing that (H2) could be verified.
For (O2), we kept the frame of the whole-body dynamic control with robotic arms or (non-walking) humanoid robots and studied the precision at two levels: in the solution found by the controller and in the inputs of the controller, with an emphasize on not recomputing all inputs at each control cycle, what can be considered as having low-precision inputs. We study this over a small number of scenario and found that (H1) was verified in these cases: even with large degradations (on the scale of the motors maximum acceleration) of the control outputs or low-frequency refreshment of some input data (typically up to 20 times lower frequency), the quality of tracking of the robots could be kept within the required precision of the task to be done.
For (O3), we mostly worked on leveraging the findings of (O2) to reduce the overall computation of the controller. In particular, we used the fact that input data could be updated less often to reduce the computations done by the underlying QP solver. This was done by adapting a solver (JRL-QP) previously developed by the researcher to avoid computation made unnecessary by the input data rate. This allowed to reduce the average computation time of the controller by more than 25 in the case of the humanoid robot, showing that (H2) could be verified.
The work done clearly shows that leveraging the precision really needed at the different steps of a controller is a very potent way to decrease the computational effort. This opens a shit of paradigm in the way we look at computation, with a realm of possible improvements. To that end, the project only pioneered the approach and opens the door to many more study. The approach taken was generic, but it was necessarily tested only on a subset of robots and controller types. Further studies are required to evaluate the magnitude of the decrease in other cases.