Optimization for Control and Planning of Multi-contact Dynamic Motion

anonymous@undisclosed.example.com (Anonymous) — Mon, 01 Apr 2024 02:45:01 +0000

Optimization for Control and Planning of Multi-contact Dynamic Motion

Michael Posa and Cecilia Cantu and Russ Tedrake, "A Direct Method for Trajectory Optimization of Rigid Bodies Through Contact", International Journal of Robotics Research, vol. 33, no. 1, pp. 69-81, January, 2014

Abstract

The fundamental promise of robotics centers on the ability to productively interact with a complex and changing world. Yet, current robots are largely limited to basic tasks in structured environments and act slowly and cautiously, afraid of incidental contact. In this thesis, we consider a class of control and planning problems for robots dynamically interacting with their environment. We address challenges that arise from non-smooth motions induced by contact, where discontinuities result from impact events and frictional forces. First, we examine the problem of trajectory optimization in contact-rich environments, and present two algorithms for synthesizing motions which make and break contact. The novel contact-implicit trajectory optimization algorithm lifts the problem and reasons over the set of possible contacts forces. In doing so, we eliminate the requirement for an a priori sequencing of the active contacts, and avoid explicit combinatorial complexity. We also introduce a direct collocation algorithm for optimizing high-accuracy trajectories, given an arbitrary contact schedule. This approach eliminates drift in the numerical integration of contact constraints, even when constraints result in closed kinematic chains and require non-minimal coordinates.

Second, this thesis concerns questions of control synthesis and provable stability verification of a robot making and breaking contact. To verify stability, we introduce an algorithm for discovering polynomial Lyapunov functions, where the system dynamics include impacts and friction. We leverage the measure differential inclusion representation of non-smooth contact mechanics to efficiently optimize over Lyapunov functions in multi-contact settings. Since avoiding hazardous falls is a primary necessity for bipedal walking robots, we use similar tools to characterize the capabilities of multiple simple models used for balancing and push recovery. Using the notions of barrier functions and occupation measures, we explicitly bound the set of disturbances from which a robot can recover by balancing or stepping.

The primary contributions of this thesis are computational in nature, and we heavily leverage modern approaches to both general nonlinear programming and convex optimization. Sums-of-squares, an approach to polynomial optimization utilizing semidefinite programming, plays a central role in our methods for formal stability analysis.

MIT, Robotics, Optimization, Control, Planning, Multi-contact, Michael-Posa, contact-implicit-MPC, 2017

Towards Computational Design of Shape and Control for Rigid Robots

anonymous@undisclosed.example.com (Anonymous) — Mon, 01 Apr 2024 02:10:03 +0000

Towards Computational Design of Shape and Control for Rigid Robots

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Phd Thesis: Towards Computational Design of Shape and Control for Rigid Robots

MSc Thesis: Learning to Fly: Computational Controller Design for Hybrid UAVs with Reinforcement Learning

Abstract

Designing a performing robotic system for given tasks is traditionally labor-intensive for finding the optimal configurations of its hardware shape and/or software con- troller. The underlying coupling of the hardware shape and the software control of a robot results in an enormous parameter space involving both discrete parameters (i.e., topology structure of the robot) and continuous parameters (i.e., morphologi- cal dimensions of each robot link, the control parameters), optimizing which tradi- tionally requires significant amounts of expert knowledge from roboticists and many manual design iterations. Intending to automate the robot design process, compu- tational robot design has attracted increasing attention from robotics, graphs, and artificial intelligence researchers. However, building a general computational robot design process is extremely hard due to several challenging problems, including but not limited to representation, performance evaluation, and optimization problems. This thesis identifies some key challenges in the computational robot design pipeline and proposes our corresponding solutions. We first take the manipulator design as an example to present our robot design representations for both discrete and continuous robot shape parameters. With the proposed robot representations, we then explore the corresponding robot optimization techniques. In this part, we first introduce how we leverage differentiable simulators to efficiently optimize the robot control policy with the robot configuration fixed. Next, we delve into the more complicated co- design problems requiring optimization of both the shape and control of a robot. We present two novel algorithms for optimizing discrete shape parameters and continu- ous shape parameters, respectively. Finally, we step further toward the more realistic multi-objective robot design problems and present our solutions for finding a set of Pareto-optimal robot designs trading off multiple different objectives and tasks. We conclude this thesis by envisioning an ultimate computational design pipeline and discussing open research directions toward this ultimate goal.

MIT, Computational-Design, Robotics, Rigid-Robots, Jie-Xu, 2022

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Optimization for Control and Planning of Multi-contact Dynamic Motion

Optimization for Control and Planning of Multi-contact Dynamic Motion

Towards Computational Design of Shape and Control for Rigid Robots

Towards Computational Design of Shape and Control for Rigid Robots