Safe and Robust Robot Maneuvers Based on Reach Control Marijan - - PowerPoint PPT Presentation

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Safe and Robust Robot Maneuvers Based on Reach Control Marijan - - PowerPoint PPT Presentation

Aug 01, 2023 252 likes •318 views

Safe and Robust Robot Maneuvers Based on Reach Control Marijan Vukosavljev, Ivo Jansen, Mireille E. Broucke, Angela P. Schoellig Overview Hybrid Control Methodology Results 1 3 4 Novel hybrid control framework 1) The allowable region is that

slide-1
SLIDE 1

Safe and Robust Robot Maneuvers Based on Reach Control

Marijan Vukosavljev, Ivo Jansen, Mireille E. Broucke, Angela P. Schoellig

1

Overview

Novel hybrid control framework that achieves specifications involving safety and sequence of events Demonstrated for side-to-side motion on indoor quadrocopter

2

Control Specifications

Safety constraints form an allowable polytopic region in the state space Temporal logic specifications induce allowable directions to flow within the polytopic region

3

Hybrid Control Methodology

1) The allowable region is triangulated 2) A sequence of triangles, satisfying the temporal logic specifications, is determined 3) The sequence is implemented by low level affine feedback controllers defined for each triangle

Results

A demonstration on an indoor quadrocopter shows that the proposed methodology can meet the safety and strict sequencing specifications, even under severe unmodeled disturbances

4

Results Future Work

We are currently working towards temporal logic specifications in 2D and 3D for single and multiple quadrocopters in the presence of

  • bstacles. Our approach reuses this 1D result in each direction to

reduce complexity

4

velocity position constraints

1) 2) 3)

www.dynsyslab.org www.control.toronto.edu/~broucke/

slide-2
SLIDE 2

1

Overview

Novel hybrid control framework that achieves specifications involving safety and sequence of events Demonstrated for side-to-side motion on indoor quadrocopter

2

Control Specifications

Safety constraints form an allowable polytopic region in the state space Temporal logic specifications induce allowable directions to flow within the polytopic region

velocity position constraints

Safe and Robust Robot Maneuvers Based on Reach Control

Marijan Vukosavljev, Ivo Jansen, Mireille E. Broucke, Angela P. Schoellig

3

Hybrid Control Methodology

1) The allowable region is triangulated 2) A sequence of triangles, satisfying the temporal logic specifications, is determined 3) The sequence is implemented by low level affine feedback controllers defined for each triangle

Results

A demonstration on an indoor quadrocopter shows that the proposed methodology can meet the safety and strict sequencing specifications, even under severe unmodeled disturbances

4

1) 2) 3)

www.dynsyslab.org www.control.toronto.edu/~broucke/

Objective: transport the quadrocopter back and forth along the x-direction Safety:

  • (S1) room wall boundaries
  • (S2) speed limit
  • (S3) deceleration towards walls

Liveness:

  • (L1) minimum cruise speed
  • (L2) and (L3) turnaround acceleration

Desired Temporal Sequence:

  • (T1) pass through Bright and Bleft

alternatingly

2

Control Specifications - Application

Bleft Bright x ˙ x (S2) (S3) (S1) (L1) (L2) (L3) (T1) ¨ x = g tan θ := u,

Modeling: Reduced dynamics in x-direction are where the input to design is the pitch angle, The other directions are stabilized in a standard way

θ

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SLIDE 3

3

Hybrid Control Methodology

1) The allowable region is triangulated 2) A sequence of triangles, satisfying the temporal logic specifications, is determined 3) The sequence is implemented by low level affine feedback controllers defined for each triangle

Results

A demonstration on an indoor quadrocopter shows that the proposed methodology can meet the safety and strict sequencing specifications, even under severe unmodeled disturbances

4

1) 2) 3)

Safe and Robust Robot Maneuvers Based on Reach Control

Marijan Vukosavljev, Ivo Jansen, Mireille E. Broucke, Angela P. Schoellig

1

Overview

Novel hybrid control framework that achieves specifications involving safety and sequence of events Demonstrated for side-to-side motion on indoor quadrocopter

2

Control Specifications

Safety constraints form an allowable polytopic region in the state space Temporal logic specifications induce allowable directions to flow within the polytopic region

velocity position constraints

www.dynsyslab.org www.control.toronto.edu/~broucke/

1) Triangulation into 20 triangles 2) A sequence of triangles to reach the right side. Symmetry is used to implement moving to the

  • left. Automation of this

procedure is formalized in [1] 3) Affine feedback controllers constructed on each

  • triangle. Overall results in

a closed-loop behavior satisfying the safety and temporal specifications

3

Hybrid Control Methodology - Application

, , .

x(m)

  • 3
  • 2
  • 1

1 2 3 ˙ x(m/s)

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 S17 S18 S19 S20

ˆ v1 ˆ v2 ˆ v3 ˆ v4 ˆ v5 ˆ v6 ˆ v7 ˆ v8 ˆ v9 ˆ v10 ˆ v11 ˆ v12 ˆ v13 ˆ v14 ˆ v15 ˆ v16 x(m)

  • 3
  • 2
  • 1

1 2 3 ˙ x(m/s)

  • 2.5
  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2 2.5

[1] M. Kloetzer and C. Belta, “A fully automated framework for control of linear systems from temporal logic specifications,” IEEE Transactions

  • n Automatic Control, vol. 53, no. 1, pp. 287-297, 2008.

Nominal closed-loop response Left-to-right closed-loop response

slide-4
SLIDE 4

3

Hybrid Control Methodology

1) The allowable region is triangulated 2) A sequence of triangles, satisfying the temporal logic specifications, is determined 3) The sequence is implemented by low level affine feedback controllers defined for each triangle

Results

A demonstration on an indoor quadrocopter shows that the proposed methodology can meet the safety and strict sequencing specifications, even under severe unmodeled disturbances

4

1) 2) 3)

Safe and Robust Robot Maneuvers Based on Reach Control

Marijan Vukosavljev, Ivo Jansen, Mireille E. Broucke, Angela P. Schoellig

1

Overview

Novel hybrid control framework that achieves specifications involving safety and sequence of events Demonstrated for side-to-side motion on indoor quadrocopter

2

Control Specifications

Safety constraints form an allowable polytopic region in the state space Temporal logic specifications induce allowable directions to flow within the polytopic region

velocity position constraints

www.dynsyslab.org www.control.toronto.edu/~broucke/

The Reach Control Problem (RCP) Given a simplex with a specified exit facet (e.g. F0) and restricted facets (e.g. F1 and F2), solving the RCP determines an affine feedback controller such that trajectories starting in the simplex only leave through the exit facet

3

Hybrid Control Methodology – Reach Control Problem

.

F1 F2 F0

L.C.G.J.M. Habets and J.H. van Schuppen, “A control problem for affine dynamical systems

  • n a full-dimensional polytope,” Automatica, vol. 40, no. 1, pp. 21-35, 2004.
  • B. Roszak and M. E. Broucke, “Necessary and sufficient conditions for reachability on a

simplex,” Automatica, vol. 42, no. 11, pp. 1913-1918, 2006. M.E. Broucke and M. Ganness, “Reach control on simplices by piecewise affine feedback,” SIAM Journal on Control and Optimization, vol. 52, no. 5, pp. 3261 - 3286, 2014.

u = k1x + k2 ˙ x + k3.

Quadropter Application Affine feedback control law in terms of position and velocity: Gains determined by interpolating feasible control values selected at simplex vertices

slide-5
SLIDE 5

Safe and Robust Robot Maneuvers Based on Reach Control

Marijan Vukosavljev, Ivo Jansen, Mireille E. Broucke, Angela P. Schoellig

1

Overview

Novel hybrid control framework that achieves specifications involving safety and sequence of events Demonstrated for side-to-side motion on indoor quadrocopter

2

Control Specifications

Safety constraints form an allowable polytopic region in the state space Temporal logic specifications induce allowable directions to flow within the polytopic region

3

Hybrid Control Methodology

1) The allowable region is triangulated 2) A sequence of triangles, satisfying the temporal logic specifications, is determined 3) The sequence is implemented by low level affine feedback controllers defined for each triangle

Results

A demonstration on an indoor quadrocopter shows that the proposed methodology can meet the safety and strict sequencing specifications, even under severe unmodeled disturbances

4

velocity position constraints

1) 2) 3)

www.dynsyslab.org www.control.toronto.edu/~broucke/

4

Results

t(s) 50 100 x(m)

  • 3
  • 2
  • 1

1 2 3

Right side Left side 1: Nominal .ight Reference Trajectory Take-o,

  • 2. Manually held
  • 3. Manually pushed

Landed

t(s) 20 40 60 80 100 x(m)

  • 3
  • 2
  • 1

1 2 3

Right side Left side 1: Nominal .ight Take-o, RCP started

  • 2. Manually held
  • 3. Manually pushed

Landed

x(m)

  • 2.5
  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2 2.5 _ x(m=s)

  • 2
  • 1.5
  • 1
  • 0.5

0.5 1 1.5 2

  • 2. & 3. Manual Holds and Push

Standard Tracking Aproach Hybrid Control Approach